Bayesian Model Averaging (BMA) enhances predictive performance by integrating over competing models, but its scalability is often limited by the computational burden of Markov Chain Monte Carlo (MCMC)–based posterior inference. Recent variational approaches such as VBMA (Kejzlar et al., 2023) offer scalability but rely on restrictive mean-field assumptions that fail to capture posterior dependencies, leading to suboptimal uncertainty quantification in complex settings. We propose Neural Autoregressive Flow Bayesian Model Averaging (NAF-BMA), a novel variational BMA framework that replaces the simple variational family with expressive neural autoregressive flows. This innovation enables NAF-BMA to model highly correlated, multimodal posterior structures with MCMC-level accuracy while retaining near–VBMA scalability. The method jointly estimates individual model evidences and posterior model probabilities within a unified optimization scheme, producing an optimal combined posterior over the entire model space. Designed as a general and modular framework requiring minimal model-specific derivations, NAF-BMA extends naturally to a broad class of Bayesian models. Across extensive simulation and real-data studies, it consistently outperforms VBMA and closely matches MCMC accuracy, establishing NAF-BMA as a flexible and scalable new paradigm for Bayesian model averaging.

Parameter estimation of a distribution can be performed through two main approaches: the classical method and the Bayesian method. The Bayesian method integrates the sample distribution with the prior distribution, where random sampling is conducted via simulation techniques such as Markov Chain Monte Carlo (MCMC) with the Gibbs Sampling algorithm. This algorithm works by constructing a Markov Chain through recursive sampling from the full conditional posterior distribution for each parameter until convergence is reached. This study applies the Bayesian method with MCMC using the Gibbs Sampling algorithm to estimate the parameters of the Stochastic Volatility model, which allows asset price volatility to vary over time. The obtained Stochastic Volatility model is then used to predict the stock returns of PT. Aneka Tambang Tbk. (ANTM.JK), where the prediction results show good conformity with actual data. The resulting prediction values can be utilized by investors as a reference in making optimal investment portfolio decisions.

ABSTRACT This paper examines a multi-stage system characterized by different mechanisms at different stages. This system refines the operational processes of traditional systems and is more suitable for systems with stages. Such systems are commonly found in applications including nuclear power plants, offshore drilling platforms, and UAV systems. The degradation of the system is due to the impact of valid shocks. Whenever the state of the system reaches predetermined values, different mechanisms will be triggered to slow down the degradation of the system until the system can no longer support the operation of these mechanisms. To evaluate the reliability of the system, we employ a finite Markov chain imbedding approach along with phase-type distributions. Based on this, a maintenance strategy of the system is proposed and the optimal inspection interval has been found. Finally, we present some numerical examples to demonstrate the practical application and effectiveness of the proposed system.

The mechanistic integration of cellular aging drivers remains a central challenge in biogerontology. We present the Centriolar Damage Accumulation Theory of Aging (CDATA) v3.3.0, a unified theory and an accompanying high-performance digital twin simulator (Cell-DT v3.0) that proposes the centriole as a primary timekeeper and damage integrator of somatic aging. The core formalism models the accumulation of centriolar damage as a function of replication, decaying youth protection programs, and modifiers including hormetic senescence-associated secretory phenotype (SASP) signaling, asymmetric division fidelity, and tissue-specific kinetics. The theory is implemented via eight integrated mechanisms. A novel five-component Model Composite Aging Index (MCAI) – distinguished from clinical frailty indices – synthesizes centriole damage, SASP burden, stem pool depletion, telomere attrition, and CHIP variant allele frequency. The model’s 32 parameters were calibrated using Markov Chain Monte Carlo (MCMC) methods on a cohort of 62,000 synthetic records scaled to established human aging trajectories (20–50 years). The Cell-DT simulator, built in Rust using an Entity-Component-System architecture, achieves high-performance deterministic simulation. Internal consistency was demonstrated on the MCMC cohort and independent hold-out validation for the composite MCAI (combined R² = 0.84). This validation is against synthetic data; prospective biological validation against longitudinal human cohort data (e.g., NHATS, UK Biobank) is required to assess predictive biological power. CDATA v3.3.0 provides a quantitative, testable, and simulatable framework for in silico hypothesis generation.

{Simulation studies and an illustrative real-data analysis are used to validate a competing-risks inference framework under balanced joint progressive censoring, demonstrating significant improvements in reliability analysis. } Comparative lifetime testing is essential for research assessing the relative performance of two identical products produced on separate manufacturing lines. This article proposes a statistical inference framework for analyzing competing risks data under balanced joint progressive censoring using the Burr-XII distribution, providing a systematic approach for the analysis of competing risks in comparative lifetime studies. We develop the maximum likelihood estimation procedures for the unknown parameters, rigorously establishing the existence and uniqueness of the resulting estimators. Additionally, we construct four types of confidence intervals: approximate confidence intervals (ACIs), lognormal ACIs, as well as bootstrap-p and bootstrap-t confidence intervals. For Bayesian inference, we present the parameter estimation under three distinct loss functions and derive the highest posterior density credible intervals through Markov Chain Monte Carlo simulations. The performance of all methods is comprehensively evaluated through simulation studies and real data analysis.

ABSTRACT Both the U.S. stock and bond returns exhibit distinct Markovian regimes. However, because these regimes display limited coherence, conventional models typically require highly parameterized systems to adequately capture their joint distribution. This paper proposes a novel framework for the bivariate MS‐VAR model that more effectively characterizes the regime dynamics of U.S. stock and bond returns. The specification leverages six latent Markov chains to govern the evolution of the model's parameters. Empirical evidence shows that this approach delivers more interpretable estimates of conditional moments and yields more informative decoding of the latent states than the standard MS‐VAR model. The maximum likelihood estimator is implemented via an expectation–conditional maximization algorithm with closed‐form conditional maximization steps. Moreover, the large‐sample properties of the estimator are formally established.

Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here, we consider continuous-time Markov networks, which we subject to perturbations along a single edge. We find that in steady state the probabilities of any two states are linearly related to one another. We show that this mutual linearity of probabilities extends to a broad class of observables, including currents but also generic counting and state-dependent observables. Moreover, we derive an exact relation between the relative response of any state's probability and the ratio of two steady-state probabilities. Leveraging the Markov chain tree theorem, we further show that probabilities and the considered observables are constrained by the topological and kinetic properties of the network and provide analytical expressions in terms of spanning tree polynomials. Our results are general, holding for arbitrary rate parametrizations and extending far from equilibrium.

Abstract The Hubble tension refers to the significant discrepancy in the Hubble constant $H_{0}$ obtained from two different measurement methods in cosmology which has persisted for decades. To theoretically explore potential solutions to this problem, this paper examines a model within the framework of Einstein-Cartan (EC) theory, where torsion is introduced with spin as the corresponding entity, allowing for a linear assumption between $H$ and $\phi$. By employing the Markov Chain Monte Carlo (MCMC) algorithm and utilizing Cosmic Chronometers (CC) data, we impose parameter constraints on various parameters in the Friedmann equations, particularly focusing on the curvature density parameter $\Omega_k$, to assess whether the model remains stable under this assumption and whether the estimated parameters align more closely with either of the observational results. In conclusion, we find that the parameter constraints in the model incorporating torsion ($ H_0 = 67.6^{+2.1}_{-2.7} \ \mathrm{km\ s^{-1}\ Mpc^{-1}}$, obtained under the Big Bang Nucleosynthesis (BBN) constraint with $\Omega_{k}=0$; $ H_0 = 66.2^{+4.4}_{-2.9} \ \mathrm{km\ s^{-1}\ Mpc^{-1}}$, obtained under same constraint but set $\Omega_{k}$ as a free variable; $ H_0 = 68.8^{+2.9}_{-4.2} \ \mathrm{km\ s^{-1}\ Mpc^{-1}}$, obtained under the Planck constraint) are more consistent with the value derived from CMB data, favoring lower $H_0$ value.

Abstract In this paper, we study Bayesian approach for solving large scale linear inverse problems arising in various scientific and engineering fields. We propose a fused L 1/2 prior with edge-preserving and sparsity-promoting properties and show that it can be formulated as a Gaussian mixture Markov random field. Since the density function of this family of prior is neither log-concave nor Lipschitz, gradient-based Markov chain Monte Carlo methods can not be applied to sample the posterior. Thus, we present a Gibbs sampler in which all the conditional posteriors involved have closed form expressions. The Gibbs sampler works well for small size problems but it is computationally intractable for large scale problems due to the need for sample high dimensional Gaussian distribution. To reduce the computation burden, we construct a Gibbs bouncy particle sampler (Gibbs-BPS) based on a piecewise deterministic Markov process. This new sampler combines elements of Gibbs sampler with bouncy particle sampler and its computation complexity is an order of magnitude smaller. We show that the new sampler converges to the target distribution. With computed tomography examples, we demonstrate that the proposed method shows competitive performance with existing popular Bayesian methods and is highly efficient in large scale problems.

This article investigates the problem of almost sure convergence for nonhomogeneous switching Markov chains with absorbing states. Two types of graphs are used to describe the switching walks of state components in the Markov chain under deterministic transfer-restricted switching and arbitrary switching. The transfer-restricted switching among nonhomogeneous Markov chains is characterized by a switching directed graph, while the stochastic transitions within each Markov chain are depicted by state transition component graphs. The reachability relationship between nonabsorbing and absorbing state components is then analyzed by using the Lyapunov function constructed from the state space of Markov chains. Building on the two types of graphs, cycle-dependent switching strategies for almost sure convergence to the target absorbing state are established. Furthermore, necessary and sufficient conditions for almost sure convergence to the common absorbing state under arbitrary switching are derived, which utilize the properties of absorbing Markov chains and state transition component graphs with self-loops. Finally, the effectiveness of the proposed method is validated through two examples.

• A crop rotation mapping framework was developed using Markov chains. • Framework uses crop type data at field scale resolution across Kansas. • Results show detailed spatial patterns and highlight dominant winter wheat rotations. • Study shows framework’s potential for analyzing crop sequences at a regional scale. Current U.S. crop rotation data lacks adequate spatial coverage, resolution, and explicitness, all crucial for effective and sustainable agricultural planning. This study presents a standardized framework combining data-driven techniques with expert insights and satellite-based crop maps to generate detailed maps of regional crop rotations. Using Markov chains, the model predicts likely crop sequences from historical data, which are classified into distinct rotations via a knowledge-based lookup table. This framework was applied to USDA Economic Research Service’s field boundaries in Kansas. Further, the accuracy was assessed using surveyed reference data from 280 field sites. Findings show soybeans, winter wheat, and corn dominate one-third of Kansas farmland. Winter wheat, prevalent in central and western Kansas, features in 13 of 18 dominant rotations, either as continuous crop or with summer crops and fallow. Corn is the primary irrigated crop in western Kansas, typically rotated with non-irrigated crops. Corn and soybeans-based rotations cover 40% of the area. These rotations, along with continuous winter wheat, show high consistency, unlike more variable sorghum rotations. The framework achieved 71% accuracy for high-probability sites. Considering the high performance of crop rotation predictive model, it can be expanded to map current and historical rotations in the other U.S. regions and resulting maps can be used for analyzing the environmental consequences.

A multinomial hierarchical model for meta-analysis of diagnostic test accuracy of ordered or unordered multicategory tests.

Abstract Seismic attenuation, resulting from anelasticity of Earth's materials, provides critical information on the thermal and compositional characteristics of Earth's interior. Accurately measuring the seismic wave energy loss during propagation and conducting seismic attenuation is challenging, as conventional methods for measuring attenuation suffer from the trade‐offs between estimated source signature and along‐path energy decay, and between damping and smoothing in linear tomography inversions. In this study, we first incorporate independently constrained source parameters to invert for path‐average attenuation, , thereby minimizing the trade‐offs between path and source terms. Then, based on the refined data set, we apply a transdimensional Bayesian Markov Chain Monte Carlo (MCMC) approach to image the 3D attenuation structure with robust uncertainty estimations. We apply these methods to a 1‐year amphibious seismic array in the Tonga subduction zone and its adjacent Lau back‐arc basin. The new measurements fit the data well, and the new 3D tomography results reveal high P‐wave attenuation anomalies in the Tonga‐Lau mantle wedge with the highest attenuation of or beneath the East Lau Spreading Center at 50 km depth. Additionally, a slightly elevated attenuation anomaly is imaged in the mantle transition zone. By combining our new model with a published SV‐wave velocity model, we quantitatively estimate melt porosity at 50 km beneath the back‐arc spreading centers, showing a southward decrease from beneath the Central Lau Spreading Center to around 0 beneath the Valu Fa Ridge.

Physics-informed band structure-integrated Continuous-time inhomogeneous Markov chains for stochastic occupancy modeling

Spontaneous reporting system databases are key resources for post-marketing surveillance, providing real-world evidence (RWE) on the adverse events (AEs) of regulated drugs or other medical products. Various statistical methods have been proposed for AE signal detection in these databases, flagging drug-specific AEs with disproportionately high observed counts compared to expected counts under independence. However, signal detection remains challenging for rare AEs or newer drugs, which receive small observed and expected counts and thus suffer from reduced statistical power. Principled information sharing on signal strengths across drugs/AEs is crucial in such cases to enhance signal detection. However, existing methods typically ignore complex between-drug associations on AE signal strengths, limiting their ability to detect signals. We propose novel local-global mixture Dirichlet process (DP) prior-based nonparametric Bayesian models to capture these associations, enabling principled information sharing between drugs while balancing flexibility and shrinkage for each drug, thereby enhancing statistical power. We develop efficient Markov chain Monte Carlo algorithms for implementation and employ a false discovery rate (FDR)-controlled, false negative rate (FNR)-optimized hypothesis testing framework for AE signal detection. Extensive simulations demonstrate our methods' superior sensitivity-often surpassing existing approaches by a twofold or greater margin-while strictly controlling the FDR. An application to FDA FAERS data on statin drugs further highlights our methods' effectiveness in real-world AE signal detection. Software implementing our methods is provided as supplementary material.

Fuel cell hybrid vehicles (FCHVs) have drawn tremendous attention due to the advantages of zero emissions. Existing energy management strategies (EMSs) typically fail to adequately address the coupled relationship between power allocation and thermal dynamics in the powertrain system, which is a gap that affects the economic and durability performance of FCHVs. To address this, this research proposes a hierarchical EMS that innovatively integrates: (1) a fuzzy-encode Markov Chain speed predictor for speed forecasting at the upper level, and (2) a multi-objective model predictive control that optimizes system operating cost, durability and thermal safety of battery and fuel cell system at the lower level. In the validation phase, the impacts of different membership functions and state numbers on speed prediction accuracy are explored firstly. Then, the effects of weighting factors in multi-objective function are studied. Furthermore, an effectiveness evaluation method is set up to score each strategy with dynamic programming (DP) as the upper benchmark. The comparison with the other three benchmark strategies proves that the suggested strategy is more cost-effective, thermally safe and life-extended, bringing an overall performance improvement of at least 20.61% and a score improvement of at least 14.02 points in the [0,100] range.

Cross-border tourism in North America: A hybrid deep learning framework with macroeconomic indicators

ABSTRACTSurvival analysis is an important area of medical research, yet existing models often struggle to balance simplicity with flexibility. Simple models require minimal adjustments but come with strong assumptions, while more flexible models require significant input and tuning from researchers. We present a survival model using a Bayesian hierarchical shrinkage method that automatically determines whether each covariate should be treated as static, time‐varying, or excluded altogether. This approach strikes a balance between simplicity and flexibility, minimizes the need for tuning, and naturally quantifies uncertainty. The method is supported by an efficient Markov chain Monte Carlo sampler, implemented in the R package shrinkDSM. Comprehensive simulation studies and an application to a clinical dataset involving patients with adenocarcinoma of the gastroesophageal junction showcase the advantages of our approach compared to existing models.

Given a unichain Markov reward process (MRP), we provide an explicit expression for the bias values in terms of mean first passage times. This result implies a generalization of known Markov chain perturbation bounds for the stationary distribution to the case where the perturbed chain is not irreducible. It further yields an improved perturbation bound in 1-norm. As a special case, Kemeny’s constant can be interpreted as the translated bias in an MRP with constant reward − 1 , which offers an intuitive explanation why it is a constant. • Presents a new identity for the bias in Markov reward processes. • Generalizes results for Markov chain perturbation from irreducible to arbitrary chains. • Gives a new improved perturbation bound in 1-norm for the stationary distribution. • Provides a new intuitive explanation why Kemeny’s constant is a constant.

Mixing times of a Burnside process Markov chain on set partitions