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We introduce a generalized micro–macro Markov chain Monte Carlo (mM-MCMC) method with pseudo-marginal approximation to the free energy that is able to accelerate sampling of the microscopic Gibbs distributions when there is a time-scale separation between the macroscopic dynamics of a reaction coordinate and the remaining microscopic degrees of freedom. The mM-MCMC method attains this efficiency by iterating four steps: (i) propose a new value of the reaction coordinate, (ii) accept or reject the macroscopic sample, (iii) run a biased simulation that creates a microscopic molecular instance that lies close to the newly sampled macroscopic reaction coordinate value, and (iv) microscopic accept/reject step for the new microscopic sample. In the present paper, we eliminate the main computational bottleneck of earlier versions of this method: the necessity to have an accurate approximation of free energy. We show that the introduction of a pseudo-marginal approximation significantly reduces the computational cost of the microscopic accept/reject step while still providing unbiased samples. We illustrate the method's behavior on several molecular systems with low-dimensional reaction coordinates. [ABSTRACT FROM AUTHOR]

We study the dynamics of the end monomers of a real chain confined in a spherical cavity to search for a small target on the cavity surface using Langevin dynamics simulation. The results are compared and contrasted with those of a Rouse chain to understand the influence of excluded volume interactions on the search dynamics, as characterized by the first passage time (FPT). We analyze how the mean FPT depends on the cavity size Rb, the target size a, and the degree of confinement quantified by Rg/Rb, with Rg being the polymer radius of gyration in free space. As a basic finding, the equilibrium distribution of the end monomers of a real chain in a closed spherical cavity differs from that of a Rouse chain at a given Rg/Rb, which leads to the differences between the mean FPTs of real and Rouse chains. Fitting the survival probability S(t) by a multi-exponential form, we show that the S(t) of real chains exhibits multiple characteristic times at large Rg/Rb. Our simulation results indicate that the search dynamics of a real chain exhibit three characteristic regimes as a function of Rg/Rb, including the transition from the Markovian to non-Markovian process at Rg/Rb ≈ 0.39, along with two distinct regimes at 0.39 < Rg/Rb < 1.0 and Rg/Rb > 1.0, respectively, where S(t) exhibits a single characteristic time and multiple characteristic times. [ABSTRACT FROM AUTHOR]

Hidden Markov models (HMMs), which can characterize dynamic heterogeneity, are valuable tools for analyzing longitudinal data. The order of HMMs (ie, the number of hidden states) is typically assumed to be known or predetermined by some model selection criterion in conventional analysis. As prior information about the order frequently lacks, pairwise comparisons under criterion‐based methods become computationally expensive with the model space growing. A few studies have conducted order selection and parameter estimation simultaneously, but they only considered homogeneous parametric instances. This study proposes a Bayesian double penalization (BDP) procedure for simultaneous order selection and parameter estimation of heterogeneous semiparametric HMMs. To overcome the difficulties in updating the order, we create a brand‐new Markov chain Monte Carlo algorithm coupled with an effective adjust‐bound reversible jump strategy. Simulation results reveal that the proposed BDP procedure performs well in estimation and works noticeably better than the conventional criterion‐based approaches. Application of the suggested method to the Alzheimer's Disease Neuroimaging Initiative research further supports its usefulness. [ABSTRACT FROM AUTHOR]

AbstractMarkov chain Monte Carlo (MCMC) allows one to generate dependent replicates from a posterior distribution for effectively any Bayesian hierarchical model. However, MCMC can produce a significant computational burden. This motivates us to consider finding expressions of the posterior distribution that are computationally straightforward to obtain independent replicates from directly. We focus on a broad class of Bayesian hierarchical models for spatially dependent data, which are often modeled via a latent Gaussian process (LGP). First, we derive a new class of distributions referred to as the generalized conjugate multivariate (GCM) distribution. The GCM distribution’s theoretical development follows that of the conjugate multivariate (CM) distribution with two main differences: the GCM allows for latent Gaussian process assumptions, and the GCM explicitly accounts for hyperparameters through marginalization. The development of GCM is needed to obtain independent replicates directly from the exact posterior distribution, which has an efficient regression form. Hence, we refer to our method as Exact Posterior Regression (EPR). Simulation studies with weakly stationary spatial processes and spatial basis function expansions are provided. We provide an analysis of poverty incidence from the U.S. Census Bureau, and an analysis of high-dimensional remote sensing data. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Objective: To assess the impact of self-medication on the transmission dynamics of COVID-19 across different age groups, examine the interplay of vaccination and self-medication in disease spread, and identify the age group most prone to self-medication. Methods: We developed an age-structured compartmentalized epidemiological model to track the early dynamics of COVID-19. Age-structured data from the Government of Gauteng, encompassing the reported cumulative number of cases and daily confirmed cases, were used to calibrate the model through a Markov Chain Monte Carlo (MCMC) framework. Subsequently, uncertainty and sensitivity analyses were conducted on the model parameters. Results: We found that self-medication is predominant among the age group 15-64 (74.52%), followed by the age group 0-14 (34.02%), and then the age group 65+ (11.41%). The mean values of the basic reproduction number, the size of the first epidemic peak (the highest magnitude of the disease), and the time of the first epidemic peak (when the first highest magnitude occurs) are 4.16499, 241,715 cases, and 190.376 days, respectively. Moreover, we observed that self-medication among individuals aged 15-64 results in the highest spreading rate of COVID-19 at the onset of the outbreak and has the greatest impact on the first epidemic peak and its timing. Conclusion: Studies aiming to understand the dynamics of diseases in areas prone to self-medication should account for this practice. There is a need for a campaign against COVID-19-related self-medication, specifically targeting the active population (ages 15-64). [ABSTRACT FROM AUTHOR]

The quality performance of many vital systems depends on how long the units are performing; hence, research works started focusing on increasing the reliability of systems while taking into consideration that many factors may cause the failures of operating systems. In this study, the combination of a parametric generalized linear failure rate distribution model and an adaptive progressive Type-II censoring scheme for practical purposes is explored. A comprehensive investigation is performed on the risk factors that cause failure and determines which of the factors has a more harmful effect on the units. A lifetime experiment is performed under the condition of an adaptive progressive Type-II censoring scheme to obtain observations as a result of the competing factors of failures. The obtained observations are assumed to follow a three-parameter generalized linear failure rate distribution and are assumed to be competing to cause failure. Two statistical inference methods are employed for estimating this model's parameters: the frequentist maximum likelihood method and the Bayesian approach. Our model's validity is demonstrated through extensive simulations and real data applications in the medical and electrical engineering fields. [ABSTRACT FROM AUTHOR]

Bayesian methods provide a valuable framework for rigorously quantifying the model uncertainty arising from the inherent non-uniqueness in the magnetotelluric (MT) inversion. However, widely used Markov chain Monte Carlo (MCMC) sampling approaches usually require a significant number of model samples for accurate uncertainty estimates, making their applications computationally challenging for 2-D or 3-D MT problems. In this study, we explore the applicability of the Hamiltonian Monte Carlo (HMC) method for 2-D probabilistic MT inversion. The HMC provides a mechanism for efficient exploration in high-dimensional model space by making use of gradient information of the posterior probability distribution, resulting in a substantial reduction in the number of samples needed for reliable uncertainty quantification compared to the conventional MCMC methods. Numerical examples with synthetic data demonstrate that the HMC method achieves rapid convergence to the posterior probability distribution of model parameters with a limited number of model samples, indicating the computational advantages of the HMC in high-dimensional model space. Finally, we applied the developed approach to the COPROD2 field data set. The statistical models derived from the HMC approach agree well with previous results obtained by 2-D deterministic inversions. Most importantly, the probabilistic inversion provides valuable quantitative model uncertainty information associated with the resistivity structures derived from the observed data, which facilitates model interpretation. [ABSTRACT FROM AUTHOR]

Time-lapse seismic full-waveform inversion (FWI) provides estimates of dynamic changes in the Earth's subsurface by performing multiple seismic surveys at different times. Since FWI problems are highly non-linear and non-unique, it is important to quantify uncertainties in such estimates to allow robust decision making based on the results. Markov chain Monte Carlo (McMC) methods have been used for this purpose, but due to their high computational cost, those studies often require a pre-existing accurate baseline model and estimates of the locations of potential velocity changes, and neglect uncertainty in the baseline velocity model. Such detailed and accurate prior information is not always available in practice. In this study we use an efficient optimization method called stochastic Stein variational gradient descent (sSVGD) to solve time-lapse FWI problems without assuming such prior knowledge, and to estimate uncertainty both in the baseline velocity model and the velocity change over time. We test two Bayesian strategies: separate Bayesian inversions for each seismic survey, and a single joint inversion for baseline and repeat surveys, and compare the methods with standard linearized double difference inversion. The results demonstrate that all three methods can produce accurate velocity change estimates in the case of having fixed (exactly repeatable) acquisition geometries. However, the two Bayesian methods generate significantly more accurate results when acquisition geometries changes between surveys. Furthermore, joint inversion provides the most accurate velocity change and uncertainty estimates in all cases tested. We therefore conclude that Bayesian time-lapse inversion using a joint inversion strategy may be useful to image and monitor subsurface changes, in particular where variations in the results would lead to different consequent decisions. [ABSTRACT FROM AUTHOR]

Summary: Generalised linear mixed regression models are fundamental in statistics. Modelling random effects that are shared by individuals allows for correlation among those individuals. There are many methods and statistical packages available for analysing data using these models. Most require some form of numerical or analytic approximation because the likelihood function generally involves intractable integrals over the latents. The Bayesian approach avoids this issue by iteratively sampling the full conditional distributions for various blocks of parameters and latent random effects. Depending on the choice of the prior, some full conditionals are recognisable while others are not. In this paper we develop a novel normal approximation for the random effects full conditional, establish its asymptotic correctness and evaluate how well it performs. We make the case for hierarchical binomial and Poisson regression models with canonical link functions, for hierarchical gamma regression models with log link and for other cases. We also develop what we term a sufficient reduction (SR) approach to the Markov Chain Monte Carlo algorithm that allows for making inferences about all model parameters by replacing the full conditional for the latent variables with a considerably reduced dimensional function of the latents. We expect that this approximation could be quite useful in situations where there are a very large number of latent effects, which may be occurring in an increasingly 'Big Data' world. In the sequel, we compare our methods with INLA, which is a particularly popular method and which has been shown to be excellent in terms of speed and accuracy across a variety of settings. Our methods appear to be comparable to theirs in terms of accuracy, while INLA was faster, for the settings we considered. In addition, we note that our methods and those of others that involve Gibbs sampling trivially handle parameters that are functions of multiple parameters, while INLA approximations do not. Our primary illustration is for a three‐level hierarchical binomial regression model for data on health outcomes for patients who are clustered within physicians who are clustered within particular hospitals or hospital systems. [ABSTRACT FROM AUTHOR]

The area of functional principal component analysis (FPCA) has seen relatively few contributions from the Bayesian inference. A Bayesian method in FPCA is developed under the cases of continuous and binary observations for sparse and irregularly spaced data. In the proposed Markov chain Monte Carlo (MCMC) method, Gibbs sampler approach is adopted to update the different variables based on their conditional posterior distributions. In FPCA, a set of eigenfunctions is suggested under Stiefel manifold, and samples are drawn from a Langevin–Bingham matrix variate distribution. Penalized splines are used to model mean trajectory and eigenfunction trajectories in generalized functional mixed models; and the proposed model is casted into a mixed-effects model framework for Bayesian inference. To determine the number of principal components, reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm is implemented. Four different simulation settings are conducted to demonstrate competitive performance against non-Bayesian approaches in FPCA. Finally, the proposed method is illustrated to the analysis of body mass index (BMI) data by gender and ethnicity. [ABSTRACT FROM AUTHOR]

Bipartite graph representation learning aims to obtain node embeddings by compressing sparse vectorized representations of interactions between two types of nodes, e.g., users and items. Incorporating structural attributes among homogeneous nodes, such as user communities, improves the identification of similar interaction preferences, namely, user/item embeddings, for downstream tasks. However, existing methods often fail to proactively discover and fully utilize these latent structural attributes. Moreover, the manual collection and labeling of structural attributes is always costly. In this article, we propose a novel approach called Dirichlet Max-margin Matrix Factorization (DM3F), which adopts a self-supervised strategy to discover latent structural attributes and model discriminative node representations. Specifically, in self-supervised learning, our approach generates pseudo group labels (i.e., structural attributes) as a supervised signal using the Dirichlet process without relying on manual collection and labeling, and employs them in a max-margin classification. Additionally, we introduce a Variational Markov Chain Monte Carlo algorithm (Variational MCMC) to effectively update the parameters. The experimental results on six real datasets demonstrate that, in the majority of cases, the proposed method outperforms existing approaches based on matrix factorization and neural networks. Furthermore, the modularity analysis confirms the effectiveness of our model in capturing structural attributes to produce high-quality user embeddings. [ABSTRACT FROM AUTHOR]

Dengue fever is transmitted to humans through the bite of an infected mosquito and is prevalent in all tropical and subtropical climates worldwide. It is thus essential to model weekly dengue fever counts and other infectious diseases that exhibit spatial-temporal dynamics, overdispersion, spatial dependence, and a high number of zeros. To address these characteristics, this study introduces a spatial hurdle integer-valued GARCH (INGARCH) model and an improved version of the spatial zero-inflated generalized Poisson (ZIGP) INGARCH model with and without meteorological variables. Implementing two parameters in the distance function influences the spatial weight between two locations: one controls the decay rate, while the other shapes the decay curve. We employ these newly designed models to analyze time-series counts of infectious diseases - specifically, weekly cases of dengue hemorrhagic fever in four northeastern provinces of Thailand. Applying these models allow us to offer inferences, predictions, and model selections within a Bayesian framework through Markov chain Monte Carlo (MCMC) methods. We then compare models based on the Bayes factors and the mean squared error of fitting errors. The results for the spatial ZIGP INGARCH models are remarkably good, but the spatial INGARCH model incorporating meteorological variables outperforms the other two. [ABSTRACT FROM AUTHOR]

We propose a novel Bayesian model framework for discrete ordinal and count data based on conditional transformations of the responses. The conditional transformation function is estimated from the data in conjunction with an a priori chosen reference distribution. For count responses, the resulting transformation model is novel in the sense that it is a Bayesian fully parametric yet distribution-free approach that can additionally account for excess zeros with additive transformation function specifications. For ordinal categoric responses, our cumulative link transformation model allows the inclusion of linear and non-linear covariate effects that can additionally be made category-specific, resulting in (non-)proportional odds or hazards models and more, depending on the choice of the reference distribution. Inference is conducted by a generic modular Markov chain Monte Carlo algorithm where multivariate Gaussian priors enforce specific properties such as smoothness on the functional effects. To illustrate the versatility of Bayesian discrete conditional transformation models, applications to counts of patent citations in the presence of excess zeros and on treating forest health categories in a discrete partial proportional odds model are presented. [ABSTRACT FROM AUTHOR]

I discuss a framework to allow dynamic sparsity in time-varying parameter regression models. The conditional variances of the innovations of time-varying parameters are time varying and equal to zero adaptively via thresholding. The resulting model allows the dynamics of the time-varying parameters to mix over different frequencies of parameter changes in a data driven way and permits great flexibility while achieving model parsimony. A convenient strategy is discussed to infer if each coefficient is static or dynamic and, if dynamic, how frequent the parameter change is. An MCMC scheme is developed for model estimation. The performance of the proposed approach is illustrated in studies of both simulated and real economic data. [ABSTRACT FROM AUTHOR]

In this paper, we construct an approximation to the Pitman–Yor process by truncating its two‐parameter Poisson–Dirichlet representation. The truncation is based on a decreasing sequence of random weights, thus having a lower approximation error compared to the popular truncated stick‐breaking process. We develop an exact simulation algorithm to sample from the approximation process and provide an alternative MCMC algorithm for the parameter regime where the exact simulation algorithm becomes slow. The effectiveness of the simulation algorithms is demonstrated by the estimation of the functionals of a Pitman–Yor process. Then we adapt the approximation process into a Pitman–Yor process mixture model and devise a blocked Gibbs sampler for posterior inference. [ABSTRACT FROM AUTHOR]

In this paper, we develop an eigenvector-assisted estimation framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many applications. The framework is built upon a novel asymptotically unbiased estimating equation using the leading eigenvectors of the data matrix. However, the estimator obtained by directly solving the estimating equation could be numerically unstable in practice and lacks robustness against model misspecification. We propose to use the quasi-posterior distribution by exponentiating a criterion function whose maximizer coincides with the estimating equation estimator. The proposed framework can incorporate heteroskedastic variance information, but does not require the complete specification of the sampling distribution and is also robust to the potential misspecification of the distribution of the noise matrix. Computationally, the quasi-posterior distribution can be obtained via a Markov chain Monte Carlo sampler, which exhibits superior numerical stability over some of the existing optimization-based estimators and is straightforward for uncertainty quantification. Under mild regularity conditions, we establish the large sample properties of the quasi-posterior distributions. In particular, the quasi-posterior credible sets have the correct frequentist nominal coverage probability provided that the criterion function is carefully selected. The validity and usefulness of the proposed framework are demonstrated through the analysis of synthetic datasets and the real-world ENZYMES network datasets. [ABSTRACT FROM AUTHOR]

We propose an empirical Bayes formulation of the structure learning problem, where the prior specification assumes that all node variables have the same error variance, an assumption known to ensure the identifiability of the underlying causal directed acyclic graph. To facilitate efficient posterior computation, we approximate the posterior probability of each ordering by that of a best directed acyclic graph model, which naturally leads to an order-based Markov chain Monte Carlo algorithm. Strong selection consistency for our model in high-dimensional settings is proved under a condition that allows heterogeneous error variances, and the mixing behaviour of our sampler is theoretically investigated. Furthermore, we propose a new iterative top-down algorithm, which quickly yields an approximate solution to the structure learning problem and can be used to initialize the Markov chain Monte Carlo sampler. We demonstrate that our method outperforms other state-of-the-art algorithms under various simulation settings, and conclude the paper with a single-cell real-data study illustrating practical advantages of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study linear regression models in which the error term has shape mixtures of skew-normal distribution. This type of distribution belongs to the skew-normal (SN) distribution class that can be used for heavy tails and asymmetry data. For the first time, for the classical (non-Bayesian) estimation of the parameters of the SN family, we apply the Markov chains Monte Carlo ECM (MCMC-ECM) algorithm where the samples are generated by Gibbs sampling, denoted by Gibbs-ECM, and also, we extend two other types of the EM algorithm for the above model. Finally, the proposed method is evaluated through a simulation and compared with the Numerical Math-ECM algorithm and Monte Carlo ECM (MC-ECM) using a real data set. [ABSTRACT FROM AUTHOR]

The ability of individuals to recall events is influenced by the time interval between the monitoring time and the occurrence of the event. In this article, we introduce a non-recall probability function that incorporates this information into our modeling framework. We model the time-to-event using the Weibull distribution and adopt a latent variable approach to handle situations where recall is not possible. In the classical framework, we obtain point estimators using expectation-maximization algorithm and construct the observed Fisher information matrix using missing information principle. Within the Bayesian paradigm, we derive point estimators under suitable choice of priors and calculate highest posterior density intervals using Markov Chain Monte Carlo samples. To assess the performance of the proposed estimators, we conduct an extensive simulation study. Additionally, we utilize age at menarche and breastfeeding datasets as examples to illustrate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

The non-inferiority (NI) trial is designed to show that an experimental treatment is not worse than an active reference by more than a pre-specified margin. Traditional NI trials do not include a placebo for ethical reasons; however, three-arm NI trials consisting of placebo, reference, and experimental treatment, can test the NI of experimental treatment to the reference while assessing the superiority of the reference over placebo. Assay sensitivity (AS) of a clinical trial is defined as its ability to distinguish between an effective and ineffective treatment and has been used to assess the superiority of the reference over placebo. Bayesian approaches have been predominantly used in clinical trials, particularly in NI trials. Most previous Bayesian approaches have focused on parametric priors of treatment effects. Restriction to parametric priors can mislead investigators into an inappropriate illusion of posterior certainty, leading to misleading decisions and inference. In this paper, we develop a novel semiparametric Bayesian approach to simultaneously assess NI of experimental treatment over the reference and AS of the reference over placebo in a three-arm trial with normally distributed endpoints. We use Dirichlet process priors to specify the priors of treatment effects. A Markov chain Monte Carlo algorithm is developed to calculate the posterior probability for assessing NI and AS. Simulation studies show that our proposed method is comparable to, or better than, the frequentist approach and parametric Bayesian methods in terms of the ability of controlling the type I errors and empirical statistical powers for testing NI. Data from two real trials are illustrated by the proposed methods. We recommend the usage of the proposed method in a three-arm trial. [ABSTRACT FROM AUTHOR]

It is recommended to use two-part models for analyzing zero-inflated data that exhibit a spike at zero or have a large proportion of participants with zero values. This paper presents a variational Bayesian inference procedure for the analysis of a two-part latent variable model. We take advantage of the Pólya Gamma stochastic representation to approximate the posterior distribution via a mean-field variational method. We propose a scheme to update the variational parameters using the coordinate ascent inference algorithm and develop a variational Bayes based procedure for the variable selection and model assessment. We conduct simulation studies to assess the performance of our proposed method and compare it with the Markov Chains Monte Carlo sampling method. Our results show that the proposed variational Bayesian approach achieves computational efficiency without sacrificing estimation accuracy. We further illustrate the practical merits of the proposed approach by analyzing household finance survey data. [ABSTRACT FROM AUTHOR]

To reduce total test time and increase the efficiency of statistical analysis of a life-testing experiment adaptive progressive Type-II censoring scheme has been proposed. This paper addresses the statistical inference of the unknown parameters, reliability, and hazard rate functions of logistic exponential distribution under adaptive progressive Type-II censored samples. Maximum likelihood estimates (MLEs) and maximum product spacing estimates (MPSEs) for the model parameters, reliability, and hazard rate functions can not be obtained explicitly, hence these are derived numerically using the Newton–Raphson method. Bayes estimates for the unknown parameters and reliability and hazard rate functions are computed under squared error loss function (SELF) and linear exponential loss function (LLF). It has been observed that the Bayes estimates are not in explicit forms, hence an approximation method such as Markov Chain Monte Carlo (MCMC) method is employed. Further, asymptotic confidence intervals (ACIs) and highest posterior density (HPD) credible intervals for the unknown parameters, reliability, and hazard rate functions are constructed. Besides, point and interval Bayesian predictions have been derived for future samples. A Monte Carlo simulation study has been carried out to compare the performance of the proposed estimates. Furthermore, three different optimality criteria have been considered to obtain the optimal censoring plan. Two real-life data sets, one from electronic industry and other one from COVID-19 data set containing the daily death rate from France are re-analyzed to demonstrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Background: Patients with chronic hepatitis C (CHC) can be cured with the new highly effective interferon‐free combination treatments (DAA) that were approved in 2014. However, CHC is a largely silent disease, and many individuals are unaware of their infections until the late stages of the disease. The impact of wider access to effective treatments and improved awareness of the disease on the number of infections and the number of patients who remain undiagnosed is not known in Canada. Such evidence can guide the development of strategies and interventions to reduce the burden of CHC and meet World Health Organization's (WHO) 2030 elimination targets. The purpose of this study is to use a back‐calculation framework informed by provincial population‐level health administrative data to estimate the prevalence of CHC and the proportion of cases that remain undiagnosed in the three most populated provinces in Canada: British Columbia (BC), Ontario and Quebec. Methods: We have conducted a population‐based retrospective analysis of health administrative data for the three provinces to generate the annual incidence of newly diagnosed CHC cases, decompensated cirrhosis (DC), hepatocellular carcinoma (HCC) and HCV treatment initiations. For each province, the data were stratified in three birth cohorts: individuals born prior to 1945, individuals born between 1945 and 1965 and individuals born after 1965. We used a back‐calculation modelling approach to estimate prevalence and the undiagnosed proportion of CHC. The historical prevalence of CHC was inferred through a calibration process based on a Bayesian Markov chain Monte Carlo (MCMC) algorithm. The algorithm constructs the historical prevalence of CHC for each cohort by comparing the model‐generated outcomes of the annual incidence of the CHC‐related health events against the data set of observed diagnosed cases generated in the retrospective analysis. Results: The results show a decreasing trend in both CHC prevalence and undiagnosed proportion in BC, Ontario and Quebec. In 2018, CHC prevalence was estimated to be 1.23% (95% CI:.96%–1.62%),.91% (95% CI:.82%–1.04%) and.57% (95% CI:.51%–.64%) in BC, Ontario and Quebec respectively. The CHC undiagnosed proportion was assessed to be 35.44% (95% CI: 27.07%–45.83%), 34.28% (95% CI: 26.74%–41.62%) and 46.32% (95% CI: 37.85%–52.80%) in BC, Ontario and Quebec, respectively, in 2018. Also, since the introduction of new DAA treatment in 2014, CHC prevalence decreased from 1.39% to 1.23%,.97% to.91% and.65% to.57% in BC, Ontario and Quebec respectively. Similarly, the CHC undiagnosed proportion decreased from 38.78% to 35.44%, 38.70% to 34.28% and 47.54% to 46.32% in BC, Ontario and Quebec, respectively, from 2014 to 2018. Conclusions: We estimated that the CHC prevalence and undiagnosed proportion have declined for all three provinces since the new DAA treatment has been approved in 2014. Yet, our findings show that a significant proportion of HCV cases remain undiagnosed across all provinces highlighting the need to increase investment in screening. Our findings provide essential evidence to guide decisions about current and future HCV strategies and help achieve the WHO goal of eliminating hepatitis C in Canada by 2030. [ABSTRACT FROM AUTHOR]

Rayleigh wave exploration is a powerful method for estimating near-surface shear-wave (S-wave) velocities, providing valuable insights into the stiffness properties of subsurface materials inside the Earth. The dispersion curve inversion of Rayleigh wave corresponds to the optimization process of searching for the optimal solutions of earth model parameters based on the measured dispersion curves. At present, diversified inversion algorithms have been introduced into the process of Rayleigh wave inversion. However, limited studies have been conducted to uncover the variations in inversion performance among commonly used inversion algorithms. To obtain a comprehensive understanding of the optimization performance of these inversion algorithms, we systematically investigate and quantitatively assess the inversion performance of two bionic algorithms, two probabilistic algorithms, a gradient-based algorithm, and two neural network algorithms. The evaluation indices include the computational cost, accuracy, stability, generalization ability, noise effects, and field data processing capability. It is found that the Bound-constrained limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS-B) algorithm and the broad learning (BL) network have the lowest computational cost among candidate algorithms. Furthermore, the transitional Markov Chain Monte Carlo algorithm, deep learning (DL) network, and BL network outperform the other four algorithms regarding accuracy, stability, resistance to noise effects, and capability to process field data. The DL and BL networks demonstrate the highest level of generalization compared to the other algorithms. The comparison results reveal the variations in candidate algorithms for the inversion task, causing a clear understanding of the inversion performance of candidate algorithms. This study can promote the S-wave velocity estimation by Rayleigh wave inversion. [ABSTRACT FROM AUTHOR]

The dark compact object at the centre of the Milky Way is well established to be a supermassive black hole with mass |$M_{\bullet } \sim 4.3 \times 10^6 \, {\rm M}_{\odot }$|⁠ , but the nature of its environment is still under debate. In this work, we used astrometric and spectroscopic measurements of the motion of the star S2, one of the closest stars to the massive black hole, to determine an upper limit on an extended mass composed of a massive vector field around Sagittarius A*. For a vector with effective mass |$10^{-19} \lesssim m_\mathrm{ s} \lesssim 10^{-18} \, \rm eV$|⁠ , our Markov chain Monte Carlo analysis shows no evidence for such a cloud, placing an upper bound |$M_{\rm cloud} \lesssim 0.1 \% \, M_{\bullet }$| at 3σ confidence level. We show that dynamical friction exerted by the medium on S2 motion plays no role in the analysis performed in this and previous works, and can be neglected thus. [ABSTRACT FROM AUTHOR]

Reproductive performance is a key determinant of cow longevity in a pasture-based, seasonal dairy system. Unfortunately, direct fertility phenotypes such as intercalving interval or pregnancy rate tend to have low heritabilities and occur relatively late in an animal's life. In contrast, age at puberty (AGEP) is a moderately heritable, early-in-life trait that may be estimated using an animal's age at first measured elevation in blood plasma progesterone (AGEP4) concentrations. Understanding the genetic architecture of AGEP4 in addition to genetic relationships between AGEP4 and fertility traits in lactating cows is important, as is its relationship with body size in the growing animal. Thus, the objectives of this research were 3-fold. First, to estimate the genetic and phenotypic (co)variances between AGEP4 and subsequent fertility during first and second lactations. Second, to quantify the associations between AGEP4 and height, length, and BW measured when animals were approximately 11 mo old (standard deviation = 0.5). Third, to identify genomic regions that are likely to be associated with variation in AGEP4. We measured AGEP4, height, length, and BW in approximately 5,000 Holstein-Friesian or Holstein-Friesian × Jersey crossbred yearling heifers across 54 pasture-based herds managed in seasonal calving farm systems. We also obtained calving rate (CR42, success or failure to calve within the first 42 d of the seasonal calving period), breeding rate (PB21, success or failure to be presented for breeding within the first 21 d of the seasonal breeding period) and pregnancy rate (PR42, success or failure to become pregnant within the first 42 d of the seasonal breeding period) phenotypes from their first and second lactations. The animals were genotyped using the Weatherby's Versa 50K SNP array (Illumina, San Diego, CA). The estimated heritabilities of AGEP4, height, length, and BW were 0.34 (90% credibility interval [CRI]: 0.30, 0.37), 0.28 (90% CRI: 0.25, 0.31), 0.21 (90% CRI: 0.18, 0.23), and 0.33 (90% CRI: 0.30, 0.36), respectively. In contrast, the heritabilities of CR42, PB21 and PR42 were all <0.05 in both first and second lactations. The genetic correlations between AGEP4 and these fertility traits were generally moderate, ranging from 0.11 to 0.60, whereas genetic correlations between AGEP4 and yearling body-conformation traits ranged from 0.02 to 0.28. Our GWAS highlighted a genomic window on chromosome 5 that was strongly associated with variation in AGEP4. We also identified 4 regions, located on chromosomes 14, 6, 1, and 11 (in order of decreasing importance), that exhibited suggestive associations with AGEP4. Our results show that AGEP4 is a reasonable predictor of estimated breeding values for fertility traits in lactating cows. Although the GWAS provided insights into genetic mechanisms underpinning AGEP4, further work is required to test genomic predictions of fertility that use this information. [ABSTRACT FROM AUTHOR]

Effective monitoring of the control charts requires the establishment of appropriate control limits. Various methods have been proposed to determine the fixed control limits (FCLs) based on a specified in‐control average run‐length value, such as Markov chains, integral equations, and Monte Carlo simulations.With the FCLs, the conditional false alarm rate (CFAR) of a control chart varies over time in an unexpected and undesirable way, where the CFAR refers to the probability of a false alarm at a particular time given no previous false alarm. To address this issue, dynamic probability control limits (DPCLs) can be employed to keep the CFAR constant over time. In this study, we determine the DPCLs using fixed and time‐varying sample sizes for the adaptive multivariate EWMA chart when the underlying process is assumed to follow a multivariate normal distribution. The DPCLs are designed to automatically adjust to changes in the probability distribution of the sample size, while maintaining a consistent CFAR. This results in a closely matched run‐length performance for an in‐control process compared to that of the geometric distribution. [ABSTRACT FROM AUTHOR]

In this paper, we have performed a comparative study of different types of oscillating dark energy (DE) models using the Metropolis algorithm of Markov Chain Monte Carlo. Eight different oscillating parameterizations are examined herein that have demonstrated considerable ability to fit the overall cosmological observations, including the Pantheon sample of Type Ia supernovae, baryon acoustic oscillations, cosmic chronometer Hubble data, and distance priors of the Planck cosmic microwave background. In order to compare the consistency of these models with observations, we have used both the Akaike and deviance information criteria. Although the values of the Akaike information criterion for different models indicate that there is no support for oscillating DE models, the deviance information criterion showed that there is significant support for some of these models. Our results showed that these models are capable of solving the cosmic coincidence problem and alleviating the Hubble tension. Comparing the H 0 values obtained for different oscillating scenarios with that of ΛCDM, we observed that our oscillating models led to H 0 ¯ = 69.78 , which is 0.29 greater than H 0,Λ and thus reduces the Hubble tension. Among all of the models, model 1, with H 0 = 70.00 ± 0.71, is the most capable of alleviating the H 0 tension. Furthermore, we examined our models assuming H 0 = 73.0 ± 1.4 from SHoES measurements. We find that adding this data point to our data combination led to a Δ H 0 ¯ = 0.95 increase in the H 0 value for different models. [ABSTRACT FROM AUTHOR]

In this paper, the Integrated Nested Laplace Algorithm (INLA) is applied to the Epidemic Type Aftershock Sequence (ETAS) model, and the parameters of the ETAS model are obtained for the earthquake sequences active in different regions of Xinjiang. By analyzing the characteristics of the model parameters over time, the changes in each earthquake sequence are studied in more detail. The estimated values of the ETAS model parameters are used as inputs to forecast strong aftershocks in the next period. We find that there are significant differences in the aftershock triggering capacity and aftershock attenuation capacity of earthquake sequences in different seismic regions of Xinjiang. With different cutoff dates set, we observe the characteristics of the earthquake sequence parameters changing with time after the mainshock occurs, and the model parameters of the Ms7.3 earthquake sequence in Hotan region change significantly with time within 15 days after the earthquake. Compared with the MCMC algorithm, the ETAS model fitted with the INLA algorithm can forecast the number of earthquakes in the early period after the occurrence of strong aftershocks more effectively and can forecast the sudden occurrence time of earthquakes more accurately. [ABSTRACT FROM AUTHOR]

The field load test is a direct and effective method for evaluating the performance of bridge structures. However, the existing bridge static load tests on site are costly, inefficient, and obstruct traffic; moreover, improper loading may also cause some damage to the bridge structure. This paper proposes a random model update method based on bridge dynamic load tests and the Bayesian inference as an alternative to the static load test. The Gaussian process model was used instead of the finite element model to reduce the cost of model calculation. Furthermore, choose the Markov Chain Monte Carlo (MCMC) method based on delay rejection adaptive Metropolis algorithm for Bayesian inference to improve the speed of the Bayesian method inferring the posterior probability density of updated parameters. First, the parameters to be updated for the bridge structure analysis model were determined based on the global sensitivity analysis method. Second, a uniform design sampling method was used to establish the Gaussian process optimization model to update the random model of the bridge structure. Finally, a reinforced concrete truss arch bridge was used to verify the correctness of the static load results of the bridge predicted by the random model update method based on dynamic load testing and Bayesian inference. The results show that the predicted results of the bridge static load test based on the dynamic load test and Bayesian reasoning method have an excellent agreement with the measured results, and this method can effectively overcome the adverse effects of the existing bridge static load test. [ABSTRACT FROM AUTHOR]

Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can help us better model and predict the dynamics of an epidemic, and provide insight into the efficacy of control and intervention strategies. We present a method for likelihood‐based estimation of parameters in the stochastic susceptible‐infected‐removed model under a time‐inhomogeneous transmission rate comprised of piecewise constant components. In doing so, our method simultaneously learns change points in the transmission rate via a Markov chain Monte Carlo algorithm. The method targets the exact model posterior in a difficult missing data setting given only partially observed case counts over time. We validate performance on simulated data before applying our approach to data from an Ebola outbreak in Western Africa and COVID‐19 outbreak on a university campus. [ABSTRACT FROM AUTHOR]

Background: Recently revised WHO guidelines on malaria chemoprevention have opened the door to more tailored implementation. Countries face choices on whether to replace old drugs, target additional age groups, and adapt delivery schedules according to local drug resistance levels and malaria transmission patterns. Regular routine assessment of protective efficacy of chemoprevention is key. Here, we apply a novel modelling approach to aid the design and analysis of chemoprevention trials and generate measures of protection that can be applied across a range of transmission settings. Methods and findings: We developed a model of genotype-specific drug protection, which accounts for underlying risk of infection and circulating genotypes. Using a Bayesian framework, we fitted the model to multiple simulated scenarios to explore variations in study design, setting, and participant characteristics. We find that a placebo or control group with no drug protection is valuable but not always feasible. An alternative approach is a single-arm trial with an extended follow-up (>42 days), which allows measurement of the underlying infection risk after drug protection wanes, as long as transmission is relatively constant. We show that the currently recommended 28-day follow-up in a single-arm trial results in low precision of estimated 30-day chemoprevention efficacy and low power in determining genotype differences of 12 days in the duration of protection (power = 1.4%). Extending follow-up to 42 days increased precision and power (71.5%) in settings with constant transmission over this time period. However, in settings of unstable transmission, protective efficacy in a single-arm trial was overestimated by 24.3% if recruitment occurred during increasing transmission and underestimated by 15.8% when recruitment occurred during declining transmission. Protective efficacy was estimated with greater precision in high transmission settings, and power to detect differences by resistance genotype was lower in scenarios where the resistant genotype was either rare or too common. Conclusions: These findings have important implications for the current guidelines on chemoprevention efficacy studies and will be valuable for informing where these studies should be optimally placed. The results underscore the need for a comparator group in seasonal settings and provide evidence that the extension of follow-up in single-arm trials improves the accuracy of measures of protective efficacy in settings with more stable transmission. Extension of follow-up may pose logistical challenges to trial feasibility and associated costs. However, these studies may not need to be repeated multiple times, as the estimates of drug protection against different genotypes can be applied to different settings by adjusting for transmission intensity and frequency of resistance. Using a novel modelling approach, Mousa and colleagues investigate the design and analysis of malaria chemoprevention trials and generate measures of protection that can be applied across a range of transmission settings. Author summary: Why was this study done?: In 2022, the World Health Organisation (WHO) released updated guidelines for the implementation of malaria chemoprevention and guidance for undertaking chemoprevention efficacy studies. We sought to understand how study design and trial setting characteristics influence the ability to assess chemoprevention efficacy and duration of drug protection. The impact of drug resistance on chemoprevention is not well understood, and there is a need for a method that produces measures of drug resistance effects, which can be applied to different settings. What did the researchers do and find?: We fitted a Bayesian Markov Chain Monte Carlo (MCMC) to simulated trial data for a number of trial designs and scenarios. We find that the WHO recommendation of 28 days of follow-up is insufficient to precisely estimate duration of drug protection or protective efficacy. In seasonal settings, in the absence of a control arm, it is impossible to distinguish between changing transmission and waning drug protection when estimating protective efficacy. What do these findings mean?: Where feasible, particularly in settings of seasonal transmission and/or trials without a control arm, extending follow-up to 42 or 63 days can substantially improve the ability to accurately estimate chemoprevention outcomes. Although long follow-up can improve precision and power, decisions on study design should also consider costs and trial feasibility. [ABSTRACT FROM AUTHOR]

Context. The fitting of spectral lines is a common step in the analysis of line observations and simulations. However, the observational noise, the presence of multiple velocity components, and potentially large data sets make it a non-trivial task. Aims. We present a new computer program Spectrum Iterative Fitter (SPIF) for the fitting of spectra with Gaussians or with hyperfine line profiles. The aim is to show the computational efficiency of the program and to use it to examine the general accuracy of approximating spectra with simple models. Methods. We describe the implementation of the program. To characterise its performance, we examined spectra with isolated Gaussian components or a hyperfine structure, also using synthetic observations from numerical simulations of interstellar clouds. We examined the search for the globally optimal fit and the accuracy to which single-velocity-component and multi-component fits recover true values for parameters such as line areas, velocity dispersion, and optical depth. Results. The program is shown to be fast, with fits of single Gaussian components reaching on graphics processing units speeds approaching one million spectra per second. This also makes it feasible to use Monte Carlo simulations or Markov chain Monte Carlo calculations for the error estimation. However, in the case of hyperfine structure lines, degeneracies affect the parameter estimation and can complicate the derivation of the error estimates. Conclusions. The use of many random initial values makes the fits more robust, both for locating the global χ2 minimum and for the selection of the optimal number of velocity components. [ABSTRACT FROM AUTHOR]

Context. Magnification bias, an observational effect of gravitational lensing in the weak regime, allows the cosmological model to be tested through angular correlations of sources at different redshifts. This effect has been observed in various contexts, particularly with sub-millimetre galaxies (SMGs), offering valuable astrophysical and cosmological insights. Aims. The study aims to investigate the magnification bias effect exerted by galaxy clusters on SMGs and its implications for astrophysical and cosmological parameters within the Λ-CDM model. Methods. Magnification bias was explored by quantifying the cross-correlation function, which we then utilised to derive constraints on cosmological and astrophysical parameters with a Markov chain Monte Carlo algorithm. Two distinct galaxy cluster samples were used to assess result robustness and understand the influence of sample characteristics. Results. Cluster samples show higher cross-correlation values than galaxies, with an excess at larger scales suggesting contributions from additional large-scale structures. The parameters obtained, while consistent with those of galaxies, are less constrained due to broader redshift distributions and limited cluster statistics. Results align with weak lensing studies, hinting at slightly lower σ8 and Ωm values than Planck's cosmic microwave background data, emphasising the need for enhanced precision and alternative low-redshift universe tests. Conclusions. While this method yields constraints that are compatible with the Λ-CDM model, its limitations include broader redshift distributions and a limited number of lenses, resulting in less constrained parameters compared to previous galaxy studies. Nonetheless, our study underscores the potential of using galaxy clusters as lenses for magnification bias studies, capitalising on their elevated masses and thus providing a promising avenue to test current cosmology theories. Further progress can be made by expanding the lens sample size. [ABSTRACT FROM AUTHOR]

In this paper we investigate the impact of lensing magnification on the analysis of Euclid's spectroscopic survey using the multipoles of the two-point correlation function for galaxy clustering. We determine the impact of lensing magnification on cosmological constraints as well as the expected shift in the best-fit parameters if magnification is ignored. We considered two cosmological analyses: (i) a full-shape analysis based on the Λ cold dark matter (CDM) model and its extension w0waCDM and (ii) a model-independent analysis that measures the growth rate of structure in each redshift bin. We adopted two complementary approaches in our forecast: the Fisher matrix formalism and the Markov chain Monte Carlo method. The fiducial values of the local count slope (or magnification bias), which regulates the amplitude of the lensing magnification, have been estimated from the Euclid Flagship simulations. We used linear perturbation theory and modelled the two-point correlation function with the public code coffe. For a ΛCDM model, we find that the estimation of cosmological parameters is biased at the level of 0.4–0.7 standard deviations, while for a w0waCDM dynamical dark energy model, lensing magnification has a somewhat smaller impact, with shifts below 0.5 standard deviations. For a model-independent analysis aimed at measuring the growth rate of structure, we find that the estimation of the growth rate is biased by up to 1.2 standard deviations in the highest redshift bin. As a result, lensing magnification cannot be neglected in the spectroscopic survey, especially if we want to determine the growth factor, one of the most promising ways to test general relativity with Euclid. We also find that, by including lensing magnification with a simple template, this shift can be almost entirely eliminated with minimal computational overhead. [ABSTRACT FROM AUTHOR]

We propose a new method for estimating the distances of molecular clouds traced by CO line emission. Stars from 2MASS and Gaia EDR3 are selected as on-cloud stars when they are projected on a cloud. The background on-cloud stars have redder colors on average than the foreground stars. Instead of searching for stars projected away from the cloud, we employed the TRILEGA galaxy model to mimic the stellar population without cloud extinction along the sightline toward the cloud. Our method does not require an exact boundary of a cloud. The boundaries are highly variable and depend on the sensitivity of the molecular line data. For each cloud, we compared the distributions of on-cloud stars to the TRILEGAL stellar populations in the diagram of J−Ks color versus distance. The intrinsic J−Ks colors of main-sequence and evolved stars from TRILEGAL were considered separately, and they were used as the baseline for subtracting the observed J−Ks colors. The baseline-corrected J−Ks color was deployed with the Bayesian analysis and Markov chain Monte Carlo sampling to determine the distance at which the J−Ks color jump is largest. This method was successfully applied to measure the distances of 27 molecular clouds, which were selected from previously published cloud samples. By replacing TRILEGAL with the GALAXIA galaxy model, we were able to measure the distances for 21 of the 27 clouds. The distances of the 21 clouds based on the GALAXIA model agree well with those based on the TRILEGAL model. The distances of the 27 clouds estimated by this method are consistent with previous estimates. We will apply this new method to a larger region of the gaseous galactic plane, in particular, for the inner galactic region, where a region free of CO emission is hard to separate from the crowded field of clouds. [ABSTRACT FROM AUTHOR]

Strongly lensed systems with peculiar configurations allow us to probe the local properties of the deflecting lens mass while simultaneously testing general profile assumptions. The quasar HE0230−2130 is lensed by two galaxies at similar redshifts (Δz ∼ 0.003) into four observed images. Using modeled quasar positions from fitting the brightness of the quasar images in ground-based imaging data from the Magellan telescope, we find that lens-mass models where each of these two galaxies is parametrized with a singular power-law (PL) profile predict five quasar images. One of the predicted images is unobserved despite it being distinctively offset from the lensing galaxies and likely bright enough to be observable. This missing image gives rise to new opportunities to study the mass distribution of these galaxies. To interpret the quad configuration of the system, we tested 12 different profile assumptions with the aim of obtaining lens-mass models that correctly predict only four observed images. We tested the effects of adopting: cored profiles for the lensing galaxies; external shear; and additional profiles to represent a dark matter clump. We find that half of our model classes can produce the correct image multiplicity. By comparing the Bayesian evidence of different model parametrizations, we favor two model classes: (i) one that incorporates two singular PL profiles for the lensing galaxies and a cored isothermal sphere in the region of the previously predicted fifth image (rNIS profile), and (ii) one with a bigger lensing galaxy parametrized by a singular PL profile and the smaller galaxy by a cored PL profile with external shear. We estimated the mass of the rNIS clump for each candidate model of our final Markov chain Monte Carlo sample, and find that only 2% are in the range of 106 M⊙ ≤ MrNIS ≤ 109 M⊙, which is the predicted mass range of dark matter subhalos in cold dark matter simulations, or the mass of dark-matter-dominated and low-surface-brightness galaxies. We therefore favor the models with a cored mass distribution for the lens galaxy close to the predicted fifth image. Our study further demonstrates that lensed quasar images are sensitive to the dark matter structure in the gravitational lens. We are able to describe this exotic lensing configuration with relatively simple models, which demonstrates the power of strong lensing for studying galaxies and lens substructure. [ABSTRACT FROM AUTHOR]

The interpretation of the thermal evolution of the transiently accreting neutron stars MXB 1659−29 and KS 1731−260 after an outburst is challenging, both within the traditional deep-crustal heating paradigm and the thermodynamically consistent approach of Gusakov and Chugunov that accounts for neutron diffusion throughout the crust. All these studies assume that the neutron superfluid in the crust is at rest. However, we have recently shown that a finite superflow could exist and could lead to a new gapless superfluid phase if quantized vortices are pinned. We have revisited the cooling of MXB 1659−29 and KS 1731−260 and we have found that gapless superfluidity could naturally explain their late time cooling. We pursue here our investigation by performing new simulations of the thermal relaxation of the crust of MXB 1659−29 and KS 1731−260 within a Markov Chain Monte Carlo method accounting for neutron diffusion and allowing for gapless superfluidity. We have varied the global structure of the neutron star, the composition of the heat-blanketing envelope, and the mass accretion rate. In all cases, observations are best fitted by models with gapless superfluidity. Finally, we make predictions that could be tested by future observations. [ABSTRACT FROM AUTHOR]

In the current study, we have considered three different parameterizations of deceleration parameter to describe the cosmological dynamics of the accelerating universe in f (Q) gravity. The power law symmetric teleparallel gravity with a specific form f (Q) = Q + n Q m is assumed for the modelling purpose. Here, m and n are constants and Q is the non-metricity term that describes the gravitational interaction in space time. We constructed the field equations depending on the power law f (Q) gravity and parameters are extracted using experimental observations. Latest observational datasets of BAO, H (z) and Pantheon are utilized to predict the best fit values of parameters and current value of Hubble constant. The Markov Chain Monte Carlo (MCMC) algorithm has been used to decide the best plausible values of parameters. We numerically represent the physical and geometrical features of the models and thoroughly explore their development. We analyzed our models using the jerk and Om diagnosis that depict the derived cosmic models are different from the Λ CDM model expressing late time accelerated expansion of cosmos with phantom type of the universe. We also discussed the viability of models by the analysis of energy conditions. [ABSTRACT FROM AUTHOR]

In this article, we attempt to explore the dark sector of the universe i.e. dark matter and dark energy, where the dark energy components are related to the modified f(Q) Lagrangian, particularly a power law function f (Q) = γ Q Q 0 n , while the dark matter component is described by the Extended Bose–Einstein Condensate (EBEC) equation of state for dark matter, specifically, p = α ρ + β ρ 2 . We find the corresponding Friedmann-like equations and the continuity equation for both dark components along with an interacting term, specifically Q = 3 b 2 H ρ , which signifies the energy exchange between the dark sector of the universe. Further, we derive the analytical expression of the Hubble function, and then we find the best-fit values of free parameters utilizing the Bayesian analysis to estimate the posterior probability and the Markov Chain Monte Carlo (MCMC) sampling technique corresponding to CC+Pantheon+SH0ES samples. In addition, to examine the robustness of our MCMC analysis, we perform a statistical assessment using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Further from the evolutionary profile of the deceleration parameter and the energy density, we obtain a transition from the decelerated epoch to the accelerated expansion phase, with the present deceleration parameter value as q (z = 0) = q 0 = - 0. 56 - 0.03 + 0.04 ( 68 % confidence limit), that is quite consistent with cosmological observations. In addition, we find the expected positive behavior of the effective energy density. Finally, by examining the sound speed parameter, we find that the assumed theoretical f(Q) model is thermodynamically stable. [ABSTRACT FROM AUTHOR]

In this paper, we focus on Bayesian estimation of the parameters in the geometric process (GP) in which the first occurrence time of an event is assumed to have Weibull distribution. The Bayesian estimators are derived based on both symmetric (Squared Error) and asymmetric (General Entropy, LINEX) loss functions. Since the Bayesian estimators of unknown parameters cannot be obtained analytically, Lindley's approximation and the Markov Chain Monte Carlo (MCMC) methods are applied to compute the Bayesian estimates. Furthermore, by using the MCMC methods, credible intervals of the parameters are constructed. Maximum likelihood (ML) estimators are also derived for unknown parameters. The confidence intervals of the parameters are obtained based on an asymptotic distribution of ML estimators. Moreover, the performances of the proposed Bayesian estimators are compared with the corresponding ML, modified moment and modified maximum likelihood estimators through an extensive simulation study. Finally, analyses of two different real data sets are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

Modeling multimodal survival data using parametric distributions is yet a challenging task. Mixture distributions in a nonparametric Bayesian framework can be applied as a sophisticated tool. Dirichlet process mixture model (DPMM) is a suitable asset in this approach. Choosing a kernel for the mixture model is an essential issue in this context. Survival data analysis using the DPMM with a three-parameter Burr XII kernel is the objective of this article. The Monte Carlo Markov Chain algorithms, like Gibbs sampling, are developed to fit the three-parameter Burr XII mixture model. A Simulation study based on right-censored data illustrates the performance of this kind of mixture model. We compare the proposed model results with other DPMM with different kernels like Weibull, Lognormal, and two-parameter Burr XII distributions. The flexibility of the proposed mixture model is demonstrated using three real datasets. In some instances, DPMM with Weibull or lognormal kernels perform well; meanwhile, these kernels may not outperform in the clustering or hazard rate estimation context. In these cases, a three parameters BurXII distribution might be a suitable kernel for Dirichlet process mixture model. [ABSTRACT FROM AUTHOR]

In the correlated frailty models, it is believed that all the individuals in the population will eventually experience the event of interest. This may not always be the situation in reality. There may be a certain fraction of the population which is immune to the event and hence may not experience the event under study. For such individuals, frailty may not be active i.e., zero. Hence, frailty distribution should provide a positive mass at zero. In this article, a new correlated frailty model with compound negative binomial distribution as frailty distribution, is introduced to incorporate the non-susceptibility of individuals. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real life data set. [ABSTRACT FROM AUTHOR]

Reliability performance, especially the lower confidence limit of reliability, plays an important role in reliability assessment, and it is also of concern to researchers and engineers. In this article, a novel estimate of the lower confidence limit of the reliability for two-parameter Weibull distribution is proposed based on the generalized fiducial inference. The corresponding adaptive Metropolis-Hastings within Gibbs algorithm is provided to analyze the generalized fiducial lower confidence limit. The proposed lower confidence limit of the reliability is compared with that from frequentist method. In addition, this novel procedure is generalized to the series system and the parallel system which consists of identical Weibull components. Simulation results show that the proposed generalized fiducial lower confidence limit is more applicable than the frequentist method, especially for the case of small sample size. Finally, the MOS transistor lifetime data is used to illustrate the new procedure. [ABSTRACT FROM AUTHOR]

An alternative transcription start site (ATSS) is a major driving force for increasing the complexity of transcripts in human tissues. As a transcriptional regulatory mechanism, ATSS has biological significance. Many studies have confirmed that ATSS plays an important role in diseases and cell development and differentiation. However, exploration of its dynamic mechanisms remains insufficient. Identifying ATSS change points during cell differentiation is critical for elucidating potential dynamic mechanisms. For relative ATSS usage as percentage data, the existing methods lack sensitivity to detect the change point for ATSS longitudinal data. In addition, some methods have strict requirements for data distribution and cannot be applied to deal with this problem. In this study, the Bayesian change point detection model was first constructed using reparameterization techniques for two parameters of a beta distribution for the percentage data type, and the posterior distributions of parameters and change points were obtained using Markov Chain Monte Carlo (MCMC) sampling. With comprehensive simulation studies, the performance of the Bayesian change point detection model is found to be consistently powerful and robust across most scenarios with different sample sizes and beta distributions. Second, differential ATSS events in the real data, whose change points were identified using our method, were clustered according to their change points. Last, for each change point, pathway and transcription factor motif analyses were performed on its differential ATSS events. The results of our analyses demonstrated the effectiveness of the Bayesian change point detection model and provided biological insights into cell differentiation. [ABSTRACT FROM AUTHOR]

In multiple time series data, clustering the component profiles can identify meaningful latent groups while also detecting interesting change points in their trajectories. Conventional time series clustering methods, however, suffer the drawback of requiring the co-clustered units to have the same cluster membership throughout the entire time domain. In contrast to these "global" clustering methods, we develop a Bayesian "local" clustering method that allows the functions to flexibly change their cluster memberships over time. We design a Markov chain Monte Carlo algorithm to implement our method. We illustrate the method in several real-world datasets, where time-varying cluster memberships provide meaningful inferences about the underlying processes. These include a public health dataset to showcase the more detailed inference our method can provide over global clustering alternatives, and a temperature dataset to demonstrate our method's utility as a flexible change point detection method. for this article, including R codes implementing the method, are available online. [ABSTRACT FROM AUTHOR]

Integrated distribution models (IDMs), in which datasets with different properties are analysed together, are becoming widely used to model species distributions and abundance in space and time. To date, the IDM literature has focused on technical and statistical issues, such as the precision of parameter estimates and mitigation of biases arising from unstructured data sources. However, IDMs have an unrealised potential to estimate ecological properties that could not be properly derived from the source datasets if analysed separately. We present a model that estimates community alpha diversity metrics by integrating one species‐level dataset of presence–absence records with a co‐located dataset of group‐level counts (i.e. lacking information about species identity). We illustrate the ability of community IDMs to capture the true alpha diversity through simulation studies and apply the model to data from the UK Pollinator Monitoring Scheme, to describe spatial variation in the diversity of solitary bees, bumblebees and hoverflies. The simulation and case studies showed that the proposed IDM produced more precise estimates of the community diversity than the single models, and the analysis of the real dataset further showed that the alpha diversity estimates from the IDM were averages of the single models. Our findings also revealed that IDMs had a higher prediction accuracy for all the insect groups in most cases, with this performance linked to the information provided by a data source into the IDM. [ABSTRACT FROM AUTHOR]

In this paper, the stress–strength reliability $ R_{s,k} $ R s , k of a multicomponent s-out-of-k system for exponentiated Gumbel distribution is considered. An s-out-of-k system means a system with total k components and the system can survive only when atleast s of the total components function properly. The ability of the system to overcome the experiencing stress with its strength is termed as its stress–strengh reliability. The maximum likelihood estimator and Bayes estimator for $ R_{s,k} $ R s , k are obtained. The Bayes estimators are obtained using Markov chain Monte Carlo(MCMC) method under both symmetric and asymmetric loss functions. The loss functions we considered are squared error loss function, LINEX loss function and entropy loss function. The asymptotic, bootstrap and highest posterior density(HPD) confidence intervals for $ R_{s,k} $ R s , k are also obtained. A simulation study is conducted for evaluating the efficiency of the estimators derived in this paper. Real data sets are also considered for illustration. [ABSTRACT FROM AUTHOR]

We provide a comparison between marginal likelihood and data augmented Markov chain Monte Carlo (MCMC) algorithms for Bayesian estimation of hidden Markov models. In particular, we focus on a specification of these models based on a multivariate Gaussian distribution for the response variables. We evaluate the performance of both methods on the basis of simulated samples and an empirical application, where we compare these approaches in terms of standard measures of estimation and time efficiency. The results show that the augmented algorithm is preferable, obtaining optimal convergence properties and producing larger values of the effective sample size. Instead of using variable dimensional techniques for model selection, we suggest a method based on the so-called parallel sampling for this aim. [ABSTRACT FROM AUTHOR]

Intracrustal low-velocity zones (LVZs) indicate a mechanically weak crust and are widely observed in the southeast margin of the Tibetan Plateau. However, their spatial distributions and formation mechanisms remain controversial. To investigate their distribution and detailed morphology of the LVZs in the southeastern Tibetan Plateau, here we used teleseismic events and continuous waveform data recorded by 40 broadband seismic stations newly deployed in the Sichuan-Yunnan region from December 2018 to October 2020. A total of 12,924 high-quality P-wave receiver functions and 5–40 s fundamental Rayleigh surface wave phase velocity dispersion curves from ambient noise cross-correlation functions were obtained. The S-wave velocity model at a depth interval of 0–100 km in the study area was inverted by using the trans-dimensional Markov chain Monte Carlo strategy to jointly invert the complementary data of the receiver function waveform and Rayleigh surface wave phase velocity dispersion. Our results show that there are two separate LVZs (∼3.5 km/s) surrounding the rigid Daliangshan subblock at crustal depths of approximately 30–40 km, providing new constraints on the geometry of the LVZs in our study region. The two LVZs obtained in this study may represent the middle crustal flow channels, through which the material in the center of the Tibetan Plateau extrudes to its southeast margin. Blocked by the rigid Sichuan Basin and the spindle-like Daliangshan subblock, the material continues to flow southward through the mechanically weak middle crustal channels surrounding the Daliangshan subblock. In addition, the existence of thin LVZs in the middle crust plays an important role in understanding the decoupling between the upper and lower crust in the study area. It also provides new constraint on the complex tectonic deformation process of the southeastern margin of the Tibetan Plateau caused by the collision and compression of the Indian and the Eurasian plates. [ABSTRACT FROM AUTHOR]