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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]

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]

In this paper, we investigate the scalar field dark energy (DE) models within the context of F (T , T G) gravity. Scalar field models are known for their dynamic nature. Parameters in the dynamical equation of state are responsible for the acceleration of the cosmos in recent epochs. We determined that the power-law cosmology fits the OHD and Pantheon data nicely. Using the Bayesian analysis and likelihood function in conjunction with the Markov Chain Monte Carlo (MCMC) method, we examine the three sets of the model parameters H 0 = 6 3. 2 6 − 0. 9 7 + 0. 7 7 q = − 0. 0 3 9 0. 0 0 2 9 + 0. 0 0 2 9 obtained by 57 points of the H (z) data, H 0 = 7 0. 9 3 − 0. 0 0 3 7 + 0. 0 0 2 4 q = − 0. 3 3 8 4 0. 0 0 2 6 + 0. 0 0 2 7 1048 points of the Pantheon data and H 0 = 7 0. 7 6 7 3 2 − 0. 0 0 0 8 8 + 0. 0 0 3 0 q = − 0. 6 4 7 8 0. 0 0 7 5 + 0. 0 0 9 3 by using joint data (H (z) + BAO + Pantheon), respectively. We solved the modified Einstein's field equations by taking the bulk-viscosity component ξ = ξ 0 ρ α . We also establish a correspondence between the F (T , T G) gravity model and scalar field DE models such as quintessence, k -essence, and DBI-essence. The nature of scalar fields and their corresponding potentials are being graphically analyzed. To check the validity of F (T , T G) gravity model, we also analyze the behavior of energy conditions. [ABSTRACT FROM AUTHOR]

This paper explores inferences for a competing risk model with dependent causes of failure. When the lifetimes of competing risks are modelled by a Marshall–Olikin bivariate Kies distribution, classical and Bayesian estimations are studied under generalized progressive hybrid censoring. The existence and uniqueness results for maximum likelihood estimators of unknown parameters are established, whereas approximate confidence intervals are constructed using the observed Fisher information matrix. In addition, Bayes estimates are explored based on a flexible Gamma-Dirichlet prior information. Furthermore, when there is a priori order information on competing risk parameters being available, traditional classical likelihood and Bayesian estimates are also established under restricted parameter case. The behavior of the proposed estimators is evaluated through extensive simulation studies, and a real data study is presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

AbstractAsymptotic goodness-of-fit methods in contingency table analysis can struggle with sparse data, especially in multi-way tables where it can be infeasible to meet sample size requirements for a robust application of distributional assumptions. However, algebraic statistics provides exact alternatives to these classical asymptotic methods that remain viable even with sparse data. We apply these methods to a context in psychometrics and education research that leads naturally to multi-way contingency tables: the analysis of differential item functioning (DIF). We explain concretely how to apply the exact methods of algebraic statistics to DIF analysis using the R package algstat, and we compare their performance to that of classical asymptotic methods. [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]

Summary Bayesian mixture modelling is widely used for density estimation and clustering. The Dirichlet process mixture model (DPMM) is the most popular Bayesian non‐parametric mixture modelling approach. In this manuscript, we study the choice of prior for the variance or precision matrix when Gaussian kernels are adopted. Typically, in the relevant literature, the assessment of mixture models is done by considering observations in a space of only a handful of dimensions. Instead, we are concerned with more realistic problems of higher dimensionality, in a space of up to 20 dimensions. We observe that the choice of prior is increasingly important as the dimensionality of the problem increases. After identifying certain undesirable properties of standard priors in problems of higher dimensionality, we review and implement possible alternative priors. The most promising priors are identified, as well as other factors that affect the convergence of MCMC samplers. Our results show that the choice of prior is critical for deriving reliable posterior inferences. This manuscript offers a thorough overview and comparative investigation into possible priors, with detailed guidelines for their implementation. Although our work focuses on the use of the DPMM in clustering, it is also applicable to density estimation. [ABSTRACT FROM AUTHOR]

Enlightening our understanding of the first galaxies responsible for driving reionization requires detecting the 21-cm signal from neutral hydrogen. Interpreting the wealth of information embedded in this signal requires Bayesian inference. Parameter inference from the 21-cm signal is primarily restricted to the spherically averaged power spectrum (1D PS) owing to its relatively straightforward derivation of an analytic likelihood function enabling traditional Monte Carlo Markov Chain approaches. However, in recent years, simulation-based inference (SBI) has become feasible which removes the necessity of having an analytic likelihood, enabling more complex summary statistics of the 21-cm signal to be used for Bayesian inference. In this work, we use SBI, specifically marginal neural ratio estimation to learn the likelihood-to-evidence ratio with swyft , to explore parameter inference using the cylindrically averaged 2D PS. Since the 21-cm signal is anisotropic, the 2D PS should yield more constraining information compared to the 1D PS which isotropically averages the signal. For this, we consider a mock 1000 h observation of the 21-cm signal using the Square Kilometre Array and compare the performance of the 2D PS relative to the 1D PS. Additionally, we explore two separate foreground mitigation strategies, perfect foreground removal and wedge avoidance. We find the 2D PS outperforms the 1D PS by improving the marginalized uncertainties on individual astrophysical parameters by up to |$\sim 30\!-\!40$|  per cent irrespective of the foreground mitigation strategy. Primarily, these improvements stem from how the 2D PS distinguishes between the transverse, |$k_{\perp }$|⁠ , and redshift-dependent, |$k_{\parallel }$|⁠ , information which enables greater sensitivity to the complex reionization morphology. [ABSTRACT FROM AUTHOR]

Abstract–Mixture models are widely employed in the analysis of heterogeneous data. However, existing approaches are based on the assumption that the observations in each component are normally distributed. The main objective of this article is to propose mixture models with Yeo-Johnson transformation to handle general heterogeneous data. Bayesian methods are developed for estimation and model comparison. The empirical performance of the proposed methodology is assessed through simulation studies. A real analysis of a data set derived from the National Longitudinal Survey of Youth 1997 is presented for illustration. [ABSTRACT FROM AUTHOR]

This paper investigates constant-stress accelerated life tests interrupted by a progressive type-I interval censoring regime. We provide a model based on the Chen distribution with a constant shape parameter and a log-linear connection between the scale parameter and stress loading. Inferential methods, whether classical or Bayesian, are employed to address model parameters and reliability attributes. Classical methods involve the estimation of model parameters through maximum likelihood and midpoint techniques. Bayesian approximations are achieved via the utilization of the Metropolis–Hastings algorithm, Tierney-Kadane procedure, and importance sampling methods. Furthermore, we engage in a discourse on the estimation of confidence intervals, making references to both asymptotic confidence intervals and credible intervals. To conclude, we furnish a simulation study, a corresponding discussion, and supplement these with an analysis of real data. [ABSTRACT FROM AUTHOR]

AbstractA model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family are then considered as kernels of a finite mixture model with an unknown number of components. Conjugate Bayesian inference has been derived for the parameters of the Hamming distribution model. The mixture is framed in a Bayesian nonparametric setting, and a transdimensional blocked Gibbs sampler is developed to provide full Bayesian inference on the number of clusters, their structure, and the group-specific parameters, facilitating the computation with respect to customary reversible jump algorithms. The proposed model encompasses a parsimonious latent class model as a special case when the number of components is fixed. Model performances are assessed via a simulation study and reference datasets, showing improvements in clustering recovery over existing approaches. [ABSTRACT FROM AUTHOR]

AbstractThis article proposes a factor model-based counterfactual analysis. We explicitly estimate the underlying factor structure of the outcome variables and estimate the counterfactual values of the unit subject to an intervention. With the help of the non-parametric Bayesian Indian Buffet Process prior, our approach is capable of exploring heterogeneous factor exposures, and the number of latent factors is endogenously determined in the estimation process. The flexible Markov Chain Monte Carlo algorithm utilizes the maximal intervention-free information provided by the data, whereas the original synthetic control only uses pre-intervention data. The counterfactual values are estimated by simulating from the posterior predictive distribution so that we can integrate out any parameter estimation uncertainty. We also calculate the posterior predictive upper- and lower-quantile bounds for inference. The two applications, namely California’s Tobacco Control Program and the West German Reunification, demonstrate the usefulness of our approach compared to the synthetic control method and the elastic net model. The Monte Carlo simulation study also shows the robustness of our approach with respect to nonlinear dynamics in the underlying factor process. [ABSTRACT FROM AUTHOR]

Stars in the Galactic disk are born on cold, nearly circular orbits with small vertical excursions. After their birth, their orbits evolve, driven by small- or large-scale perturbations in the Galactic disk's gravitational potential. Here, we study the vertical motions of young stars over their first few orbital periods, using a sample of OBA stars from Gaia E/DR3, which includes radial velocities and ages τ from LAMOST. We construct a parametric model for the time evolution of the stellar orbits' mean vertical actions J z as a function of Galactocentric radius, R GC. Accounting for data uncertainties, we use Markov Chain Monte Carlo analysis in annuli of Galactocentric radius (R GC) to constrain the model parameters. Our best-fit model shows a remarkably linear increase of vertical actions with age across all Galactocentric radii examined. Orbital heating by random scattering could offer a straightforward interpretation for this trend. However, various other dynamical aspects of the Galactic disk, such as stars being born in a warped disk, might offer alternative explanations that could be tested in the future. [ABSTRACT FROM AUTHOR]

We propose a multivariate GARCH model for non‐stationary health time series by modifying the observation‐level variance of the standard state space model. The proposed model provides an intuitive and novel way of dealing with heteroskedastic data using the conditional nature of state‐space models. We follow the Bayesian paradigm to perform the inference procedure. In particular, we use Markov chain Monte Carlo methods to obtain samples from the resultant posterior distribution. We use the forward filtering backward sampling algorithm to efficiently obtain samples from the posterior distribution of the latent state. The proposed model also handles missing data in a fully Bayesian fashion. We validate our model on synthetic data and analyze a data set obtained from an intensive care unit in a Montreal hospital and the MIMIC dataset. We further show that our proposed models offer better performance, in terms of WAIC than standard state space models. The proposed model provides a new way to model multivariate heteroskedastic non‐stationary time series data. Model comparison can then be easily performed using the WAIC. [ABSTRACT FROM AUTHOR]

A kernel interpolation method for the acoustic transfer function (ATF) between regions constrained by the physics of sound while being adaptive to the data is proposed. Most ATF interpolation methods aim to model the ATF for fixed source by using techniques that fit the estimation to the measurements while not taking the physics of the problem into consideration. We aim to interpolate the ATF for a region-to-region estimation, meaning we account for variation of both source and receiver positions. By using a very general formulation for the reproducing kernel function, we have created a kernel function that considers both directed and residual fields as two separate kernel functions. The directed field kernel considers a sparse selection of reflective field components with large amplitudes and is formulated as a combination of directional kernels. The residual field is composed of the remaining densely distributed components with lower amplitudes. Its kernel weight is represented by a universal approximator, a neural network, in order to learn patterns from the data freely. These kernel parameters are learned using Bayesian inference both under the assumption of Gaussian priors and by using a Markov chain Monte Carlo simulation method to perform inference in a more directed manner. We compare all established kernel formulations with each other in numerical simulations, showing that the proposed kernel model is capable of properly representing the complexities of the ATF. [ABSTRACT FROM AUTHOR]

Reverse epidemiology is a mathematical modelling tool used to ascertain information about the source of a pathogen, given the spatial and temporal distribution of cases, hospitalisations and deaths. In the context of a deliberately released pathogen, such as Bacillus anthracis (the disease-causing organism of anthrax), this can allow responders to quickly identify the location and timing of the release, as well as other factors such as the strength of the release, and the realized wind speed and direction at release. These estimates can then be used to parameterise a predictive mechanistic model, allowing for estimation of the potential scale of the release, and to optimise the distribution of prophylaxis. In this paper we present two novel approaches to reverse epidemiology, and demonstrate their utility in responding to a simulated deliberate release of B. anthracis in ten locations in the UK and compare these to the standard grid-search approach. The two methods—a modified MCMC and a Recurrent Convolutional Neural Network—are able to identify the source location and timing of the release with significantly better accuracy compared to the grid-search approach. Further, the neural network method is able to do inference on new data significantly quicker than either the grid-search or novel MCMC methods, allowing for rapid deployment in time-sensitive outbreaks. Author summary: In this paper we demonstrate three methods for estimating the source location and timing of a deliberate release of Bacillus anthracis based on the temporal and spatial distribution of cases. Two of our proposed methods, a modified MCMC approach and a neural network based approach, provide significant improvements over previous methods by directly addressing the problematic parameter-likelihood surface, and, in the case of the neural network approach, addressing the slow deployment speeds of existing methods. Our results represent a major step forward in the accuracy and speed of epidemiological back-calculation. [ABSTRACT FROM AUTHOR]

We consider a problem of inferring contact network from nodal states observed during an epidemiological process. In a black-box Bayesian optimisation framework this problem reduces to a discrete likelihood optimisation over the set of possible networks. The cardinality of this set grows combinatorially with the number of network nodes, which makes this optimisation computationally challenging. For each network, its likelihood is the probability for the observed data to appear during the evolution of the epidemiological process on this network. This probability can be very small, particularly if the network is significantly different from the ground truth network, from which the observed data actually appear. A commonly used stochastic simulation algorithm struggles to recover rare events and hence to estimate small probabilities and likelihoods. In this paper we replace the stochastic simulation with solving the chemical master equation for the probabilities of all network states. Since this equation also suffers from the curse of dimensionality, we apply tensor train approximations to overcome it and enable fast and accurate computations. Numerical simulations demonstrate efficient black-box Bayesian inference of the network. [ABSTRACT FROM AUTHOR]

Iterative geostatistical seismic inversion is a vital technique for estimating subsurface properties. However, a conventional single-scale strategy faces challenges in preserving large-scale geological features due to the limited restoration of the type of data template, and conventional multiscale strategies face the challenge in that it is easy to lose the large-scale structure that was previously preserved. This paper introduces a novel smoothed multiscale strategy aimed at overcoming these limitations, which comprises two components: Simulated annealing at the coarsest scale and smooth conversation between two scale grids. This approach offers a smoother way to simultaneously retain large-scale and small-scale structures, improving the overall accuracy of the subsurface property estimations. To validate the effectiveness of our approach, we apply it to both synthetic and real examples. The results show that the simulated annealing strategy at the coarsest scale grid explores the prior space and finds the best large structures to avoid the generated models trapping in the local minimal. Meanwhile, the smooth conversation strategy between two scale grids helps us avoid the damage of the coarser structure. It can be explained that a large weight is assigned to the coarse structure at the beginning of the conversation of two grid scale, reducing the likelihood of the replacing proposed local small-scale geological patterns, which prone to be accepted in the conventional multiscale strategies. The combination of the two strategies used in the proposed smoothed multiscale strategy displays a significant improvement in subsurface property estimation accuracy compared to traditional multiscale strategies. This innovation can have far-reaching implications, benefiting a wide range of geophysical applications and contributing to more accurate and informed decision-making in geological and hydrogeological assessments. [ABSTRACT FROM AUTHOR]

A bridge-randomized penalization that employs a prior for the shrinkage parameter, as opposed to the conventional bridge penalization with a fixed penalty, often delivers more superior performance compared to many other traditional shrinkage methods. In this paper, we develop an efficient Bayesian computational algorithm via the two-block Markov Chain Monte Carlo method for the bridge-randomized penalization in quantile regression to perform inference in the high-dimensional 'large-p' and 'large-p-small-n' settings. To construct a fully Bayesian formulation, we utilize the asymmetric Laplace distribution as an auxiliary error distribution and the generalized Gaussian distribution prior for the regression coefficients. Simulation studies encompassing a wide range of scenarios indicate that the proposed method performs at least as well as, and often better than, other existing procedures in terms of both parameter estimation and variable selection. Finally, a real-data application is provided for illustrative purposes. [ABSTRACT FROM AUTHOR]

Hysteretic quantile autoregressive model combines the hysteretic patterns and quantile autoregression, which can capture the dynamic relationship and nonlinear characteristics at different quantiles in time series data. In this paper, the Bayesian quantile inference and order shrinkage are studied for a class of hysteretic quantile autoregressive time series models. By using Markov Chain Monte Carlo (MCMC) techniques, the proposed Bayesian quantile method can handle the sparse hysteretic quantile autoregressive model well. It can accurately determine order of the model and estimate non-zero coefficients. Both simulation studies and a data example show that the proposed methods are feasible, reliable and appropriate for analysing the US Gross National Product data set. [ABSTRACT FROM AUTHOR]

The characterisation of the thickness and geology of cover sequences significantly improves targeting for mineral exploration in buried terrains. Audio-frequency Magnetotelluric (AMT) data is applicable to characterise cover sequences, where their conductivity (inverse resistivity) can be differentiated. We present a regional study from the under-cover East Tennant region in the Northern Territory (Australia) where we have applied deterministic and probabilistic inversion methods to derive 2D and 1D resistivity models. We integrated these models with information of co-located basement penetrating boreholes (lithological and geophysical logs) to ground-truth and validate the models and to improve geophysical interpretations. In the East Tennant region, borehole lithology and wireline logging demonstrate that the modelled AMT response is largely controlled by the mineralogy of the cover and basement rocks. The bulk conductivity is due primarily to bulk mineralogy and the success of using the AMT models to predict cover thickness is shown to be dependent on whether the bulk mineralogy of cover and basement rocks are sufficiently different to provide a detectable conductivity contrast. Our investigation of a range of geological scenarios that differ in thickness, complexity and geology of the cover and basement rocks suggests that in areas where there is sufficient difference in bulk mineralogy and where the stratigraphy is relatively simple, AMT models predict the cover thickness with high certainty. In more complex scenarios interpretation of AMT models may be more ambiguous and requires integration with other data (e.g. drilling, wireline logging, potential field modelling). Overall, we conclude that the application of the method has been validated and the results compare favourably with borehole stratigraphy logs once geological (i.e. bulk mineralogical) complexity is understood. This demonstrates that the method is capable of identifying major litho-stratigraphic units with resistivity contrasts. Our results have assisted with the planning of regional drilling programs and have helped to reduce the uncertainty and risk associated with intersecting targeted stratigraphic units in covered terrains. [ABSTRACT FROM AUTHOR]

Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the Bayesian context, importance sampling provides a possible solution but classical approaches can easily produce estimators whose asymptotic variance is infinite, making them potentially unreliable. Here we propose and analyze a novel mixture estimator to compute Bayesian LOO-CV criteria. Our method retains the simplicity and computational convenience of classical approaches, while guaranteeing finite asymptotic variance of the resulting estimators. Both theoretical and numerical results are provided to illustrate the improved robustness and efficiency. The computational benefits are particularly significant in high-dimensional problems, allowing to perform Bayesian LOO-CV for a broader range of models, and datasets with highly influential observations. The proposed methodology is easily implementable in standard probabilistic programming software and has a computational cost roughly equivalent to fitting the original model once. for this article are available online. [ABSTRACT FROM AUTHOR]

Spectral clustering views the similarity matrix as a weighted graph, and partitions the data by minimizing a graph-cut loss. Since it minimizes the across-cluster similarity, there is no need to model the distribution within each cluster. As a result, one reduces the chance of model misspecification, which is often a risk in mixture model-based clustering. Nevertheless, compared to the latter, spectral clustering has no direct ways of quantifying the clustering uncertainty (such as the assignment probability), or allowing easy model extensions for complicated data applications. To fill this gap, we propose the Bayesian forest model as a generative graphical model for spectral clustering. This is motivated by our discovery that the posterior connecting matrix in a forest model has almost the same leading eigenvectors, as the ones used by normalized spectral clustering. To induce a distribution for the forest, we develop a "forest process" as a graph extension to the urn process, while we carefully characterize the differences in the partition probability. We derive a simple Markov chain Monte Carlo algorithm for posterior estimation, and demonstrate superior performance compared to existing algorithms. We illustrate several model-based extensions useful for data applications, including high-dimensional and multi-view clustering for images. for this article are available online. [ABSTRACT FROM AUTHOR]

The envelope model aims to increase efficiency in multivariate analysis by using dimension reduction techniques. It has been used in many contexts including linear regression, generalized linear models, matrix/tensor variate regression, reduced rank regression, and quantile regression, and has shown the potential to provide substantial efficiency gains. Virtually all of these advances, however, have been made from a frequentist perspective, and the literature addressing envelope models from a Bayesian point of view is sparse. The objective of this article is to propose a Bayesian framework that is applicable across various envelope model contexts. The proposed framework aids straightforward interpretation of model parameters and allows easy incorporation of prior information. We provide a simple block Metropolis-within-Gibbs MCMC sampler for practical implementations of our method. Simulations and data examples are included for illustration. for this article are available online. [ABSTRACT FROM AUTHOR]

In this article, we present a novel methodology to perform Bayesian inference for Cox processes in which the intensity function is driven by a diffusion process. The novelty lies in the fact that no discretization error is involved, despite the non-tractability of both the likelihood function and the transition density of the diffusion. The methodology is based on an MCMC algorithm and its exactness is built on retrospective sampling techniques. The efficiency of the methodology is investigated in some simulated examples and its applicability is illustrated in some real data analyzes. for this article are available online. [ABSTRACT FROM AUTHOR]

This paper presents a multiple step-stress accelerated life test using type II censoring. Assuming that the lifetimes of the test item follow the gamma distribution, the maximum likelihood estimation and Bayesian approaches are used to estimate the distribution parameters. In the Bayesian approach, new parametrizations can lead to new prior distributions and can be a useful technique to improve the efficiency and effectiveness of Bayesian modeling, particularly when dealing with complex or high-dimensional models. Therefore, in this paper, we present two sets of prior distributions for the parameters of the accelerated test where one of them is based on the reparametrization of the other. The performance of the proposed prior distributions and maximum likelihood approach are investigated and compared by examining the summaries and frequentist coverage probabilities of intervals. We introduce the Markov Chain Monte Carlo (MCMC) algorithms to generate samples from the posterior distributions in order to evaluate the estimators and intervals. Numerical simulations are conducted to examine the approach's performance and one-sample lifetime data are presented to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

When assessing radar anti-jamming performance, the challenge of limited sample sizes is a significant hurdle. In response, this paper introduces a logistic fusion model that leverages Bayesian techniques and a Monte Carlo Markov chain (MCMC) sampling method based on a logistic regression model that characterizes the relationship between the signal-to-interference ratio (SIR) and the anti-jamming rate. The logistic curve's inflection point and growth rate serve as crucial indices for evaluating radar anti-jamming performance, providing insights into the SIR threshold for successful jamming mitigation. The proposed model allows for the derivation of posterior distributions for these parameters using the MCMC sampling method and kernel density estimation. It also enables the fusion of anti-jamming data from multiple stages, including mathematical simulations, hardware-in-the-loop tests, and field tests. Through extensive simulations, our method achieves a remarkably low root mean square error (RMSE) of 0.0552 . Compared with a conventional BETA fusion model, our proposed logistic fusion approach demonstrates superior performance and robustness in accurately estimating the anti-jamming rate. The fusion of multi-stage data, even with varying levels of reliability, improves the overall accuracy of the performance evaluation. [ABSTRACT FROM AUTHOR]

Post-earthquake safety assessment of buildings and infrastructure poses significant challenges, often relying on time-consuming visual inspections. To expedite this process, safety criteria based on a demand-capacity model are utilized. However, rapid assessment frameworks require accurate estimations of intensity measures (IMs) to estimate seismic demand and assess structural health. Unfortunately, post-earthquake IM values are typically only available at monitored locations equipped with sensors or monitoring systems, limiting broader assessments. Simple spatial interpolation methods, while possible, struggle to consider crucial physical factors such as earthquake magnitude, epicentral distance, and soil type, leading to substantial estimation errors, especially in areas with insufficient or non-uniform seismic station coverage. To address these issues, a novel framework, BN-GMPE, combining a Bayesian network (BN) and a ground motion prediction equation (GMPE), is proposed. BN-GMPE enables inference and prediction under uncertainty, incorporating physical parameters in seismic wave propagation. A further novelty introduced in this work regards separating the near and far seismic fields in the updating process to attain a clearer understanding of uncertainty and more accurate IM estimation. In the proposed approach, a GMPE is employed for the estimation, and the bias and standard deviation of the prediction error are updated after any new information is entered into the network. The proposed method is benchmarked against a classic Kriging interpolator technique, considering some recent earthquake shocks in Italy. The proposed BN framework can naturally extend for estimating the probability of failure of various structures in a targeted region, which represents the ultimate aim of this research. [ABSTRACT FROM AUTHOR]

The interest in considering the relation among random variables in quantiles instead of the mean has emerged in various fields, and data collected from complex survey designs are of fundamental importance to different areas. Despite the extensive literature on survey data analysis and quantile regression models, research papers exploring quantile regression estimation accounting for an informative design have primarily been restricted to a frequentist framework. In this paper, we introduce different Bayesian methods relying on the survey-weighted estimator and the estimating equations. A model-based simulation study evaluates the proposed methods compared to alternative approaches and a naïve model fitting ignoring the informative sampling design under different scenarios. In addition, we illustrate and conduct a prior sensitivity analysis in a design-based simulation study that uses data from Prova Brasil 2011. [ABSTRACT FROM AUTHOR]

We show that the slice sampler generates Markov chains whose variables are mean independent and thus uncorrelated when the target density is centrally symmetric. Skewness instead boosts correlations. Popular implementation algorithms such as stepping-out and multivariate-sampling-with-hyperrectangles add statistical inefficiency, the first in case of multimodality, the second in all circumstances. A new sampler which exploits these structural and algorithmic characteristics to reduce the variance of Monte Carlo estimates is experimented in several sampling problems. An insight into the properties of the product slice sampler is also provided. [ABSTRACT FROM AUTHOR]

In this paper, we compile a Fermi sample of the long gamma-ray bursts (GRB) observations from 15 years of GBM catalogue with identified redshift, in which the GOLD sample contains 123 long GRBs at |$z\le 5.6$| and the FULL sample contains 151 long GRBs with redshifts at |$z\le 8.2$|⁠. The Amati relation (the |$E_{\rm p,i}$| – |$E_{\rm iso}$| correlation) is calibrated at |$z\lt 1.4$| by a Gaussian Process from the latest observational Hubble data with the cosmic chronometers method so that GRBs at high-redshift |$z\ge 1.4$| can be used to constrain cosmological models via the Markov chain Monte Carlo (MCMC) method. From the cosmology-independent GRBs with the GOLD sample at |$z\ge 1.4$| and the Pantheon + sample of type Ia supernovae (SNe Ia) at |$0.01\lt z\le 2.3$|⁠ , we obtain |$\Omega _{\rm m} = 0.354\pm 0.018, H_0 = 73.05\pm 0.2\, \rm {km\,s^{-1}\,Mpc^{-1}}$| for the flat Lambda cold dark matter (⁠|$\Lambda$| CDM) model; |$w_0 = -1.22^{+0.18}_{-0.15}$| for the flat w CDM model; and |$w_{a} = -1.12^{+0.45}_{-0.83}$| for the flat Chevallier–Polarski–Linder model at the 1 |$\sigma$| confidence level. Our results with the GOLD and FULL sample are almost identical, which are more stringent than the previous results with GRBs. [ABSTRACT FROM AUTHOR]

SUMMARY: Inverse problems occur in many fields of geophysics, wherein surface observations are used to infer the internal structure of the Earth. Given the non-linearity and non-uniqueness inherent in these problems, a standard strategy is to incorporate a priori information regarding the unknown model. Sometimes a solution is obtained by imposing that the inverted model remains close to a reference model and with smooth lateral variations (e.g. a correlation length or a minimal wavelength are imposed). This approach forbids the presence of strong gradients or discontinuities in the recovered model. Admittedly, discontinuities, such as interfaces between layers, or shapes of geological provinces or of geological objects such as slabs can be a priori imposed or even suggested by the data themselves. This is however limited to a small set of possible constraints. For example, it would be very challenging and computationally expensive to perform a tomographic inversion where the subducting slabs would have possible top discontinuities with unknown shapes. The problem seems formidable because one cannot even imagine how to sample the prior space: is each specific slab continuous or broken into different portions having their own interfaces? No continuous set of parameters seems to describe all the possible interfaces that we could consider. To circumvent these questions, we propose to train a Generative Adversarial neural Network (GAN) to generate models from a geologically plausible prior distribution obtained from geodynamic simulations. In a Bayesian framework, a Markov chain Monte Carlo algorithm is used to sample the low-dimensional model space depicting the ensemble of potential geological models. This enables the integration of intricate a priori information, parametrized within a low-dimensional model space conducive to efficient sampling. The application of this approach is demonstrated in the context of a downscaling problem, where the objective is to infer small-scale geological structures from a smooth seismic tomographic image. [ABSTRACT FROM AUTHOR]

A metric tensor for Riemann manifold Monte Carlo particularly suited for nonlinear Bayesian hierarchical models is proposed. The metric tensor is built from symmetric positive semidefinite log‐density gradient covariance (LGC) matrices, which are also proposed and further explored here. The LGCs generalize the Fisher information matrix by measuring the joint information content and dependence structure of both a random variable and the parameters of said variable. Consequently, positive definite Fisher/LGC‐based metric tensors may be constructed not only from the observation likelihoods as is current practice, but also from arbitrarily complicated nonlinear prior/latent variable structures, provided the LGC may be derived for each conditional distribution used to construct said structures. The proposed methodology is highly automatic and allows for exploitation of any sparsity associated with the model in question. When implemented in conjunction with a Riemann manifold variant of the recently proposed numerical generalized randomized Hamiltonian Monte Carlo processes, the proposed methodology is highly competitive, in particular for the more challenging target distributions associated with Bayesian hierarchical models. [ABSTRACT FROM AUTHOR]

The transformation model with partly interval-censored data offers a highly flexible modeling framework that can simultaneously support multiple common survival models and a wide variety of censored data types. However, the real data may contain unexplained heterogeneity that cannot be entirely explained by covariates and may be brought on by a variety of unmeasured regional characteristics. Due to this, we introduce the conditionally autoregressive prior into the transformation model with partly interval-censored data and take the spatial frailty into account. An efficient Markov chain Monte Carlo method is proposed to handle the posterior sampling and model inference. The approach is simple to use and does not include any challenging Metropolis steps owing to four-stage data augmentation. Through several simulations, the suggested method's empirical performance is assessed and then the method is used in a leukemia study. [ABSTRACT FROM AUTHOR]

We propose a Bayesian nonparametric clustering approach to study the spatial heterogeneity effect for functional data observed at spatially correlated locations. We consider a geographically weighted Chinese restaurant process equipped with a conditional autoregressive prior to capture fully the spatial correlation of function curves. To sample efficiently from our model, we customize a prior called Quadratic Gamma, which ensures conjugacy. We design a Markov chain Monte Carlo algorithm to infer simultaneously the posterior distributions of the number of groups and the grouping configurations. The superior numerical performance of the proposed method over competing methods is demonstrated using simulated examples and a U.S. annual precipitation study. [ABSTRACT FROM AUTHOR]

Optimizing structural designs is crucial today, with additive manufacturing, particularly selective laser melting, gaining prominence. Thorough mechanical characterization of new materials remains vital. This paper investigates fatigue crack growth behavior in SLM 316L specimens under cyclic loading conditions. The study addresses result uncertainties by using CT specimens aligned along three building directions per ASTM E647 standards and a constant loading ratio (R = 0.1), necessitating mean value and confidence interval predictions. Departing from linear prediction models, innovative Bootstrap Polynomial and Power Regression Models and Bayesian Nonlinear Regression Model updated posterior distribution by Markov Chain Monte Carlo are employed. These approaches leverage bootstrapping to construct confidence intervals, offering robustness and flexibility in handling non‐normal data behavior and limited sample sizes. They provide tailored fits to data curvature, revealing limitations of linear prediction models in capturing observed nonlinear behavior, enhancing reliability in additive manufacturing applications, and advancing material science and engineering. Highlights: Fatigue crack growth in SLM316L is evaluated.Robust nonlinear regression techniques are utilized.Distribution approximation is done using Kernel estimator.Confidence intervals are estimated employing Bootstrap and Bayesian regression models. [ABSTRACT FROM AUTHOR]

This study examined the estimations of Weibull distribution using progressively first-failure censored data, under the assumption that removals follow the beta-binomial distribution. Classical and Bayesian approaches for estimating unknown model parameters have been established. The estimations included scale and shape parameters, reliability and failure rate metrics as well as betabinomial parameters. Estimations were considered from both point and interval viewpoints. The Bayes estimates were developed by using the squared error loss and generating samples for the posterior distribution through the Markov Chain Monte Carlo technique. Two interval estimation approaches are considered: approximate confidence intervals based on asymptotic normality of likelihood estimates and Bayes credible intervals. To investigate the performance of classical and Bayesian estimations, a simulation study was considered by various kinds of experimental settings. Furthermore, two examples related to real datasets were thoroughly investigated to verify the practical importance of the suggested methodologies. [ABSTRACT FROM AUTHOR]

The self-adjoint, positive Markov operator defined by the Pólya-Gamma Gibbs sampler (under a proper normal prior) is shown to be trace-class, which implies that all non-zero elements of its spectrum are eigenvalues. Consequently, the spectral gap is 1 - λ ∗ , where λ ∗ ∈ [ 0 , 1) is the second largest eigenvalue. A method of constructing an asymptotically valid confidence interval for an upper bound on λ ∗ is developed by adapting the classical Monte Carlo technique of Qin et al. (Electron J Stat 13:1790–1812, 2019) to the Pólya-Gamma Gibbs sampler. The results are illustrated using the German credit data. It is also shown that, in general, uniform ergodicity does not imply the trace-class property, nor does the trace-class property imply uniform ergodicity. [ABSTRACT FROM AUTHOR]

The present work intends to discuss parameter estimation and statistical analysis in adsorption. The Langmuir and Tóth isotherm models are compared for a set of carbon dioxide adsorption data on 13X zeolite from literature at different temperatures: 303, 323, 373, and 423 K. Statistical analyses were performed under frequentist and Bayesian perspectives. Under the frequentist statistical view, parameters were estimated using Maximum Likelihood estimation (MLE). Statistical analyses of parameters were performed by confidence regions in terms of elliptical approximation and likelihood region, while the evaluation of models was performed by chi-square statistics. The results showed that, for these nonlinear models, the elliptical region offers a poor approximation of the parameter estimates' confidence region, especially for the most correlated parameter pairs. Additionally, the four-parameter Tóth's equation yields less correlated parameters than the three-parameter Langmuir model. From a Bayesian perspective, the Markov chain Monte Carlo (MCMC) technique facilitated the reconstruction of the probability density functions of parameters as well as enabled the propagation of parametric uncertainties in the model responses. Finally, the accurate assessment of experimental uncertainty significantly influences the evaluation of models and their respective parameters. [ABSTRACT FROM AUTHOR]

Widespread flooding in Africa has devastating repercussions on communities, and sometimes leading to loss of life, displacement of populations, and significant damage to infrastructure and agriculture. Despite this, there are limited studies that investigate the behaviour of high time frequency river flows for the major river systems of Africa to inform adaptation and mitigation strategies for improved resilience of society. This paper fills this gap by assessing the occurrence time of annual maximum daily discharge for five of the longest rivers of Africa using a statistical modelling approach. This is the first of such a study covering all of the five longest rivers of Africa in one paper. Annual maximum daily discharge time for each river was modeled by mixtures of von Mises distributions, fitted by a Markov chain Monte Carlo algorithm. Data on mean daily discharge was obtained from the Global Runoff Data Centre database for the Niger, Zambezi, Okavango, Limpopo and Orange rivers in Africa. Estimates were inferred for the location parameter of the major mode, location parameter of the minor mode, concentration parameter of the major mode, concentration parameter of the minor mode, mean time, mean resultant, circular variance, circular skewness, and circular kurtosis. The developed models reveal distinctive temporal patterns of peak discharge events in each river, which can have significant implications for flood management, water resource planning, hydrological modeling, risk assessment and infrastructure design. [ABSTRACT FROM AUTHOR]

Free-fall penetration (FFP) testing has drawn wide attention in evaluating in-situ undrained shear-strength (Su) of marine clay because it can save time and reduce costs. However, model parameters for interpreting Su are empirical and usually determined based on engineering experience, leading to great uncertainties in Su results. In this study, FFP model tests were conducted using conical, hemispherical and T-shaped penetrometers to gather data. Subsequently, Bayesian theory was employed to ascertain the optimal model parameters. The penetrometer motion state and influencing factors of penetration depth are analysed and discussed. By considering prior knowledge and inherent variability of Su, optimal model parameters for the three types of penetrometers are obtained using maximum likelihood estimation method. The reasons for the different model parameters of three type penetrometers are discussed. In order to assess the effectiveness of the proposed models, field tests were conducted to gather in-situ data. To reduce uncertainty inherent in limited amount of data, a Bayesian updating approach combined with Markov chain Monte Carlo method were used to evaluate posterior distribution of Su of the three penetrometers. Results show that updated Su samples were consistent with those determined by vane shear tests, which verified the reliability of proposed model parameters. [ABSTRACT FROM AUTHOR]

Catastrophe bonds (cat bond in short) are an alternative risk‐transfer instrument used to transfer peril‐specific financial risk from governments, financial institutions, or (re)insurers, to the capital market. Current approaches for cat bond pricing are calibrated on seismic mainshocks, and thus do not account for potential effects induced by earthquake sequences. This simplifying assumption implies that damage arises from mainshocks only, while aftershocks yield no damage. Postearthquake field surveys reveal that this assumption is inaccurate. For example, in the 2011 Christchurch Earthquake sequence and 2016–2017 Central Italy Earthquake sequence, aftershocks were responsible for higher economic losses when compared to those caused by mainshocks. This article proposes a time‐dependent aggregate loss model that takes into account seismicity clustering and damage accumulation effects in the computation of damage. The model is calibrated on the seismic events recorded during the recent 2016–2017 Central Italy Earthquake sequence. Furthermore, the effects of earthquake sequence on cat bond pricing is explored by implementing the proposed model on five Italian municipalities. The investigation showed that neglecting time‐dependency may lead to higher difference (up to 45%) in the cat bond price when compared to standard approaches. [ABSTRACT FROM AUTHOR]

Determination of cosmological parameters is a major goal in cosmology at present. The availability of improved data sets necessitates the development of novel statistical tools to interpret the inference from a cosmological model. In this paper, we combine the principal component analysis (PCA) and Markov Chain Monte Carlo (MCMC) method to infer the parameters of cosmological models. We use the No U-Turn Sampler (NUTS) to run the MCMC chains in the model parameter space. After determining the observable by PCA, we replace the observational and error parts of the likelihood analysis with the PCA reconstructed observable and find the most preferred model parameter set. To demonstrate our methodology, we assume a polynomial expansion as the parametrization of the dark energy equation of state and plug it into the reconstruction algorithm as our model. After testing our methodology with simulated data, we apply the same to the observed data sets, the Hubble parameter data, Supernova Type Ia data, and the Baryon acoustic oscillation data. This method effectively constrains cosmological parameters from data, including sparse data sets. [ABSTRACT FROM AUTHOR]

In this study, we investigate a scalar field cosmological model with Lyra’s geometry to explain the present cosmic expansion in a homogeneous and isotropic flat FRW universe. In Einstein’s field equations, we presupposed a variable displacement vector as an element of Lyra’s geometry. In the context of the conventional theory of gravity, we suggest a suitable parametrization of the scalar field’s dark energy density in the hybrid function of redshift z, confirming the essential transition behavior of the universe from a decelerating era to the present accelerated scenario. We present constraints on model parameters using the most recent observational datasets from OHD, BAO/CMB and Pantheon, taking Markov Chain Monte Carlo (MCMC) analysis into account. For the proposed model, the best estimated values of parameters for the combined dataset (OHD, BAO/CMB and Pantheon) are H0 = 71.15 ± 0.26km/s/Mpc, Ωm0 = 0.2625 ± 0.0024, Ωϕ0 = 0.676 ± 0.038, α = −0.22 ± 0.13, n = 0.096 ± 0.079 and k = 0.38 ± 0.32. The model exhibits a flipping nature, and the redshift transition occurs at zt = 0.756−0.015+0.005. The current value of the decelerated parameter for the proposed model is calculated as q0 = −0.625−0.085+0.067 for the combined dataset. Some dynamical properties of the model like energy density (ρϕ), scalar field pressure (pϕ), EoS parameter of scalar field (ωϕ), and effective EoS parameter (ωeff) are analyzed and presented. Further, we have also examined the statefinder diagnosis and jerk parameters of the derived model. The total density parameter for the derived model is found to be unity which is in nice agreement with recent standard findings. [ABSTRACT FROM AUTHOR]

AbstractGaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian methods can measure the uncertainty of conditional relationships and include prior information. However, frequentist methods are often preferred due to the computational burden of the Bayesian approach. Over the last decade, Bayesian methods have seen substantial improvements, with some now capable of generating accurate estimates of graphs up to a thousand variables in mere minutes. Despite these advancements, a comprehensive review or empirical comparison of all recent methods has not been conducted. This paper delves into a wide spectrum of Bayesian approaches used for structure learning and evaluates their efficacy through a comprehensive simulation study. We also demonstrate how to apply Bayesian structure learning to a real-world data set and provide directions for future research. This study gives an exhaustive overview of this dynamic field for newcomers, practitioners, and experts. [ABSTRACT FROM AUTHOR]

AbstractDuring an epidemic, the daily number of reported infected cases, deaths or hospitalizations is often lower than the actual number due to reporting delays. Nowcasting aims to estimate the cases that have not yet been reported and combine it with the already reported cases to obtain an estimate of the daily cases. In this paper, we present a fast and flexible Bayesian approach for nowcasting by combining P-splines and Laplace approximations. Laplacian-P-splines provide a flexible framework for nowcasting that is computationally less demanding as compared to traditional Markov chain Monte Carlo techniques. The proposed approach also permits to naturally quantify the prediction uncertainty. Model performance is assessed through simulations and the nowcasting method is applied to COVID-19 mortality and incidence cases in Belgium. [ABSTRACT FROM AUTHOR]

AbstractData transformations are essential for broad applicability of parametric regression models. However, for Bayesian analysis, joint inference of the transformation and model parameters typically involves restrictive parametric transformations or nonparametric representations that are computationally inefficient and cumbersome for implementation and theoretical analysis, which limits their usability in practice. This paper introduces a simple, general, and efficient strategy for joint posterior inference of an unknown transformation and all regression model parameters. The proposed approach directly targets the posterior distribution of the transformation by linking it with the marginal distributions of the independent and dependent variables, and then deploys a Bayesian nonparametric model via the Bayesian bootstrap. Crucially, this approach delivers (1) joint posterior consistency under general conditions, including multiple model misspecifications, and (2) efficient Monte Carlo (not Markov chain Monte Carlo) inference for the transformation and all parameters for important special cases. These tools apply across a variety of data domains, including real-valued, positive, and compactly-supported data. Simulation studies and an empirical application demonstrate the effectiveness and efficiency of this strategy for semiparametric Bayesian analysis with linear models, quantile regression, and Gaussian processes. The R package SeBR is available on CRAN. [ABSTRACT FROM AUTHOR]