Markov Chain Monte Carlo Research Articles

Inference for Bayesian Nonparametric Models with Binary Response Data via Permutation Counting

Since the beginning of Bayesian nonparametrics in the early 1970s, there has been a wide interest in constructing models for binary response data. Such data arise naturally in problems dealing with bioassay, current status data and sensitivity testing, and are equivalent to left and right censored observations if the inputs are one-dimensional. For models based on the Dirichlet process, inference is possible via Markov chain Monte Carlo (MCMC) simulations. However, there exist multiple processes based on different principles, for which such MCMC-based methods fail. Examples include logistic Gaussian processes and quantile pyramids. These require MCMC for posterior inference given exact observations, and thus become intractable when the data comprise both left and right censored observations. Here we present a new importance sampling algorithm for nonparametric models given exchangeable binary response data. It can be applied to any model from which samples can be generated, or even only approximately generated. The main idea behind the algorithm is to exploit the symmetries introduced by exchangeability. Calculating the importance weights turns out to be equivalent to evaluating the permanent of a certain class of (0,1)-matrix, which we prove can be done in polynomial time by deriving an explicit algorithm.

Statistical inference for Nadarajah-Haghighi distribution under unified hybrid censored competing risks data

Nadarajah and Haghighi distribution (NHD) inferences problem has been discussed under unified hybrid censoring scheme (UHCS) in the existence of competing risks model. Competing risks model is defined by time-to-failure under more than one cause of failure, which can be dependent or independent. This study focuses on discussing the case of failure partially observed causes of failure competing risks model. We obtain various inferences: we first obtain the MLE, in addition, we construct approximate confidence intervals (ACIs). Second, we obtain the Bayes estimator via SELF and related highest posterior density (HPD) using Markov Chain Monte Carlo (MCMC). Finally, an electrical appliances data set and simulation studies have been analyzed for further illustrations.

An Outbursting Protostar: The Environment of L1251 VLA 6

Young protostars that undergo episodic accretion can provide insight into the impact on their circumstellar environments while matter is accreted from the disk onto the protostar. IRAS 22343+7501 is a four-component protostar system with one of those being a fading outbursting protostar, which was obseved with the Karl G. Jansky Very Large Array (VLA) and is referred to as L1251 VLA 6. Given the rarity of young stellar objects undergoing this type of accretion, L1251 VLA 6 can elucidate the fading phase of the post-outburst process. Here, we examine structure in the disk around L1251 VLA 6 at frequencies of 10 and 33 GHz with the VLA. We model the disk structure using Markov Chain Monte Carlo (MCMC). This method is then combined with a parametric ray-tracing code to generate synthetic model images of an axisymmetric disk, allowing us to characterize the radial distribution of dust in the system. The results of our MCMC fit show that the most probable values for the mass and radius are consistent with values typical of Class I objects. We find that the total mass of the disk is 0.070−0.2+0.031M☉ and investigate the conditions that could cause the accretion outburst. We conclude that the eruption is not caused by gravitational instability and consider alternative explanations and trigger mechanisms.

Fast Bayesian Inference of Reparameterized Gamma Process With Random Effects

In the field of reliability engineering, the gamma process plays an important role in modeling degradation processes. However, extracting lifetime information from product degradation observations has long been suffering from both ineffective modeling techniques and inefficient statistical inference methods. To overcome these challenges, we propose a reparameterized gamma process with random effects in this article. Compared with the classical gamma process, the proposed model has a more intuitive physical interpretation. In addition, statistical inference for the model can be readily done through the variational Bayesian algorithm. Combining with the Gauss–Hermite quadrature and the Laplace approximation, the algorithm yields closed-form variational posteriors for the proposed model. Its superiority over two other inference methods (expectation maximization and Monte Carlo Markov Chain) in terms of computational efficiency and estimation accuracy is demonstrated by simulation.

A Metropolized Adaptive Subspace Algorithm for High-Dimensional Bayesian Variable Selection

A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable selection. The MAdaSub algorithm is based on an independent Metropolis-Hastings sampler, where the individual proposal probabilities of the explanatory variables are updated after each iteration using a form of Bayesian adaptive learning, in a way that they finally converge to the respective covariates’ posterior inclusion probabilities. We prove the ergodicity of the algorithm and present a parallel version of MAdaSub with an adaptation scheme for the proposal probabilities based on the combination of information from multiple chains. The effectiveness of the algorithm is demonstrated via various simulated and real data examples, including a high-dimensional problem with more than 20,000 covariates.

Unveiling hidden companions in post-common-envelope binaries: A robust strategy and uncertainty exploration

Context. Some post-common-envelope binaries (PCEBs) are binary stars with short periods that exhibit significant period variations over long observational time spans. These eclipse timing variations (ETVs) are most likely to be accounted for by the presence of an unseen massive companion, potentially of planetary or substellar nature, and the light-travel time (LTT) effect. The existence of such companions challenges our current understanding of planetary formation and stellar evolution. Aims. In this study, our main objective is to describe the diversity of compatible nontransit companions around PCEBs and explore the robustness of the solutions by employing tools for uncertainty estimation. We select the controversial data of the QS Vir binary star, which previous studies have suggested hosts a planet. Methods. We employ a minimizing strategy, using genetic algorithms to explore the global parameter space followed by refinement of the solution using the simplex method. We evaluate errors through the classical Markov chain Monte Carlo (MCMC) approach and discuss the error range for parameters, considering the 1σ values obtained from the minimization. Results. Our results highlight the strong dependence of ETV models for close binaries on the dataset used, which leads to relatively loose constraints on the parameters of the unseen companion. We find that the shape of the O – C curve is influenced by the dataset employed. We propose an alternative method to evaluate errors on the orbital fits based on a grid search surrounding the best-fit values, obtaining a wider range of plausible solutions that are compatible with goodness-of-fit statistics. We also analyze how the parameter solutions are affected by the choice of the dataset, and find that this system continuously changes the compatible solutions as new data are obtained from eclipses. Conclusions. The best-fit parameters for QS Vir correspond to a low-mass stellar companion (57.71 Mjup ranging from ~40 to ~64 Mjup) on an eccentric orbit (e = 0.91−0.17+0.07) with a variety of potential periods (P = 16.69−0.42+0.47 yr.). Most solutions within 1σ exhibit regular orbits, despite their high eccentricity. Additional observations are required to accurately determine the period and other parameters of the unseen companion. In this context, we propose that a fourth body should not be modeled to fit the data, unless new observations considerably modify the computed orbital parameters. This methodology can be applied to other evolved binary stars suspected of hosting companions.

Is natural inflation in agreement with CMB data?

Natural inflation is a well-motivated model for the early universe in which an inflaton potential of the pseudo-Nambu-Goldstone form, V(ϕ) = Λ4[1 + cos(ϕ/f)], can naturally drive a cosmic accelerated epoch. This paper investigates the observational viability of the minimally and non-minimally coupled natural inflation scenarios in light of current Cosmic Microwave Background (CMB) observations. We find that a small and negative coupling of the field with gravity can alleviate the well-known observational discrepancies of the minimally coupled model. We perform a Monte Carlo Markov Chain analysis of the Planck 2018 CMB and BICEP/Keck Array B-mode polarization data to estimate how strong the coupling ξ should be to achieve concordance with data. We also briefly discuss the impact of these results on the physical interpretation of the natural inflation scenario.

Parallel tempering in trans-dimensional Bayesian inversion for seabed geoacoustic models with many parameters per layer

Trans-dimensional (trans-D) Bayesian inversion is a powerful tool for estimating seabed geoacoustic models from ocean-acoustic data, combining quantitative model selection with parameter/uncertainty estimation. The approach applies reversible-jump Markov-chain Monte Carlo methods to sample probabilistically over the number of seabed layers and the corresponding geoacoustic parameters for each layer. Layers are added and removed during sampling, referred to as birth and death moves, respectively, changing the dimension of the model. However, the probability of accepting birth and death moves can approach zero for formulations that include many parameters per layer. This paper considers the use of parallel tempering to mitigate this degradation in efficiency. Parallel tempering employs a series of interacting Markov chains with successfully-relaxed acceptance criteria, achieved by raising the likelihood to powers of 1/T, with T greater than or equal to 1 referred to as the sampling temperature. While only the T = 1 chain provides unbiased sampling, probabilistic interchange between chains provides a robust ensemble sampler that mixes more readily over the trans-D model space. The approach is illustrated for wide-angle reflection-coefficient inversion including compressional and shear parameters in the seabed model, resulting in a total of 5 unknown parameters per layer.

Length at life stages of the white shark Carcharodon carcharias in the western North Atlantic

Length at life stages of the white shark Carcharodon carcharias is not well known for most of the 9 populations of this species, including in the western North Atlantic (WNA). We analyzed length and maturity data by sex for 87 white sharks with sizes ranging 138-501 cm total length (TL), captured, studied, and released by OCEARCH during 2012-2022, off the US and Canadian Atlantic coasts. A binary logistic regression was used to estimate the length-at-maturity (L50) for the WNA white shark with a Bayesian statistical framework using a Markov chain Monte Carlo method for numerical integration. Different trials using noninformative and informative priors were tested. The posterior probability distribution for L50, steepness of the model (φ), and 95% credible intervals (CI) of the logistic model for females were L50 = 411.3 cm TL (CI: 390.8-432.6 cm TL) and φ = 10.5 (CI: 5.7-17.8) and for males were L50 = 334.9 cm TL (CI: 321.2-348.2 cm TL) and φ = 7.5 (CI: 4.2-12.4). These L50 values are somewhat smaller than previously reported sizes-at-maturity for both sexes of this species. An ordinal logistic regression allowed us to determine the probability of being in the various life stages (young-of-the-year, juvenile, and adult) at a particular size. Estimating the length at any life-history stage of white sharks along with age estimates is useful for determining the reproductive value of the population and ultimately for estimating the relative contribution (elasticity) of vital rates to population growth.

Hospital Volume of Elective Abdominal Aortic Aneurysm Repair as a Predictor of Mortality After Ruptured Abdominal Aortic Aneurysm Repair

Registry data suggest that centralising abdominal aortic aneurysm (AAA) surgery decreases the mortality rate after AAA repair. However, the impact of higher elective volumes on ruptured AAA (rAAA) repair associated mortality rates remains uncertain. This study aimed to examine associations between intact AAA (iAAA) repair volume and post-operative rAAA death. Using data from official national registries between 2015 - 2019, all iAAA and rAAA repairs were separately analysed across 10 public hospitals. The following were assessed: 30 day and 12 month mortality rate following open surgical repair (OSR) and endovascular aneurysm repair (EVAR). Associations between the 5 year hospital iAAA repair volumes (organised into tertiles) and rAAA associated mortality rate were analysed, regardless of treatment modality. Receiver operating characteristic (ROC) curves were generated to identify iAAA volume thresholds for decreasing the rAAA mortality rate. Subanalysis by treatment type was conducted. Threshold analysis was repeated with the Markov chain Monte Carlo (MCMC) procedure to confirm the findings. A total of 1 599 iAAAs (80.2% EVAR, 19.8% OSR) and 196 rAAAs (66.3% EVAR, 33.7% OSR) repairs were analysed. The median and interquartile range of the volume/hospital/year for all iAAA repairs were 39.2 (31.2, 47.4). The top volume iAAA tertile exhibited lower rAAA associated 30 day (odds ratio [OR] 0.374; p= .007) and 12 month (OR 0.264; p < .001) mortality rates. The ROC analysis revealed a threshold of 40 iAAA repairs/hospital/year (EVAR+ OSR) for a reduced rAAA mortality rate. Middle volume hospitals for open iAAA repair had reduced 30 day (OR 0.267; p= .033) and 12 month (OR 0.223; p= .020) mortality rates, with a threshold of five OSR procedures/year. The MCMC procedure found similar thresholds. No significant association was found between elective EVAR volumes and ruptured EVAR mortality. Higher iAAA repair volumes correlated with a lower rAAA mortality rate, particularly for OSR. The recommended iAAA repair threshold is 40 procedures/year and five procedures/year for OSR. These findings support high elective volumes for improving the rAAA mortality rate, especially for OSR.

Observation constraints on scalar field cosmological model in anisotropic universe

In this study, we have explored a scalar field cosmological model in the axially symmetric Bianchi type-I universe. In this study, our aim is to constrain the scalar field dark energy model in an anisotropic background. For this purpose, the explicit solution of the developed field equations for the model is determined and analyzed. Constraints on the cosmological model parameters are established utilizing Markov Chain Monte Carlo (MCMC) analysis and using the latest observational datasets of OHD, BAO, and Pantheon. For the combined dataset (OHD, BAO, and Pantheon), the best-fit values of Hubble and density parameters are estimated as [Formula: see text], [Formula: see text] [Formula: see text] and [Formula: see text]. The model shows a flipping nature and redshift transition occurs at [Formula: see text], and the present value of decelerated parameter is computed to be [Formula: see text] for the combined dataset. We have explored characteristics like the universe’s age, particle horizon, deceleration parameter, and jerk parameter. The dynamical properties, such as energy density [Formula: see text], scalar field pressure [Formula: see text], and equation of state parameter [Formula: see text], are analyzed and presented. We have also described the behavior of the scalar potential [Formula: see text] and scalar field. Furthermore, the authors also described the behavior of energy conditions in scalar-tensor cosmology. The scenario of the present accelerated expansion of the universe is described by the contribution of the scalar field.

BDFLUX: A new bounded domain model for quantifying vertical fluxes in streambeds using heat as a tracer

The use of heat as a tracer has become a widely used approach to estimate vertical streambed fluxes (VSFs). We present BDFLUX, a new bounded domain model that can be used as a rapid-screening tool to quantify VSFs and thermal properties of streambed sediments by analyzing on-site temperature–time series. BDFLUX uses a closed-form analytical solution that takes thermal advection and thermal conduction into account. BDFLUX, unlike other one-dimensional closed-form analytical solutions, does not assume a semi-infinite half-space. The initial and boundary conditions are described by arbitrary functions that can be directly determined by fitting the measured temperature–time series in the streambed at various depths. The particle swarm optimization (PSO) method and Markov Chain Monte Carlo (MCMC) method are used to estimate VSFs using temperature–time series observed at three depths. BDFLUX is validated using synthetic temperature–time series, demonstrating that it can perform well when the top and bottom boundary conditions are determined directly by the measured data. The capabilities of BDFLUX are further evaluated using laboratory and field data. The simulation results show that BDFLUX performed well in terms of interpreting laboratory experiments and field data, with a root mean square error as low as 0.059. The simulation of laboratory experiments shows that the MCMC method has a lower computational efficiency than PSO method. The magnitude of nonvertical flow components at a field site were quantified by analyzing the results of estimated VSFs in different vertical subdomains. Overall, BDFLUX improves one-dimensional heat analytical models in terms of assessing the magnitude of the nonvertical flow component in heterogeneous streambed sediments.

Estimating and Calibrating Markov Chain Sample Error Variance

Markov chain Monte Carlo (MCMC) methods are a powerful and versatile tool with applications spanning a wide spectrum of fields, including Bayesian inference, computational biology, and physics. One of the key challenges in applying MCMC algorithms is to deal with estimation error. The main result in this article is a closed form, non-asymptotic solution for the sample error variance of a single MCMC&amp;nbsp; estimate. Importantly, this result assumes that the state-space is finite and discrete. We demonstrate with examples how this result can help estimate and calibrate MCMC estimation error variance in the more general case, when the state-space is continuous and/or unbounded.

A new factor analysis model for factors obeying a Gamma distribution

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

Shear capacity model of rectangular RC columns based on Bayesian update

Reinforced concrete (RC) columns are function as structural member resisting vertical loading. The combined effects of vertical loading and transverse loading might induce shear failure of RC columns, posing a significant threat to the structure's integrity. While the accuracy of existing models to determine the shear strength of RC column is crucial for design, there is a need for further refinement. In this context, a study introduces a probabilistic shear capacity model based on the truss-arch theory and incorporating the Bayesian theory Monte Carlo Markov Chain (MCMC) method. This model delineates the shear contribution into four distinct components: concrete, stirrup, axial compression force and longitudinal reinforcement longitudinal reinforcement in the middle of the section parallel to the loading direction. A database, comprising 233 RC column specimen sets, facilitates the model's regression analysis. Calibration is achieved against the density distribution and confidence intervals of the posterior parameters. When set against four established models, the new proposal offers a mean value closely aligned with experimental data and showcases reduced variance. To substantiate the shear mechanism of the proposed model, a thorough contribution of each shear component's contribution is made with those in four existing models: Sezen, ACI 318, Priestley, and GB50010. While the Sezen and ACI 318 models recognize the shear contributions of concrete and stirrup, the Priestley and GB50010 models extend to factor in the beneficial impact of the axial compression force component. Comparative analysis underscores the superior predictive capability of the newly proposed model.

Recursive nearest neighbor co‐kriging models for big multi‐fidelity spatial data sets

AbstractBig datasets are gathered daily from different remote sensing platforms. Recently, statistical co‐kriging models, with the help of scalable techniques, have been able to combine such datasets by using spatially varying bias corrections. The associated Bayesian inference for these models is usually facilitated via Markov chain Monte Carlo (MCMC) methods which present (sometimes prohibitively) slow mixing and convergence because they require the simulation of high‐dimensional random effect vectors from their posteriors given large datasets. To enable fast inference in big data spatial problems, we propose the recursive nearest neighbor co‐kriging (RNNC) model. Based on this model, we develop two computationally efficient inferential procedures: (a) the collapsed RNNC which reduces the posterior sampling space by integrating out the latent processes, and (b) the conjugate RNNC, an MCMC free inference which significantly reduces the computational time without sacrificing prediction accuracy. An important highlight of conjugate RNNC is that it enables fast inference in massive multifidelity data sets by avoiding expensive integration algorithms. The efficient computational and good predictive performances of our proposed algorithms are demonstrated on benchmark examples and the analysis of the High‐resolution Infrared Radiation Sounder data gathered from two NOAA polar orbiting satellites in which we managed to reduce the computational time from multiple hours to just a few minutes.

A mathematical model for evaluating the impact of nonpharmaceutical interventions on the early COVID-19 epidemic in the United Kingdom

The coronavirus disease 2019 (COVID-19) presents a severe and urgent threat to global health. In response to the COVID-19 pandemic, many countries have implemented nonpharmaceutical interventions (NPIs), including national workplace and school closures, personal protection, social distancing, contact tracing, testing, home quarantine, and isolation. To evaluate the effectiveness of these NPIs in mitigating the spread of early COVID-19 and predict the epidemic trend in the United Kingdom, we developed a compartmental model to mimic the transmission with time-varying transmission rate, contact rate, disease-induced mortality rate, proportion of quarantined close contacts, and hospitalization rate. The model was fitted to the number of confirmed new cases and daily number of deaths in five stages with a Markov Chain Monte Carlo method. We quantified the effectiveness of NPIs and found that if the transmission rate, contact rate, and hospitalization rate were approximately equal to those in the second stage of the most strict NPIs, and the proportion of quarantined close contacts increased by 3%, then the epidemic would die out as early as January 12, 2021, with around 1,533,000 final cumulative number of confirmed cases, and around 55,610 final cumulative number of deaths.

Beyond [formula omitted]CDM with [formula omitted]CDM: Criticalities and solutions of Padé Cosmography

Recently, cosmography emerged as a valuable tool to effectively describe the vast amount of astrophysical observations without relying on a specific cosmological model. Its model-independent nature ensures a faithful representation of data, free from theoretical biases. Indeed, the commonly assumed fiducial model, the ΛCDM, shows some shortcomings and tensions between data at late and early times that need to be further investigated. In this paper, we explore an extension of the standard cosmological model by adopting the f(z)CDM approach, where f(z) represents the cosmographic series characterizing the evolution of recent universe driven by dark energy. To construct f(z), we take into account the Padé series, since this rational polynomial approximation offers a better convergence at high redshifts than the standard Taylor series expansion. Several orders of such an approximant have been proposed in previous works, here we want to answer the questions: What is the impact of the cosmographic series choice on the parameter constraints? Which series is the best for the analysis? So, we analyze the most promising ones by identifying which order is preferred in terms of stability and goodness of fit. Theoretical predictions of the f(z)CDM model are obtained by the Boltzmann solver code and the posterior distributions of the cosmological and cosmographic parameters are constrained by a Monte Carlo Markov Chains analysis. We consider a joint data set of cosmic microwave background temperature measurements from the Planck collaboration, type Ia supernovae data from the latest Pantheon+ sample, baryonic acoustic oscillations and cosmic chronometers data. In conclusions, we state which series can be used when only late time data are used, while which orders has to be considered in order to achieve the necessary stability when large redshifts are considered.

Multivariate Stochastic Volatility Modeling via Integrated Nested Laplace Approximations: A Multifactor Extension

This study introduces a multivariate extension to the class of stochastic volatility models, employing integrated nested Laplace approximations (INLA) for estimation. Bayesian methods for estimating stochastic volatility models through Markov Chain Monte Carlo (MCMC) can become computationally burdensome or inefficient as the dataset size and problem complexity increase. Furthermore, issues related to chain convergence can also arise. In light of these challenges, this research aims to establish a computationally efficient approach for estimating multivariate stochastic volatility models. We propose a multifactor formulation estimated using the INLA methodology, enabling an approach that leverages sparse linear algebra and parallelization techniques. To evaluate the effectiveness of our proposed model, we conduct in-sample and out-of-sample empirical analyses of stock market index return series. Furthermore, we provide a comparative analysis with models estimated using MCMC, demonstrating the computational efficiency and goodness of fit improvements achieved with our approach.

Probabilistic fatigue stiffness variation of angle-ply GFRP composites considering stress ratio effect

Fiber-reinforced polymer (FRP) composites are frequently used in bridges, wind power installations, and marine floating structures, and there is a growing interest in understanding their fatigue behavior. However, due to a considerable dispersion of the fatigue properties of FRP composites, reliable tools for probabilistic prediction of the fatigue stiffness are required. Thus, in this work, it is proposed a method that uses Bayesian inference and Markov Chain Monte Carlo (MCMC) simulations to estimate the degradation of the stiffness in FRP composites. This methodology is suggested not only to predict the fatigue residual stiffness, but also to consider the reliability of such predictions. Currently, the existing models for stiffness degradation in FRP composites need to fit the model parameters separately under different stress ratios. To address this, a correction term is proposed to describe the relationship between the stress level, stress ratio, fatigue cycles, and residual stiffness. The results achieved validate and prove the effectiveness of the suggested stiffness model, which incorporates four material parameters to calculate the residual fatigue stiffness of FRP composites.