Markov Chain Monte Carlo Research Articles

Constraining a disformal Schwarzschild black hole in DHOST theories with the orbit of the S2 star

With the observed data of the S2 orbit around the black hole Sgr A∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^*$$\\end{document} and the Markov Chain Monte Carlo method, we make a constraint on parameters of a disformal Schwarzschild black hole in quadratic degenerate higher-order scalar-tensor (DHOST) theories. This black hole belongs to a class of non-stealth solutions and owns an extra disformal parameter described the deviation from general relativity. Our results show that the best fit value of the disformal parameter is positive. However, in the range of 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\sigma $$\\end{document}, we also find that general relativity remains to be consistent with the observation of the S2 orbit.

Modeling the 2014-2015 Vesicular Stomatitis Outbreak in the United States Using an SEIR-SEI Approach.

Vesicular stomatitis (VS) is a vector-borne livestock disease caused by the vesicular stomatitis New Jersey virus (VSNJV). This study presents the first application of an SEIR-SEI compartmental model to analyze VSNJV transmission dynamics. Focusing on the 2014-2015 outbreak in the United States, the model integrates vertebrate hosts and insect vector demographics while accounting for heterogeneous competency within the populations and observation bias in documented disease cases. Key epidemiological parameters were estimated using Bayesian inference and Markov chain Monte Carlo (MCMC) methods, including the force of infection, effective reproduction number (Rt), and incubation periods. The model revealed significant underreporting, with only 10-24% of infections documented, 23% of which presented with clinical symptoms. These findings underscore the importance of including competence and imperfect detection in disease models to depict outbreak dynamics and inform effective control strategies accurately. As a baseline model, this SEIR-SEI implementation is intended to serve as a foundation for future refinements and expansions to improve our understanding of VS dynamics. Enhanced surveillance and targeted interventions are recommended to manage future VS outbreaks.

Enhancing battery electrochemical-thermal model accuracy through a hybrid parameter estimation framework

Electrochemical-thermal models offer profound insight into the internal state of batteries, demonstrating significant potential in energy storage. However, model complexity makes accurate parameter acquisition challenging. This study proposes a novel hybrid parameter estimation framework for effective parameterisation of battery electrochemical-thermal models. A high-fidelity reduced-order electrochemical-thermal model was established to accelerate the simulation of the entire time-domain process. A global sensitivity analysis of the model parameters was conducted, comprehensively evaluating their impact on simulated voltage and temperature. Highly sensitive parameters were categorised into static and time-dependent dynamic estimation groups for hierarchical estimation. A deep learning method was applied to generate preliminary parameter estimates to accelerate the convergence of estimation process. Subsequently, a genetic algorithm was employed to optimise the preliminary estimates of static parameters. A full temporal domain estimation was conducted using Markov Chain Monte Carlo methods for time-dependent dynamic parameters. The experimental data covers six dynamic and nine constant current conditions to validate the proposed method's feasibility. After parameter estimation, the proposed method reduces the comprehensive normalised root mean square error of voltage and temperature by up to 80.36% compared to four conventional methods. The minimum average absolute errors of voltage and temperature under constant and dynamic current conditions are 10.63 mV and 0.10 °C, respectively. The proposed method provides new insights for the parameterisation of battery models.

The Effect of Plant-Based Protein Ingestion on Athletic Ability in Healthy People-A Bayesian Meta-Analysis with Systematic Review of Randomized Controlled Trials.

Plant-based protein supplements are increasingly popular, yet their efficacy in enhancing athletic performance compared to animal protein, insect protein, or other protein types remains under investigation. This study aimed to assess the effectiveness of plant-based protein on athletic abilities such as muscle strength, endurance performance, and muscle protein synthesis (MPS) rate and compare it to no- or low-protein ingestion and non-plant protein sources. Randomized controlled trials (RCTs) evaluating the beneficial and harmful effects of plant-based protein ingestion on athletic ability in healthy individuals were considered. A systematic search of six databases yielded 2152 studies, which were screened using the Covidence systematic review tool. Thirty-one studies were included for meta-analysis after independent selection, data extraction, and risk of bias assessment by two reviewers. The meta-analysis employed a Bayesian approach using the Markov chain Monte Carlo (MCMC) method through a random-effects model. The results demonstrated that plant-based protein supplements provided greater benefits for athletic performance in healthy individuals compared to the no- or low-protein ingestion group [μ(SMD): 0.281, 95% CI: 0.159 to 0.412; heterogeneity τ: 0.18, 95% CI: 0.017 to 0.362]. However, when compared to other types of protein, plant-based protein ingestion was less effective in enhancing athletic ability [μ(SMD): -0.119, 95% CI: -0.209 to -0.028; heterogeneity τ: 0.076, 95% CI: 0.003 to 0.192]. A subgroup analysis indicated significant improvements in muscle strength and endurance performance in both young and older individuals consuming plant-based protein compared to those with no- or low-protein ingestion. Nonetheless, other protein types showed greater benefits in muscle strength compared to plant-based protein [μ(SMD): -0.133, 95% CI: -0.235 to -0.034; heterogeneity τ: 0.086, 95% CI: 0.004 to 0.214]. In conclusion, while plant-based protein ingestion demonstrates superior efficacy compared to low- or no-protein ingestion, it is not as effective as other protein types such as whey, beef, or milk protein in enhancing athletic performance in healthy individuals. Registration: Registered at the International Prospective Register of Systematic Reviews (PROSPERO) (identification code CRD42024555804).

Inferring astrophysical parameters using the 2D cylindrical power spectrum from reionisation

Abstract Enlightening our understanding of the first galaxies responsible for driving reionisation 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 (MCMC) 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 hr observation of the 21-cm signal using the SKA 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 marginalised uncertainties on individual astrophysical parameters by up to ∼30 − 40 per cent irrespective of the foreground mitigation strategy. Primarily, these improvements stem from how the 2D PS distinguishes between the transverse, k⊥, and redshift dependent, k∥ information which enables greater sensitivity to the complex reionisation morphology.

Constraining the variable generalized Chaplygin gas model in matter creation cosmology

We explore the variable generalized Chaplygin gas (VGCG) model in the theory of matter creation cosmology within the framework of a spatially homogeneous and isotropic flat Friedmann—Lemaître—Robertson—Walker space-time. Matter creation cosmology is based on reinterpretation of the energy–momentum tensor in Einstein’s field equations. This creation corresponds to an irreversible energy flow from the gravitational field to the created matter constituents. The variable Chaplygin gas (VCG) is also studied as a particular solution. We use the Markov chain Monte Carlo method to constrain the free parameters of three models, namely, Lambda-Cold-Dark matter (ΛCDM), VGCG and VCG models with and without matter creation from the latest observational data from baryon acoustic oscillations, cosmic chronometer, type Ia supernovae (Pantheon) including gamma-ray bursts, quasars and the local measurement of H 0 from R21 data. Two different combinations of dataset provide a fairly tight constraint on the parameters of the ΛCDM, VGCG and VCG models. The present values of various cosmological parameters are obtained, which are very close to the ΛCDM model. Furthermore, we perform stability analysis, Bayesian evidence analysis and information criteria analysis for these models through studying the sound speed, Bayes factor, and Akaike information criteria (AIC) and Bayesian information criteria (BIC) selection criteria. The values of sound speed for VGCG and VCG models shows that both the models are stable. According to AIC, it is observed that VGCG and VCG models with matter creation are supported considerably less by current observations, while BIC shows that these models are not favoured by observational data.

A quantile-regression approach to bivariate longitudinal joint modeling

Joint modeling of longitudinal outcomes and time-to-event data has become a major re- search interest in the last thirty years. A joint model is useful since it helps (i) to under- stand the evolution of the outcome(s) of interest over time, (ii) to understand the effects of the outcomes on the time of occurrence of some event(s) of interest (e.g. death/relapse), and (iii) to study the effects of the time-varying and time-invariant predictors on the longitudinal and time-to-event process. Traditional linear mixed models are routinely used for modeling the longitudinal process. However, for non-Gaussian/skewed outcomes it is more appealing to use quantile-regression models since such models do not assume any specific probability distribution for the outcomes. In this article, we present a bivariate quantile-regression approach for jointly modeling longitudinal process and time-to-event. In a Bayesian setting we consider an Asymmetric Laplace Distribution (ALD) for modeling different quantiles of the outcomes, and a semi-parametric Proportional Hazards (PH) model for time-to-event. Model parameters are estimated using Markov chain Monte Carlo (MCMC) algorithm, and we discuss the computational complexities through several simulation studies. Our numerical studies illustrate the usefulness of our model over the other traditional models. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 111-130.

FLRW cosmology in metric-affine F(R,Q) gravity* *Supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan (AP14870191)

We investigated some Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological models in the context of metric-affine gravity, as proposed in [arXiv: 1205.5266v6]. Here, R and Q are the curvature and nonmetricity scalars using non-special connections, respectively. We obtained the modified field equations using a flat FLRW metric. We then found a connection between the Hubble constant , density parameter , and other model parameters in two different situations involving scalars u and w. Next, we used new observational datasets, such as the cosmic chronometer (CC) Hubble and Pantheon SNe Ia datasets, to determine the optimal model parameter values through a Markov chain Monte Carlo (MCMC) analysis. Using these best-fit values of the model parameters, we discussed the results and behavior of the derived models. Further, we discussed the Akaike information criterion (AIC) and Bayesian information criterion (BIC) for the derived models in the context of the Lambda cold dark matter (ΛCDM). We found that the geometrical sector dark equation of state parameter behaves just like a dark energy candidate. We also found that both models are transit phase models. Model-I approaches the ΛCDM model in the late-time universe, whereas Model-II approaches quintessence scenarios.

Joint modeling of varying-disease-state longitudinal ordinal data and time-to-event data with application to alzheimer’s disease

Joint models are routinely used in clinical trials to fit longitudinal and survival data simulta- neously in an integrated fashion. We propose a joint model that incorporates state-specific trajectories for fitting the longitudinal ordinal response and time-to-event data, focusing on its application to Alzheimer’s Disease (AD). The proposed joint model effectively captures the fluctuating cognitive conditions observed before and after the transition between two disease states. By integrating longitudinal data into the survival sub-model through shared trajectories, we can improve the fit of the survival data. A Markov chain Monte Carlo (MCMC) sampling algorithm is developed to carry out Bayesian computation. A variation of the Deviance Information Criterion is developed to assess the fit of each component of the joint model as well as the contribution of the longitudinal data in fitting the survival data. A variation of the concordance (C) index is further derived to assess the discriminatory and predictive performance of the longitudinal sub-model. An in-depth analysis of the real data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database is carried out to demonstrate the applicability of the proposed methodology. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 49-73.

Are intersectoral GDP contributions similar with nearby states? A semi-model-based spatial cluster analysis

ABSTRACT Intersectoral Gross Domestic Product (GDP) contributions reflect economic development in different industries. A good understanding of clusters of intersectoral GDP contributions among different subregions plays a vital role in making local policies and building economic development strategies. We propose a semi-model-based clustering method, i.e, a Markov random field constraint mixture of finite mixtures model to tackle this issue. Our proposed method has the advantage of 1) data-driven determination of the final number of clusters and 2) allowing for both locally spatially contiguous clusters and globally discontiguous clusters. Posterior inference is performed with an efficient Markov chain Monte Carlo (MCMC) algorithm. We demonstrate the performance of the proposed method using both simulation studies and a real-world example where intersectoral GDP contribution of year 2019 data, obtained from the U.S. Bureau of Economic Analysis, is studied.

Self-correlated spatial random variables: From an auto- to a sui- model respecification

This paper marks the 50-year publication anniversary of Besag's seminal spatial auto- models paper. His classic article synthesizes generic autoregressive specifications (i.e., a response variable appears on both sides of a regression equation and/or probability function equal sign) for the following six popular random variables: normal, logistic (i.e., Bernoulli), binomial, Poisson, exponential, and gamma. Besag dismisses these last two while recognizing failures of both as well as the more scientifically critical counts-oriented auto-Poisson. His initially unsuccessful subsequent work first attempted to repair them (e.g., pseudo-likelihood estimation), and then successfully revise them within the context of mixed models, formulating a spatially structured random effects term that effectively and efficiently absorbs and accounts for spatial autocorrelation in geospatial data. One remaining weakness of all but the auto-normal is a need to resort to Markov chain Monte Carlo (MCMC) techniques for legitimate estimation purposes. Recently, Griffith succeeded in devising an innovative uniform distribution genre—sui-uniform random variables—that accommodates spatial autocorrelation, too. Its most appealing feature is that, by applying two powerful mathematical statistical theorems (i.e., the probability integral transform, and the quantile function), it redeems Besag's auto- model failures. This paper details conversion of Besag's initial six modified variates, exemplifying them with both simulation experiments and publicly accessible real-world georeferenced data. The principal outcome is valuable spatial statistical advancements, with special reference to Moran eigenvector spatial filtering.

Bayesian analysis of multivariate mixed longitudinal ordinal and continuous data

SummaryMultivariate longitudinal ordinal and continuous data exist in many scientific fields. However, it is a rigorous task to jointly analyse them due to the complicated correlated structures of those mixed data and the lack of a multivariate distribution. The multivariate probit model, assuming there is a multivariate normal latent variable for each multivariate ordinal data, becomes a natural modeling choice for longitudinal ordinal data especially for jointly analysing with longitudinal continuous data. However, the identifiable multivariate probit model requires the variances of the latent normal variables to be fixed at 1, thus the joint covariance matrix of the latent variables and the continuous multivariate normal variables is restricted at some of the diagonal elements. This constrains to develop both the classical and Bayesian methods to analyse mixed ordinal and continuous data. In this investigation, we proposed three Markov chain Monte Carlo (MCMC) methods: Metropolis–Hastings within Gibbs algorithm based on the identifiable model, and a Gibbs sampling algorithm and parameter‐expanded data augmentation based on the constructed non‐identifiable model. Through simulation studies and a real data application, we illustrated the performance of these three methods and provided an observation of using non‐identifiable model to develop MCMC sampling methods.

Cosmological constraints on a dynamical dark energy model in F(Q) gravity

Extended teleparallel gravity, characterized by function F(Q), where Q is the non-metricity scalar, is one of the most promising approaches to general relativity. In this paper, we reexamine a specific dynamical dark energy model, which is indistinguishable from the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model at the present time and exhibits a special event in the future, within F(Q) gravity. To constrain the free parameters of the model, we perform Markov chain Monte Carlo (MCMC) analysis, using the last data from Pantheon+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Pantheon}^{+}$$\\end{document} and the latest measurements of the H(z) parameter, combined. On the basis of this analysis, we find that our dynamical dark energy model, in the context of F(Q) gravity, lies in the quintessence regime rather than in the phantom regime, as in the case of general relativity. Furthermore, this behavior affects the future expansion of the Universe, as it becomes decelerating at a 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\sigma $$\\end{document} confidence level for z<-0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z<-0.5$$\\end{document}, showing a bounce at zB≈-0.835\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z_{\ ext {B}}\\approx -0.835$$\\end{document}. We support our conclusion with a cosmographic analysis.

Late-time cosmology in [formula omitted] gravity: Analytical solutions and observational fits

In this study, we examined the late-time cosmic expansion of the universe within the framework of f(Q,Lm) gravity, where Q denotes the non-metricity and Lm represents the matter Lagrangian. We analyzed a linear f(Q,Lm) model of the form f(Q,Lm)=−αQ+2Lm+β. Using MCMC methods, we constrained the model parameters H0, α, and β with various datasets, including H(z), Pantheon+SH0ES, and BAO data. For the H(z) dataset, we found H0=67.90±0.66, α=0.1072−0.0069+0.0054, and β=−1988.2±1.0. For the Pantheon+SH0ES dataset, H0=70.05±0.68, α=0.0916−0.0033+0.0028, and β=−1988.3±1.0. For the BAO dataset, H0=68.1±1.0, α=0.1029−0.0052+0.0041, and β=−1988.24±0.99. Moreover, the energy density remains positive and approaches zero in the distant future, and the deceleration parameter indicates a transition from deceleration to acceleration, with transition redshifts of zt=0.60, zt=0.78, and zt=0.66 for the respective datasets. These findings align with previous observational studies and contribute to our understanding of the universe’s expansion dynamics.

Molecular Evolutionary Analyses of the Fusion Genes in Human Parainfluenza Virus Type 4.

The human parainfluenza virus type 4 (HPIV4) can be classified into two distinct subtypes, 4a and 4b. The full lengths of the fusion gene (F gene) of 48 HPIV4 strains collected during the period of 1966-2022 were analyzed. Based on these gene sequences, the time-scaled evolutionary tree was constructed using Bayesian Markov chain Monte Carlo methods. A phylogenetic tree showed that the first division of the two subtypes occurred around 1823, and the most recent common ancestors of each type, 4a and 4b, existed until about 1940 and 1939, respectively. Although the mean genetic distances of all strains were relatively wide, the distances in each subtype were not wide, indicating that this gene was conserved in each subtype. The evolutionary rates of the genes were relatively low (4.41 × 10-4 substitutions/site/year). Moreover, conformational B-cell epitopes were predicted in the apex of the trimer fusion protein. These results suggest that HPIV4 subtypes diverged 200 years ago and the progenies further diverged and evolved.

Development and validation of a risk prediction model for short-term progression of carotid atherosclerosis among early middle age adults

AimWe aimed at creating and validating a prognostic model incorporating easily accessible clinical and laboratory parameters to forecast the likelihood of short-term progression of carotid atherosclerosis. MethodsA prediction model was developed and validated for carotid plaque progression within 2 years in an early middle-age population in China. Progression was defined as the new appearance of carotid plaque or stenosis among participants who had normal carotid status at baseline. Leveraging data from a health check-up chain, predictors were identified using statistical methods including stepwise logistic regression, Markov Chain Monte Carlo (MCMC) simulation, random forest analysis and least absolute shrinkage selection operator (Lasso). Model performance was assessed. Bootstrap internal validation, validation on another check-up population and subgroup analysis were also conducted. ResultsAmong 7765 participants, predictors including age, diastolic blood pressure, uric acid levels, high-density lipoprotein cholesterol (HDL-C), and low-density lipoprotein cholesterol (LDL-C) were identified for carotid plaque progression in 2 years. The developed prediction model demonstrated good discrimination (AUC = 0.755, 95%CI:0.736–0.774) and calibration ability (slope = 0.922 and interception = 0.007) among development data, as well as among validation data (AUC = 0.759, 95%CI:0.674–0.770; slope = 1.076 and intercept = −0.014). Internal validation using bootstrap method yielded an adjusted AUC of 0.753. The model's performance remained consistent across different subgroups. ConclusionsOur study presents a validated risk prediction model for carotid plaque progression in an early middle age population, offering a valuable tool for early identification and monitoring of cardiovascular risks. The model's robustness and applicability across different subgroups highlight its potential utility in preemptive cerebrovascular and cardiovascular disease management.

Quantum dynamical Hamiltonian Monte Carlo

One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine-learning workflows. A ubiquitous problem in machine-learning workflows is sampling from probability distributions that we only have access to via their log probability. To this end, we extend the well-known Hamiltonian Monte Carlo (HMC) method for Markov chain Monte Carlo (MCMC) sampling to leverage quantum computation in a hybrid manner as a proposal function. Our new algorithm, Quantum Dynamical Hamiltonian Monte Carlo (QD-HMC), replaces the classical symplectic integration proposal step with simulations of quantum-coherent continuous-space dynamics on digital or analog quantum computers. We show that QD-HMC maintains key characteristics of HMC, such as maintaining the detailed balanced condition with momentum inversion, while also having the potential for polynomial speedups over its classical counterpart in certain scenarios. As sampling is a core subroutine in many forms of probabilistic inference, and MCMC in continuously parametrized spaces covers a large class of potential applications, this work widens the areas of applicability of quantum devices. Published by the American Physical Society 2024

Site-specific cancer mortality after low level exposure to ionizing radiation: Findings from an update of the International Nuclear Workers Study (INWORKS).

A major update to the International Nuclear Workers Study was undertaken that allows us to report updated estimates of associations between radiation and site-specific solid cancer mortality. A cohort of 309,932 nuclear workers employed in France, the United Kingdom, and United States were monitored for external radiation exposure and associations with cancer mortality were quantified as the excess relative rate (ERR) per gray (Gy) using a maximum likelihood and a Markov chain Monte Carlo method (to stabilize estimates via a hierarchical regression). The analysis included 28,089 deaths due to solid cancer, the most common being lung, prostate, and colon cancer. Using maximum likelihood, positive estimates of ERR per Gy were obtained for stomach, colon, rectum, pancreas, peritoneum, larynx, lung, pleura/mesothelioma, bone and connective tissue, skin, prostate, testis, bladder, kidney, thyroid, and residual cancers; negative estimates of ERR per Gy were found cancers of oral cavity and pharynx, esophagus, and ovary. A hierarchical model stabilized site-specific estimates of association, including for lung (ERR per Gy=0.65; 95% credible interval [CrI]: 0.24, 1.07), prostate (ERR per Gy=0.44; 95% CrI: -0.06, 0.91), and colon cancer (ERR per Gy=0.53; 95% CrI: -0.07, 1.11). The results contribute evidence regarding associations between low dose radiation and cancer.

Learning variational autoencoders via MCMC speed measures

Variational autoencoders (VAEs) are popular likelihood-based generative models which can be efficiently trained by maximising an evidence lower bound. There has been much progress in improving the expressiveness of the variational distribution to obtain tighter variational bounds and increased generative performance. Whilst previous work has leveraged Markov chain Monte Carlo methods for constructing variational densities, gradient-based methods for adapting the proposal distributions for deep latent variable models have received less attention. This work suggests an entropy-based adaptation for a short-run metropolis-adjusted Langevin or Hamiltonian Monte Carlo (HMC) chain while optimising a tighter variational bound to the log-evidence. Experiments show that this approach yields higher held-out log-likelihoods as well as improved generative metrics. Our implicit variational density can adapt to complicated posterior geometries of latent hierarchical representations arising in hierarchical VAEs.

Generalized fiducial inference for the GEV change-point model

Generalized extreme value (GEV) distribution is used to analyse the maximum from a block of data. It is very useful to describe the unusual event rather than the usual event. In this paper, we propose a change-point detection procedure for GEV distribution based on generalized fiducial inference. The fiducial distribution of the change-point location is constructed. Meanwhile, Markov Chain Monte Carlo method combined with Gibbs sampling and the Metropolis–Hastings algorithm is utilised to estimate the location of the change point and its confidence interval. In addition, the generalized fiducial factor is used to test whether there is a change point. Simulation results show that the proposed generalized fiducial method performs better in accuracy, robustness and the length of confidence intervals. Finally, we apply the proposed method to the annual maximum rainfall data in Beijing.