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The Markov chain Monte Carlo (MCMC) method is widely used in various fields as a powerful numerical integration technique for systems with many degrees of freedom. In MCMC methods, probabilistic state transitions can be considered as a random walk in state space, and random walks allow for sampling from complex distributions. However, paradoxically, it is necessary to carefully suppress the randomness of the random walk to improve computational efficiency. By breaking detailed balance, we can create a probability flow in the state space and perform more efficient sampling along this flow. Motivated by this idea, practical and efficient nonreversible MCMC methods have been developed over the past ten years. In particular, the lifting technique, which introduces probability flows in an extended state space, has been applied to various systems and has proven more efficient than conventional reversible updates. We review and discuss several practical approaches to implementing nonreversible MCMC methods, including the shift method in the cumulative distribution and the directed-worm algorithm. [ABSTRACT FROM AUTHOR]

Small angle x-ray scattering (SAXS) is a widely recognized solution for measuring complex nanostructures. With the increasing demand for accurately assessing structural characteristics and optimizing manufacturing processes, uncertainty quantification in SAXS inverse problems has become a critical issue. However, traditional methods face challenges such as slow computation speed and inaccurate estimation of multidimensional parameters. To overcome these issues, we propose an uncertainty quantification approach suitable for SAXS measurement that approximates the posterior using Bayesian deep learning. The effectiveness and reliability of our method are illustrated by assessing structural parameters of synthetic 2D Si grating samples. The uncertainty quantification takes only about 2.3 s, thousands of times faster than the conventional Markov Chain Monte Carlo (MCMC) methods. Also, our method has superior repeatability for parameter measurement compared to the MCMC approaches. It provides the potential of efficient and reliable SAXS measurement in increasingly intricate semiconductor manufacturing. [ABSTRACT FROM AUTHOR]

A central paradigm of polymer physics states that chains in melts behave like random walks as intra- and interchain interactions effectively cancel each other out. Likewise, θ-chains, i.e., chains at the transition from a swollen coil to a globular phase, are also thought to behave like ideal chains, as attractive forces are counterbalanced by repulsive entropic contributions. While the simple mapping to an equivalent Kuhn chain works rather well in most scenarios with corrections to scaling, random walks do not accurately capture the topology and knots, particularly for flexible chains. In this paper, we demonstrate with Monte Carlo and molecular dynamics simulations that chains in polymer melts and θ-chains not only agree on a structural level for a range of stiffnesses but also topologically. They exhibit similar knotting probabilities and knot sizes, both of which are not captured by ideal chain representations. This discrepancy comes from the suppression of small knots in real chains, which is strongest for very flexible chains because excluded volume effects are still active locally and become weaker with increasing semiflexibility. Our findings suggest that corrections to ideal behavior are indeed similar for the two scenarios of real chains and that the structure and topology of a chain in a melt can be approximately reproduced by a corresponding θ-chain. [ABSTRACT FROM AUTHOR]

The diffusion of proteins is significantly affected by macromolecular crowding. Molecular simulations accounting for protein interactions at atomic resolution are useful for characterizing the diffusion patterns in crowded environments. We present a comprehensive analysis of protein diffusion under different crowding conditions based on our recent docking-based approach simulating an intracellular crowded environment by sampling the intermolecular energy landscape using the Markov Chain Monte Carlo protocol. The procedure was extensively benchmarked, and the results are in very good agreement with the available experimental and theoretical data. The translational and rotational diffusion rates were determined for different types of proteins under crowding conditions in a broad range of concentrations. A protein system representing most abundant protein types in the E. coli cytoplasm was simulated, as well as large systems of other proteins of varying sizes in heterogeneous and self-crowding solutions. Dynamics of individual proteins was analyzed as a function of concentration and different diffusion rates in homogeneous and heterogeneous crowding. Smaller proteins diffused faster in heterogeneous crowding of larger molecules, compared to their diffusion in the self-crowded solution. Larger proteins displayed the opposite behavior, diffusing faster in the self-crowded solution. The results show the predictive power of our structure-based simulation approach for long timescales of cell-size systems at atomic resolution. [ABSTRACT FROM AUTHOR]

Individuals with end-stage kidney disease (ESKD) on dialysis experience high mortality and excessive burden of hospitalizations over time relative to comparable Medicare patient cohorts without kidney failure. A key interest in this population is to understand the time-dynamic effects of multilevel risk factors that contribute to the correlated outcomes of longitudinal hospitalization and mortality. For this we utilize multilevel data from the United States Renal Data System (USRDS), a national database that includes nearly all patients with ESKD, where repeated measurements/hospitalizations over time are nested in patients and patients are nested within (health service) regions across the contiguous U.S. We develop a novel spatiotemporal multilevel joint model (STM-JM) that accounts for the aforementioned hierarchical structure of the data while considering the spatiotemporal variations in both outcomes across regions. The proposed STM-JM includes time-varying effects of multilevel (patient- and region-level) risk factors on hospitalization trajectories and mortality and incorporates spatial correlations across the spatial regions via a multivariate conditional autoregressive correlation structure. Efficient estimation and inference are performed via a Bayesian framework, where multilevel varying coefficient functions are targeted via thin-plate splines. The finite sample performance of the proposed method is assessed through simulation studies. An application of the proposed method to the USRDS data highlights significant time-varying effects of patient- and region-level risk factors on hospitalization and mortality and identifies specific time periods on dialysis and spatial locations across the U.S. with elevated hospitalization and mortality risks.

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]

A joint maintenance decision-making framework is proposed to optimise the long-term maintenance plan and lower the maintenance cost for offshore wind farms. The historical wind speed data are screened by using the method of k-means clustering, and Markov chains are established for the wind speed in different seasons. On this basis, the approach of Markov chain Monte Carlo is applied to simulate the distribution of repair vessel's waiting time for maintenance, where the impact of wind speed on maintenance availability is considered. Moreover, the components in wind turbines are divided into four states according to their effective ages, i.e. young, mature, old and failed, respectively. A maintenance decision model is established, with the objective to minimise maintenance cost. Besides, three types of opportunistic maintenance are considered, i.e. failure-based opportunistic maintenance (FBOM), event-based opportunistic maintenance (EBOM) and age-based opportunistic maintenance (ABOM), respectively. The enhanced elitist genetic algorithm (SEGA) is adopted to solve the optimisation problem. The results indicate that among the three types of opportunistic maintenance, ABOM can reduce maintenance cost more effectively, and it is more suitable for long-term maintenance plans of offshore wind farm. [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]

We calculate the abundance of UV-bright galaxies in the presence of ultralight axion (ULA) dark matter (DM), finding that axions suppress their formation with a non-trivial dependence on redshift and luminosity. We set limits on axion DM using UV luminosity function (UVLF) data, excluding a single axion as all the DM for m ax < 10−21.6 eV and limiting axions with − 26 ≤ log (m ax / eV) ≤ − 23 to be less than 22% of the DM (both at 95% credibility). These limits use UVLF measurements from 24,000 sources from the Hubble Space Telescope (HST) at redshifts 4 ≤ z ≤ 10. We marginalize over a parametric model connecting halo mass and UV luminosity. Our results bridge a window in axion mass and fraction previously unconstrained by cosmological data, between large-scale cosmic microwave background and galaxy clustering and the small-scale Ly α forest. These high- z measurements provide a powerful consistency check of low- z tests of axion DM, including the recent hint for a sub-dominant ULA DM fraction in Ly α forest data. We also consider a sample of 25 spectroscopically confirmed high- z galaxies from the James Webb Space Telescope (JWST), finding these data to be consistent with HST. Combining HST and JWST UVLF data does not improve our constraints beyond HST alone, but future JWST measurements have the potential to improve these results. We also find an excess of low-mass halos (<109 M ⊙) at z < 3, which could be probed by subgalactic structure probes (e.g., stellar streams, satellite galaxies, and strong lensing). [ABSTRACT FROM AUTHOR]

In the exploration of recently developed Bayesian Generalized Nonlinear Models (BGNLM), this paper proposes a pragmatic scalable approximation for computing posterior distributions. Traditional Markov chain Monte Carlo within the populations of the Genetically Modified Mode Jumping Markov Chain Monte Carlo (GMJMCMC) algorithm is an NP-hard search problem. To linearize them, we suggest using instead variational Bayes, employing either mean-field approximation or normalizing flows for simplicity and scalability. This results in an evolutionary variational Bayes algorithm as a more scalable alternative to GMJMCMC. Through practical applications including inference on Bayesian linear models, Bayesian fractional polynomials, and full BGNLM, we demonstrate the effectiveness of our method, delivering accurate predictions, transparency and interpretations, and accessible measures of uncertainty, while improving the scalability of BGNLM inference through on the one hand using a novel variational Bayes method, but, on the other hand, enabling the use of GPUs for computations. [ABSTRACT FROM AUTHOR]

Strong gravitational lens system catalogues are typically used to constrain a combination of cosmological and empirical power-law lens mass model parameters, often introducing additional empirical parameters and constraints from high resolution imagery. We investigate these lens models using Bayesian methods through a novel alternative that treats spatial curvature via the non-FLRW timescape cosmology. We apply Markov Chain Monte Carlo methods using the catalogue of 161 lens systems of Chen et al. in order to constrain both lens and cosmological parameters for: (i) the standard |$\Lambda$| CDM model with zero spatial curvature; and (ii) the timescape model. We then generate large mock data sets to further investigate the choice of cosmology on fitting simple power-law lens models. In agreement with previous results, we find that in combination with single isothermal sphere parameters, models with zero FLRW spatial curvature fit better as the free parameter approaches an unphysical empty universe, |$\Omega _{\mathrm{M}0}\rightarrow 0$|⁠. By contrast, the timescape cosmology is found to prefer parameter values in which its cosmological parameter, the present void fraction, is driven to |$f_{\mathrm{v}0}\rightarrow 0.73$| and closely matches values that best fit independent cosmological data sets: supernovae Ia distances and the cosmic microwave background. This conclusion holds for a large range of seed values |$f_{\mathrm{v}0}\in \lbrace 0.1,0.9\rbrace$|⁠ , and for timescape fits to both timescape and FLRW mocks. Regardless of cosmology, unphysical estimates of the distance ratios given from power-law lens models result in poor goodness of fit. With larger data sets soon available, separation of cosmology and lens models must be addressed. [ABSTRACT FROM AUTHOR]

Accurately estimating the effective reproduction number (Rt) of a circulating pathogen is a fundamental challenge in the study of infectious disease. The fields of epidemiology and pathogen phylodynamics both share this goal, but to date, methodologies and data employed by each remain largely distinct. Here we present EpiFusion: a joint approach that can be used to harness the complementary strengths of each field to improve estimation of outbreak dynamics for large and poorly sampled epidemics, such as arboviral or respiratory virus outbreaks, and validate it for retrospective analysis. We propose a model of Rt that estimates outbreak trajectories conditional upon both phylodynamic (time-scaled trees estimated from genetic sequences) and epidemiological (case incidence) data. We simulate stochastic outbreak trajectories that are weighted according to epidemiological and phylodynamic observation models and fit using particle Markov Chain Monte Carlo. To assess performance, we test EpiFusion on simulated outbreaks in which transmission and/or surveillance rapidly changes and find that using EpiFusion to combine epidemiological and phylodynamic data maintains accuracy and increases certainty in trajectory and Rt estimates, compared to when each data type is used alone. We benchmark EpiFusion's performance against existing methods to estimate Rt and demonstrate advances in speed and accuracy. Importantly, our approach scales efficiently with dataset size. Finally, we apply our model to estimate Rt during the 2014 Ebola outbreak in Sierra Leone. EpiFusion is designed to accommodate future extensions that will improve its utility, such as explicitly modelling population structure, accommodations for phylogenetic uncertainty, and the ability to weight the contributions of genomic or case incidence to the inference. Author summary: Understanding infectious disease spread is fundamental to protecting public health, but can be challenging as disease spread is a phenomenon that cannot be directly observed. So, epidemiologists use data in conjunction with mathematical models to estimate disease dynamics. Often, combinations of different models and data can be used to answer the same questions–for example 'traditional' epidemiology commonly uses case incidence data (the number of people who have tested positive for a disease during a certain time period) whereas phylodynamic models use pathogen genomic sequence data and our knowledge of the way their genomes evolve to model disease population dynamics. Each of these approaches have strengths and limitations, and data of each type can be sparse or biased, particularly during rapidly developing outbreaks or in countries with poor pathogen surveillance. An increasing number of approaches attempt to fix this problem by incorporating diverse concepts and data types together in their models. We aim to contribute to this movement by introducing EpiFusion, a modelling framework that improves the efficiency and precision at which we can monitor important changes in pathogen transmission (specifically, in the effective reproduction number). EpiFusion uses particle filtering to simulate epidemic trajectories over time and weight their likelihood according to both case incidence data and a phylogenetic tree using separate observation models, resulting in the inference of trajectories in agreement with both sets of data. Improvements in our ability to accurately and confidently model pathogen spread help us to respond to infectious disease outbreaks and improve public health. [ABSTRACT FROM AUTHOR]

Q‐matrices are crucial components of cognitive diagnosis models (CDMs), which are used to provide diagnostic information and classify examinees according to their attribute profiles. The absence of an appropriate Q‐matrix that correctly reflects item‐attribute relationships often limits the widespread use of CDMs. Rather than relying on expert judgment for specification and post‐hoc methods for validation, there has been a notable shift towards Q‐matrix estimation by adopting Bayesian methods. Nevertheless, their dependency on Markov chain Monte Carlo (MCMC) estimation requires substantial computational burdens and their exploratory tendency is unscalable to large‐scale settings. As a scalable and efficient alternative, this study introduces the partially confirmatory framework within a saturated CDM, where the Q‐matrix can be partially defined by experts and partially inferred from data. To address the dual needs of accuracy and efficiency, the proposed framework accommodates two estimation algorithms—an MCMC algorithm and a Variational Bayesian Expectation Maximization (VBEM) algorithm. This dual‐channel approach extends the model's applicability across a variety of settings. Based on simulated and real data, the proposed framework demonstrated its robustness in Q‐matrix inference. [ABSTRACT FROM AUTHOR]

AbstractMultivariate probit models have been popularly utilized to analysis multivariate ordinal data. However, the identifiable multivariate probit models entail the covariance matrix for the underlying multivariate normal variables to be a correlation matrix, which brings a rigorous task to conduct efficient statistical analysis. Parameter expansion to make the identifiable model to be non-identifiable has been inevitably explored. However, the effect of the expanded parameters on the convergence of Markov chain Monte Carlo (MCMC) is seldomly investigated; in addition, the comparison of MCMC developed based on the identifiable model and that based on the non-identifiable model is hardly ever explored, especially for data with large sample sizes. In this paper, we conduct a thorough investigation to illustrate the effect of the expanded parameters on the convergence of MCMC and compare the behavior of MCMC between the identifiable and non-identifiable models. Our investigation provides a practical guide regarding the construction of non-identifiable models and development of corresponding MCMC sampling methods. We conduct our investigation using simulation studies and present an application using data from the Russia Longitudinal Monitoring Survey-Higher School of Economics (RLMS-HSE) study. [ABSTRACT FROM AUTHOR]

AbstractThis paper concerns the generation of random numbers from weighted distribution whose probability density function is of the form g(x)∝w(x)f(x) where f(x) is a valid probability density function and w(x)>0 is a weight function defined on the support of f(x). In particular for size-biased distributions and the Esscher transform, some boundedness conditions on f(x) are discussed for direct application of the rejection method. Several examples are given for the purpose of illustrating the proposed algorithms. [ABSTRACT FROM AUTHOR]

ABSTRACT Fretting fatigue is a common engineering failure phenomenon, often resulting in a shorter lifespan compared to plain fatigue. To consider the interaction between different scales, this study proposes a fully coupled two‐scale model based on continuum damage mechanics (CDM) and the crystal plastic finite element method (CPFEM) for the fretting fatigue crack initiation. Furthermore, the life data series are generated by employing feature engineering and long short‐term memory (LSTM) networks optimized with a genetic algorithm, ensuring the minimization of redundancy. Additionally, the genetic algorithm, enhanced by the Markov chain Monte Carlo method, was used to optimize the hyperparameters of the LSTM network. Simulation results indicate that the two‐scale model offers improved accuracy in predicting crack initiation life and provides physical information of crack initiation from different scales simultaneously. [ABSTRACT FROM AUTHOR]

The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log‐log scale. Nevertheless, there have been criticisms of the power law, for example, that a threshold needs to be preselected without its uncertainty quantified, that the power law is simply inadequate, and that subsequent hypothesis tests are required to determine whether the data could have come from the power law. We propose a modeling framework that combines two different generalizations of the power law, namely the generalized Pareto distribution and the Zipf‐polylog distribution, to resolve these issues. The proposed mixture distributions are shown to fit the data well and quantify the threshold uncertainty in a natural way. A model selection step embedded in the Bayesian inference algorithm further answers the question whether the power law is adequate. [ABSTRACT FROM AUTHOR]

In this work, we present classical and Bayesian inferential methods based on samples in the presence of progressive type-II censoring under the Very Flexible Weibull (VFW) distribution. The considered distribution is relevant because it is an alternative to traditional non-flexible distributions and also to some flexible distributions already known in the literature, keeping the low amount of two parameters. In addition, studying it in a context of progressive censoring allows attesting to its applicability in data modeling from various areas of industry and technology that can use this censoring methodology. We obtain the maximum likelihood estimators of the model parameters, as well as their asymptotic variation measures. We propose the use of Markov chain Monte Carlo methods for the computation of Bayes estimates. A simulation study is carried out to evaluate the performance of the proposed estimators under different sample sizes and progressive type-II censoring schemes. Finally, the methodology is illustrated through three real data sets. [ABSTRACT FROM AUTHOR]

We study estimation on parameter-driven models for time series of counts. This class of models follows the structure of a generalized linear model in which the serial dependency is included in the model by the link function through a time-dependent latent process. The likelihood function for this class of models commonly cannot be calculated explicitly and computationally intensive methods like importance sampling and Markov chain Monte Carlo are used to estimate the model parameters. Here, we propose a simple and fast estimation procedure in a wide class of models that accommodate both discrete and continuous data. The maximum likelihood methodology is used to obtain the parameter estimates for the models under study. The simplicity of the procedure allows for build bootstrap confidence intervals for the hyperparameters and latent states of parameter-driven models. We perform extensive simulation studies to verify the asymptotic behavior of the parameter estimates, as well as present application of the proposed procedure through set of real data. [ABSTRACT FROM AUTHOR]

With the rapid development of animal phenomics and deep phenotyping, we can obtain thousands of traditional (but also molecular) phenotypes per individual. However, there is still a lack of exploration regarding how to handle this huge amount of data in the context of animal breeding, presenting a challenge that we are likely to encounter more and more in the future. This study aimed to (1) explore the use of the mega-scale linear mixed model (MegaLMM), a factor model-based approach that is able to simultaneously estimate (co)variance components and genetic parameters in the context of thousands of milk traits, hereafter called thousand-trait (TT) models; (2) compare the phenotype values and genomic breeding value (u) predictions for focal traits (i.e., traits that are targeted for prediction, compared with secondary traits that are helping to evaluate), from single-trait (ST) and TT models, respectively; (3) propose a new approximate method of GEBV (U) prediction with TT models and MegaLMM. We used a total of 3,421 milk mid-infrared (MIR) spectra wavepoints (called secondary traits) and 3 focal traits (average fat percentage [AFP], average methane production [ACH4], and average SCS [ASCS]) collected on 3,302 first-parity Holstein cows. The 3,421 milk MIR wavepoint traits were composed of 311 wavepoints in 11 classes (months in lactation). Genotyping information of 564,439 SNPs was available for all animals and was used to calculate the genomic relationship matrix. The MegaLMM was implemented in the framework of the Bayesian sparse factor model and solved through Gibbs sampling (Markov chain Monte Carlo). The heritabilities of the studied 3,421 milk MIR wavepoints gradually increased and then decreased in units of 311 wavepoints throughout the lactation. The genetic and phenotypic correlations between the first 311 wavepoints and the other 3,110 wavepoints were low. The accuracies of phenotype predictions from the ST model were lower than those from the TT model for AFP (0.51 vs. 0.93), ACH4 (0.30 vs. 0.86), and ASCS (0.14 vs. 0.33). The same trend was observed for the accuracies of u predictions for AFP (0.59 vs. 0.86), ACH4 (0.47 vs. 0.78), and ASCS (0.39 vs. 0.59). The average correlation between U predicted from the TT model and the new approximate method was 0.90. The new approximate method used for estimating U in MegaLMM will enhance the suitability of MegaLMM for applications in animal breeding. This study conducted an initial investigation into the application of thousands of traits in animal breeding and showed that the TT model is beneficial for the prediction of focal traits (phenotype and breeding values), especially for difficult-to-measure traits (e.g., ACH4). The list of standard abbreviations for JDS is available at adsa.org/jds-abbreviations-24. Nonstandard abbreviations are available in the Notes. [Display omitted] [ABSTRACT FROM AUTHOR]

We propose a new method for real-time uncertainty monitoring of earthquake and volcano source models using data from the global navigation satellite system (GNSS) and explore its application concerning observation station placement. The Geospatial Information Authority of Japan operates two main types of GNSS earth observation network system (GEONET) coordinates for crustal deformation monitoring on different time scales: post-processing analysis values and real-time GEONET analysis system for rapid deformation monitoring (REGARD). REGARD uses the Markov Chain Monte Carlo (MCMC) method termed real-time automatic uncertainty estimation of a coseismic single rectangular model using GNSS data (RUNE) for single rectangular fault model estimation to handle uncertainty. Thus far, no GNSS monitoring system can automatically detect transient crustal deformation events, such as volcanic activity and earthquake swarms, on timescales of a day or less. We extended RUNE and developed a core program for a new monitoring system for earthquake and volcanic source models and their uncertainties. Our program achieved automatic and stable MCMC utilization for rectangular fault, dike, Mogi, and spheroid models by increasing the computational speed, improving search efficiency, and adjusting hyperparameters. The program automatically determines the standard deviation of the likelihood function assuming a normal distribution with weights for each observation station. The calculation time was within 15 s for 1 × 106 samples on a standard 1U server. We assessed the reliability of the developed method using synthetic and observed GNSS data from the 2015 Sakurajima volcanic event. The results were consistent with the assumed model and previous studies and indicated an advantage in automatically quantifying uncertainty in a short computation time. Based on MCMC samples, we developed a new visualization algorithm to indicate areas on a map in which the number of observation stations should be expanded. We assessed the reliability using data from the 2023 Noto Peninsula earthquake [Mj 6.5]. The results indicate that the algorithm is helpful in studying the placement of stations. The above model extensions and their application are essential to achieve a rapid quantitative understanding of disaster events near urban areas and for utilizing this information in emergency response activities. [ABSTRACT FROM AUTHOR]

The field load test is a direct and effective method for evaluating the performance of bridge structures. However, existing bridge field static load tests are costly and inefficient; moreover, they obstruct traffic and cause unavoidable damage to the bridge structure. As an alternative the the static load test, a random model update method based on bridge dynamic load tests and the Bayesian inference is proposed in this paper. The bridge static load test results were predicted with a high accuracy. To speed up the Bayesian method to infer the posterior probability density of the updated parameters, the Gaussian process was used in place of the finite element model, and the Bayesian inference used the Markov chain Monte Carlo method based on the delayed rejection adaptive Metropolis algorithm. First, the parameters to be modified 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 research results reveal that the prediction results of the bridge static load test based on the dynamic load test and Bayesian inference method agree with the actual test results. [ABSTRACT FROM AUTHOR]

The traditional factor analysis model assumes that the factors obey a normal distribution, which is not appropriate in fields whose data are nonnegative. For this kind of problem, we construct a more practical factor model, assuming that the factors obey a Gamma distribution. We develop a new factor analysis model and discuss its true loading matrix. Then we study its parameter estimation with the maximum likelihood estimation (MLE) method based on an Expectation-Maximization (EM) algorithm, where step E is realized by the Metropolis-Hastings (M-H) algorithm in the Markov Chain Monte Carlo (MCMC) method. We use the new model to empirically study real data, and evaluate its information extraction ability, using the defined true loading matrix to calculate the true loading of the factor. We compare the new model and traditional factor analysis models on simulated and real data, respectively, whose results show that the new model has better information extraction ability for nonnegative data when the number of factors is the same. [ABSTRACT FROM AUTHOR]

The step‐stress procedure is a popular accelerated test used to analyze the lifetime of highly reliable components. This paper considers a simple step‐stress accelerated test assuming a cumulative exposure model with uncensored lifetime data following a Weibull distribution. The maximum likelihood approach is often used to analyze accelerated stress test data. Another approach is to use the Bayesian inference, which is useful when there is limited data available. In this paper, the parameters of the model are estimated based on the objective Bayesian viewpoint using non‐informative priors. Our main aim is to propose the maximal data information prior (MDIP) presented by Zellner (1984) as an alternative prior to the conventional independent gamma priors for the unknown parameters, in situations where there is little or no a priori knowledge about the parameters. We also obtain the Bayes estimators based on both classes of priors, assuming three different loss functions: square error loss function (SELF), linear‐exponential loss function (LINEX), and generalized entropy loss function (GELF). The proposed MDIP prior is compared with the gamma priors via Monte Carlo simulations by examining their biases and mean square errors under the three loss functions, and coverage probability. Additionally, we employ the Markov Chain Monte Carlo (MCMC) algorithm to extract characteristics of marginal posterior distributions, such as the Bayes estimator and credible intervals. Finally, a real lifetime data is presented to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

In this study, we define a series system with n$n$ non‐independent and non‐identical components using a shock model with n+1$n+1$ sources of fatal shocks. Here, it is assumed that the shocks happen randomly and independently, following a Weibull distribution with various scale and shape parameters. A dependability model with 2(n+1)$2(n+1)$ unknown parameters is produced by this process. Making statistical conclusions about the model parameters is the main objective of this research. We apply the maximum likelihood and Bayes approaches to determine the model parameters' point and interval estimates. We shall demonstrate that no analytical solutions to the likelihood equations must be solved to obtain the parameters' maximum likelihood estimates. As a result, we will use the R program to approximate the parameter point and interval estimates. Additionally, we will use the bootstrap‐t and bootstrap‐p methods to approximate the confidence intervals. About the Bayesian approach, we presume that each model parameter is independent and follows a gamma prior distribution with a range of attached hyperparameter values. The model parameters' posterior distribution does not take a practical form. We are unable to derive the Bayes estimates in closed forms as a result. To solve this issue, we use the Gibbs sampler from the Metropolis‐Hasting algorithm based on the Markov chain Monte Carlo method to condense the posterior distribution. To demonstrate the relevance of this research, a real data set application is detailed. [ABSTRACT FROM AUTHOR]

In evaluating the safety of rock slopes engineering, it is imperative to account for rheological effects. These effects can lead to significant deformations that may adversely impact the overall structural integrity. Consequently, accurate determination of the rheological mechanical parameters of slope rocks is essential. However, the application of rheological parameters obtained from laboratory tests encounters limitations due to the rock's inherent heterogeneity, scale effects, and inevitable sample dispersion. By contrast, on-site monitoring data serve as critical assets for real-time calibration and risk assessment in the evaluation of rheological parameters and prediction of slope deformation. To integrate on-site monitoring data with rheological mechanical mechanisms, this study introduces a probabilistic inverse model for evaluating rock slope rheological parameters, grounded in Bayesian theory, and incorporating a No-U-Turn Sampler (NUTS) based on Markov Chain Monte Carlo (MCMC) sampling algorithm. In terms of methodological efficiency, we compared the NUTS method with the traditional Metropolis–Hastings (M-H) approach, demonstrating the superior efficiency of the former. Additionally, sensitivity analysis of rheological parameters was conducted using the Burgers constitutive model. By combining the NUTS-based MCMC method with this model, the uncertainty of creep parameters was successfully evaluated. Utilizing these updated posterior parameters, up to 3-year deformation forecast for the slope was executed, the findings demonstrate that the deformation on the left bank slope is slight, indicating a state of safety. This study integrates monitoring data with rheological mechanics to establish a physical-data-driven rheological safety assessment mechanism. It offers a scientifically robust and effective approach for the uncertainty evaluation of rheological parameters and deformation prediction, providing significant support for the safety assessment of the left bank slope of the Baihetan hydropower station, China. [ABSTRACT FROM AUTHOR]

Fractional data suffering from large proportion of values at boundaries are very common in the social and economic surveys. Existing literature usually separates the whole data into three parts and specifies a three-part regression model to them. In this article, we develop an attractive two-part latent variable model for fractional data. The separated three parts are synthesized into two parts to characterize the association among the whole data. Moveover, latent variables are incorporated into the data analysis to interpret extra heterogeneity and item-dependence. We also include a structural equation to explore the interrelationships among the multiple factors. To downweight the influence of the distributional deviations and/or outliers, we develop a semiparametric Bayesian analysis procedure. Parameter estimation and model assessment are obtained via Markov Chain Monte Carlo sampling method. A real example pertaining to the cocaine use is presented to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Seismic fragility models provide a probabilistic relation between ground-motion intensity and damage, making them a crucial component of many regional risk assessments. Estimating such models from damage data gathered after past earthquakes is challenging because of uncertainty in the ground-motion intensity the structures were subjected to. Here, we develop a Bayesian estimation procedure that performs joint inference over ground-motion intensity and fragility model parameters. When applied to simulated damage data, the proposed method can recover the data-generating fragility functions, while the traditionally used method, employing fixed, best-estimate, intensity values, fails to do so. Analyses using synthetic data with known properties show that the traditional method results in flatter fragility functions that overestimate damage probabilities for low-intensity values and underestimate probabilities for large values. Similar trends are observed when comparing both methods on real damage data. The results suggest that neglecting ground-motion uncertainty manifests in apparent dispersion in the estimated fragility functions. This undesirable feature can be mitigated through the proposed Bayesian procedure. [ABSTRACT FROM AUTHOR]

AbstractWe present parametric and semiparametric latent Markov time-interaction processes, that are point processes where the occurrence of an event can increase or reduce the probability of future events. We first present time-interaction processes with parametric and nonparametric baselines, then we let model parameters be modulated by a discrete state continuous time latent Markov process. Posterior inference is based on a novel and efficient data augmentation approach in the Markov Chain Monte Carlo framework. We illustrate with a simulation study; and an original application to terrorist attacks in Europe in the period 2001-2017, where we find two distinct latent clusters for the hazard of occurrence of terrorist events, negative association with GDP growth, and self-exciting phenomena. [ABSTRACT FROM AUTHOR]

Data integration, the joint statistical analysis of data from different observation platforms, is pivotal for data‐hungry disciplines such as spatial ecology. Pooled data types obtained from the same underlying process, analyzed jointly, can improve both precision and accuracy in models of species distributions and species–habitat associations. However, the integration of telemetry and spatial survey data has proved elusive because of the fundamentally different analytical approaches required by these two data types. Here, “spatial survey” denotes a survey that records spatial locations and has no temporal structure, for example, line or point transects but not capture–recapture or telemetry. Step selection functions (SSFs—the canonical framework for telemetry) and habitat selection functions (HSFs—the default approach to spatial surveys) differ in not only their specifications but also their results. By imposing the constraint that microscopic mechanisms (animal movement) must correctly scale up to macroscopic emergence (population distributions), a relationship can be written between SSFs and HSFs, leading to a joint likelihood using both datasets. We implement this approach using maximum likelihood, explore its estimation precision by systematic simulation, and seek to derive broad guidelines for effort allocation in the field. We find that complementarities in spatial coverage and resolution between telemetry and survey data often lead to marked inferential improvements in joint analyses over those using either data type alone. The optimal allocation of effort between the two methods (or the choice between them, if only one can be selected) depends on the overall effort expended and the pattern of environmental heterogeneity. Examining inferential performance over a broad range of scenarios for the relative cost between the two methods, we find that integrated analysis usually offers higher precision. Our methodological work shows how to integrate the analysis of telemetry and spatial survey data under a novel joint likelihood function, using traditional computational methods. Our simulation experiments suggest that even when the relative costs of the two methods favor the deployment of one field approach over another, their joint use is broadly preferable. Therefore, joint analysis of the two key methods used in spatial ecology is not only possible but also computationally efficient and statistically more powerful. [ABSTRACT FROM AUTHOR]

ABSTRACT This study proposes a heterogeneous mediation analysis for survival data that accommodates multiple mediators and sparsity of the predictors. We introduce a joint modeling approach that links the mediation regression and proportional hazards models through Bayesian additive regression trees with shared typologies. The shared tree component is motivated by the fact that confounders and effect modifiers on the causal pathways linked by different mediators often overlap. A sparsity‐inducing prior is incorporated to capture the most relevant confounders and effect modifiers on different causal pathways. The individual‐specific interventional direct and indirect effects are derived on the scale of the logarithm of hazards and survival function. A Bayesian approach with an efficient Markov chain Monte Carlo algorithm is developed to estimate the conditional interventional effects through the Monte Carlo implementation of the mediation formula. Simulation studies are conducted to verify the empirical performance of the proposed method. An application to the ACTG175 study further demonstrates the method's utility in causal discovery and heterogeneity quantification. [ABSTRACT FROM AUTHOR]

Modelling complex line emission in the interstellar medium (ISM) is a degenerate high-dimensional problem. Here, we present McFine , a tool for automated multicomponent fitting of emission lines with complex hyperfine structure, in a fully automated way. We use Markov chain Monte Carlo (MCMC) to efficiently explore the complex parameter space, allowing for characterizing model denegeracies. This tool allows for both local thermodynamic equilibrium (LTE) and radiative-transfer (RT) models. McFine can fit individual spectra and data cubes, and for cubes encourage spatial coherence between neighbouring pixels. It is also built to fit the minimum number of distinct components, to avoid overfitting. We have carried out tests on synthetic spectra, where in around 90 per cent of cases it fits the correct number of components, otherwise slightly fewer components. Typically, |$T_{\rm ex}$| is overestimated and |$\tau$| underestimated, but accurate within the estimated uncertainties. The velocity and line widths are recovered with extremely high accuracy, however. We verify McFine by applying to a large Atacama Large Millimeter/submillimeter Array (ALMA) N |$_2$| H |$^+$| mosaic of an high-mass star forming region, G316.75−00.00. We find a similar quality of fit to our synthetic tests, aside from in the active regions forming O-stars, where the assumptions of Gaussian line profiles or LTE may break down. To show the general applicability of this code, we fit CO(J = 2-1) observations of NGC 3627, a nearby star-forming galaxy, again obtaining excellent fit quality. McFine provides a fully automated way to analyse rich data sets from interferometric observations, is open source, and pip -installable. [ABSTRACT FROM AUTHOR]

Introduction: Bayesian approaches to patient phenotyping in clinical observational studies have been limited by the computational challenges associated with applying the Markov Chain Monte Carlo (MCMC) approach to real-world data. Approximate Bayesian inference via optimization of the variational evidence lower bound, variational Bayes (VB), has been successfully demonstrated for other applications. Methods: We investigate the performance and characteristics of currently available VB and MCMC software to explore the practicability of available approaches and provide guidance for clinical practitioners. Two case studies are used to fully explore the methods covering a variety of real-world data. First, we use the publicly available Pima Indian diabetes data to comprehensively compare VB implementations of logistic regression. Second, a large real-world data set, Optum™ EHR with approximately one million diabetes patients extended the analysis to large, highly unbalanced data containing discrete and continuous variables. A Bayesian patient phenotyping composite model incorporating latent class analysis (LCA) and regression was implemented with the second case study. Results: We find that several data characteristics common in clinical data, such as sparsity, significantly affect the posterior accuracy of automatic VB methods compared with conditionally conjugate mean-field methods. We find that for both models, automatic VB approaches require more effort and technical knowledge to set up for accurate posterior estimation and are very sensitive to stopping time compared with closed-form VB methods. Discussion: Our results indicate that the patient phenotyping composite Bayes model is more easily usable for real-world studies if Monte Carlo is replaced with VB. It can potentially become a uniquely useful tool for decision support, especially for rare diseases where gold-standard biomarker data are sparse but prior knowledge can be used to assist model diagnosis and may suggest when biomarker tests are warranted. [ABSTRACT FROM AUTHOR]

AbstractThe configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network’s structure can be explained by its degree structure alone. A Markov chain Monte Carlo (MCMC) algorithm, based on a degree-preserving double-edge swap, provides an asymptotic solution to sample from the configuration model. However, accurately and efficiently detecting when this Markov chain is sufficiently close to its stationary distribution remains an unsolved problem. Here, we provide a solution to sample from the configuration model using this standard MCMC algorithm. We develop an algorithm, based on the assortativity of the sampled graphs, for estimating the gap between effectively independent MCMC states, and a computationally efficient gap-estimation heuristic derived from analyzing a corpus of 509 empirical networks. We provide a convergence detection method based on the Dickey-Fuller Generalized Least Squares test, which we show is more accurate and efficient than three alternative Markov chain convergence tests. Supplementary materials for the proposed methods can be found here. [ABSTRACT FROM AUTHOR]

In this paper, we have explored a transitioning cosmic model, depicting late-time accelerated expansion in the f(R,Tϕ) theory of gravity for an isotropic and homogeneous universe, where the trace of the energy–momentum tensor Tϕ is the function of the self-interacting scalar field ϕ. We have proposed an explicit solution to the derived model by utilizing a scale factor of the hybrid form a(t)=tαeβt, where α and β are constants. To estimate the best-fit values of model parameters, statistical analysis based on the Markov Chain Monte Carlo (MCMC) method has been employed on 57 H(z) points in the range 0.07≤z≤2.36 and Pantheon Sample consisting of a total of 1048 SNe Ia in the range of 0.01

ABSTRACT We propose a semiparametric approach to Bayesian modeling of dynamic treatment regimes that is built on a Bayesian likelihood‐based regression estimation framework. Methods based on this framework exhibit a probabilistic coherence property that leads to accurate estimation of the optimal dynamic treatment regime. Unlike most Bayesian estimation methods, our proposed method avoids strong distributional assumptions for the intermediate and final outcomes by utilizing empirical likelihoods. Our proposed method allows for either linear, or more flexible forms of mean functions for the stagewise outcomes. A variational Bayes approximation is used for computation to avoid common pitfalls associated with Markov Chain Monte Carlo approaches coupled with empirical likelihood. Through simulations and analysis of the STAR*D sequential randomized trial data, our proposed method demonstrates superior accuracy over Q‐learning and parametric Bayesian likelihood‐based regression estimation, particularly when the parametric assumptions of regression error distributions may be potentially violated. [ABSTRACT FROM AUTHOR]

AbstractThe Transmutation Weibull distribution is derived from the quadratic rank transmutation map of the Weibull distribution. This distribution integrates the high adaptability of the Weibull distribution in engineering and materials fields, and has great potential utility for modeling lifetime data. Therefore, the article explores the progressive stress accelerated life test model for components under the Transmutation Weibull distribution, conducts statistical analysis using the maximum likelihood estimation (MLE), Lindley’s approximation, and Markov Chain Monte Carlo (MCMC) algorithm to provide approximate estimates for the model. Finally, by comparing the results of numerical simulations, it is confirmed that the Bayesian estimation is more accurate and effective. [ABSTRACT FROM AUTHOR]

Dengue is a vector-borne disease transmitted to humans by vectors of genus Aedes causing a global threat to health, social, and economic sectors in many of the tropical countries including Sri Lanka. In Sri Lanka, the tropical climate, marked by seasonal weather primarily influenced by monsoons, fosters optimal conditions for the virus to spread efficiently. This heightened transmission results in increased per-capita vector density. In this work, we investigate the dynamic influence of environmental conditions on dengue emergence in Colombo district − the geographical region with the highest recorded dengue threat in Sri Lanka. An iterative approach is employed to dynamically estimate dengue cases leveraging the Markov chain Monte Carlo simulations, utilizing the dynamics of four seasons per year influenced by monsoon weather patterns governing in the region. The developed algorithm allows to estimate the risk of dengue outbreaks in 2017 and 2019 with high precision, facilitating accurate forecasts of upcoming disease emergence patterns for better preparedness. The uncertainty quantification not only validated the accuracy of outbreak estimates but also showcased the model's capacity to capture extreme cases and revealed undisclosed external factors such as human mobility and environmental pollution that might affect dengue transmission in the Colombo district of Sri Lanka. [ABSTRACT FROM AUTHOR]

The recent COVID-19 pandemic has thrown the importance of accurately forecasting contagion dynamics and learning infection parameters into sharp focus. At the same time, effective policy-making requires knowledge of the uncertainty on such predictions, in order, for instance, to be able to ready hospitals and intensive care units for a worst-case scenario without needlessly wasting resources. In this work, we apply a novel and powerful computational method to the problem of learning probability densities on contagion parameters and providing uncertainty quantification for pandemic projections. Using a neural network, we calibrate an ODE model to data of the spread of COVID-19 in Berlin in 2020, achieving both a significantly more accurate calibration and prediction than Markov-Chain Monte Carlo (MCMC)-based sampling schemes. The uncertainties on our predictions provide meaningful confidence intervals e.g. on infection figures and hospitalisation rates, while training and running the neural scheme takes minutes where MCMC takes hours. We show convergence of our method to the true posterior on a simplified SIR model of epidemics, and also demonstrate our method's learning capabilities on a reduced dataset, where a complex model is learned from a small number of compartments for which data is available. [ABSTRACT FROM AUTHOR]

In order to consider the impact of source-load uncertainty on traditional power system planning methods, a medium- and long-term optimization planning method based on source-load uncertainty modeling and time-series production simulation is proposed. First, a new energy output probability model is developed using non-parametric kernel density estimation, and the spatial correlation of the new energy output is described using pair-copula theory to model the uncertainty analysis of the new energy output. Secondly, a large number of source-load scenarios are generated using the Markov chain Monte Carlo simulation method, and the optimal selection method for discrete state numbers is provided, and then the scenario reduction is carried out using the fast forward elimination technology. Finally, the typical time-series curves of the source-load uncertainty characteristics obtained are incorporated into the optimization planning method together with various flexible resources, such as the demand-side response and energy storage, and the rationality of the planning scheme is judged and optimized based on key indicators such as the cost, wind–light abandonment rate, and loss-of-load rate. Based on the above methods, this paper offers an example of the power supply planning scheme for a certain region in the next 30 years, providing effective guidance for the development of new energy in the region. [ABSTRACT FROM AUTHOR]

AbstractThe Additive Voronoi Tessellations (AddiVortes) model is a multivariate regression model that uses Voronoi tessellations to partition the covariate space in an additive ensemble model. Unlike other partition methods, such as decision trees, this has the benefit of allowing the boundaries of the partitions to be non-orthogonal and non-parallel to the covariate axes. The AddiVortes model uses a similar sum-of-tessellations approach and a Bayesian backfitting MCMC algorithm to the BART model. We utilize regularization priors to limit the strength of individual tessellations and accepts new models based on a likelihood. The performance of the AddiVortes model is illustrated through testing on several data sets and comparing the performance to other models along with a simulation study to verify some of the properties of the model. In many cases, the AddiVortes model outperforms random forests, BART and other leading black-box regression models when compared using a range of metrics. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Void number count (VNC) indicates the number of low-density regions in the large-scale structure (LSS) of the Universe, and we propose to use it as an effective cosmological probe. By generating the galaxy mock catalogue based on Jiutian simulations and considering the spectroscopic survey strategy and instrumental design of the China Space Station Telescope (CSST), which can reach a magnitude limit |$\sim$| 23 AB mag and spectral resolution |$R\gtrsim 200$| with a sky coverage of 17 500 deg2, we identify voids using the watershed algorithm without any assumption of void shape and obtain the mock void catalogue and data of the VNC in six redshift bins from |$z=0.3$| to 1.3. We use the Markov chain Monte Carlo method to constrain the cosmological and VNC parameters. The void linear underdensity threshold |$\delta _{\rm v}$| in the theoretical model is set to be a free parameter at a given redshift to fit the VNC data and explore their redshift evolution. We find that the VNC can correctly derive the cosmological information, and the constraint strength on the cosmological parameters is comparable to that from the void size function method, which can reach a few per cent level in the CSST full spectroscopic survey. This is because, since the VNC is not sensitive to void shape, the modified theoretical model can match the data better by integrating over void features, and more voids could be included in the VNC analysis by applying simpler selection criteria, which will improve the statistical significance. It indicates that the VNC can be an effective cosmological probe for exploring the LSS. [ABSTRACT FROM AUTHOR]

Heartbeat stars (HBSs) are ideal astrophysical laboratories to study the formation and evolution of binary stars in eccentric orbits and the internal structural changes of their components under strong tidal action. We discover 23 new HBSs based on TESS photometric data. The orbital parameters, including orbital period, eccentricity, orbital inclination, argument of periastron, and epoch of periastron passage of these HBSs, are derived by using a corrected version of Kumar et al.'s model based on the Markov Chain Monte Carlo (MCMC) method. The preliminary results show that these HBSs have orbital periods in the range from 2.7 to 20 d and eccentricities in the range from 0.08 to 0.70. The eccentricity-period relation of these objects shows a positive correlation between eccentricity and period and also shows the existence of orbital circularization. The Hertzsprung–Russell diagram shows that the HBSs are not all located in a particular area. The distribution of the derived parameters suggests a selection bias within the TESS survey towards HBSs with shorter periods. These objects are a very useful source to study the structure and evolution of eccentricity orbit binaries and to extend the TESS HBS catalog. [ABSTRACT FROM AUTHOR]

Multi-state transition model is typically used to analyze longitudinal data in medicine and sociology. Moreover, variables in longitudinal studies usually are error-prone, and random effects are heterogeneous, which will result in biased estimates of the interest parameters. This article is intended to estimate the parameters of the multi-state transition model for longitudinal data with measurement error and heterogeneous random effects and further consider the covariate related to the covariance matrix of random effects is also error-prone when the covariate in the transition model is error-prone. We model the covariance matrix of random effects through the modified Cholesky decomposition and propose a pseudo-likelihood method based on the Monte Carlo expectation-maximization algorithm and the Bayesian method based on Markov Chain Monte Carlo to infer and calculate the whole estimates. Meanwhile, we obtain the asymptotic properties and evaluate the finite sample performance of the proposed method by simulation, which is well in terms of Bias, RMSE, and coverage rate of confidence intervals. In addition, we apply the proposed method to the MFUS data. [ABSTRACT FROM AUTHOR]

The diagnosis of medical conditions and subsequent treatment often involves radionuclide imaging techniques. To refine localisation accuracy and improve diagnostic confidence, compared with the use of a single scanning technique, a combination of two (or more) techniques can be used but with a higher risk of misalignment. For this to be reliable and accurate, recorded data undergo processing to suppress noise and enhance resolution. A step in image processing techniques for such inverse problems is the inclusion of smoothing. Standard approaches, however, are usually limited to applying identical models globally. In this study, we propose a novel Laplace and Gaussian mixture prior distribution that incorporates different smoothing strategies with the automatic model-based estimation of mixture component weightings creating a locally adaptive model. A fully Bayesian approach is presented using multi-level hierarchical modelling and Markov chain Monte Carlo (MCMC) estimation methods to sample from the posterior distribution and hence perform estimation. The proposed methods are assessed using simulated γ-eye™ camera images and demonstrate greater noise reduction than existing methods but without compromising resolution. As well as image estimates, the MCMC methods also provide posterior variance estimates and hence uncertainty quantification takes into consideration any potential sources of variability. The use of mixture prior models, part Laplace random field and part Gaussian random field, within a Bayesian modelling approach is not limited to medical imaging applications but provides a more general framework for analysing other spatial inverse problems. Locally adaptive prior distributions provide a more realistic model, which leads to robust results and hence more reliable decision-making, especially in nuclear medicine. They can become a standard part of the toolkit of everyone working in image processing applications. [ABSTRACT FROM AUTHOR]

In order to reveal the destructive mechanism of loess landslide induced by stagnant water on the combined surface, and to clarify the influence of the main control factors, this paper takes a typical loess landslide in northern Shaanxi as the research object, analyzes the structure of the rock and soil body, and the excavation and filling construction through the geohazard survey, and analyzes the process of traction sliding caused by the stagnant water on the combined surface at the different stages of the project by combining with the calculation of the stability of the slope body. Further the article analyses the process of traction sliding caused by water on the combined area due to construction by means of a discrete element model, and delves into the mechanism of strength reduction of saturated loess. The results show that: 1) the combined surface stagnant water type loess landslide has the characteristics of sudden sliding and rapid evolution, which is highly hazardous and difficult to prevent and control; 2) the slope destabilization is controlled by the engineering geological conditions, and the slope excavation changes the original mechanical equilibrium conditions of the slope, which provides the dynamic conditions for the traction sliding of the slope; 3) the change of the hydrogeological environment results in the obstruction of the natural drainage channel, which leads to the formation of continuous sliding surface due to stagnant water on the combined surface, and the formation of a continuous sliding surface due to stagnant water on the combined surface. Surface stagnant water to form a continuous slippery surface, inducing the overall destabilization of the slope damage; 4) loess strength index with the increase of saturation and the exponential function form of reduction, and when the saturation degree reaches more than 80%, the strength index of the soil body to reach the basic stability. The article expanding the ideas of landslide control and analysis, and the research results will provide a theoretical basis for the design of junction landslide management in the loess areas of northern Shaanxi. [ABSTRACT FROM AUTHOR]

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs. Author summary: Polynomial neural ordinary differential equations (ODEs) are a recent approach for symbolic regression of dynamical systems governed by polynomials. However, they are limited in that they provide maximum likelihood point estimates of the model parameters. The domain expert using system identification often desires a specified level of confidence or range of parameter values that best fit the data. In this work, we use Bayesian inference to provide posterior probability distributions of the parameters in polynomial neural ODEs. To date, there are no studies that attempt to identify the best Bayesian inference method for neural ODEs and symbolic neural ODEs. To address this need, we explore and compare three different approaches for estimating the posterior distributions of weights and biases of the polynomial neural network: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. We have also developed lightweight JAX code to estimate posterior probability distributions using the Laplace approximation. [ABSTRACT FROM AUTHOR]

Bayesian analysis relies heavily on the Markov chain Monte Carlo (MCMC) algorithm to obtain random samples from posterior distributions. In this study, we compare the performance of MCMC stopping rules and provide a guideline for determining the termination point of the MCMC algorithm in latent variable models. In simulation studies, we examine the performance of four different MCMC stopping rules: potential scale reduction factor (PSRF), fixed‐width stopping rule, Geweke's diagnostic, and effective sample size. Specifically, we evaluate these stopping rules in the context of the DINA model and the bifactor item response theory model, two commonly used latent variable models in educational and psychological measurement. Our simulation study findings suggest that single‐chain approaches outperform multiple‐chain approaches in terms of item parameter accuracy. However, when it comes to person parameter estimates, the effect of stopping rules diminishes. We caution against relying solely on the univariate PSRF, which is the most popular method, as it may terminate the algorithm prematurely and produce biased item parameter estimates if the cut‐off value is not chosen carefully. Our research offers guidance to practitioners on choosing suitable stopping rules to improve the precision of the MCMC algorithm in models involving latent variables. [ABSTRACT FROM AUTHOR]

AbstractThis manuscript extensively reviews applications, extensions, and models derived from the Bayesian ideal point estimator. We focus our attention on studies conducted in the United States as well as Latin America. First, we provide a detailed description of the Bayesian ideal point estimator. Next, we propose a new taxonomy to synthesize and frame technical developments and applications associated with the estimator in the context of the United States Congress and Latin American governing bodies. The literature available in Latin America allows us to conclude that few legislatures in the region have been analyzed using the methodology under discussion. Also, we highlight those parliaments of Latin America embedded in democratic presidential systems as novel scenarios for operationalizing the electoral behavior of legislative bodies through nominal voting data. Our findings show some alternatives for future research. [ABSTRACT FROM AUTHOR]