Markov Chain Monte Carlo Algorithm Research Articles

An Evaluation of the Sensitivity of a Source Term Estimation Methodology of Sensor Configuration in an Urban-like Environment

Identifying unknown sources of air pollutants is vital for protecting public health, especially in cases involving the emission of toxic substances. The efficiency of this process depends highly on the accuracy of Source Term Estimation (STE) methods and the availability of robust measurements. Therefore, it is important to examine how sensor network characteristics affect STE accuracy. This study investigates the impact of different sensor configurations on STE results for a stationary point source in a complex, urban-like environment. The STE methodology employs the Metropolis–Hastings Markov Chain Monte Carlo (MCMC) algorithm alongside numerical simulations of a Computational Fluid Dynamics (CFD) model. The STE algorithm is applied across several sensor configurations in three distinct release scenarios and real sensor observations from the Michelstadt wind tunnel experiment, assessing both the number of sensors used and the agreement between measured and modeled concentrations. In general, the results indicate that increasing the number of sensors and the model’s accuracy improves the source parameters estimations. However, there is a specific number of sensors in each release scenario where STE outcomes from randomly selected, high-accuracy, and low-accuracy sensors converge to similar solutions. Overall, the findings provide valuable information for designing sensor configurations in urban areas.

AutoGFI: Streamlined Generalized Fiducial Inference for Modern Inference Problems in Models with Additive Errors

The concept of fiducial inference was introduced by R. A. Fisher in the 1930s to address the perceived limitations of Bayesian inference, particularly the need for subjective prior distributions in cases with limited prior information. However, Fisher’s fiducial approach lost favor due to complications, especially in multi-parameter problems. With renewed interest in fiducial inference in the 2000s, generalized fiducial inference (GFI) emerged as a promising extension of Fisher’s ideas, offering new solutions for complex inference challenges. Despite its potential, GFI’s adoption has been hindered by demanding mathematical derivations and complex implementation requirements, such as Markov Chain Monte Carlo (MCMC) algorithms. This paper introduces AutoGFI, a streamlined variant of GFI designed to simplify its application across various inference problems with additive noise. AutoGFI ’s accessibility lies in its simplicity—requiring only a fitting routine—making it a feasible option for a wider range of researchers and practitioners. To demonstrate its efficacy, AutoGFI is applied to three challenging problems: tensor regression, matrix completion, and network cohesion regression. These case studies showcase AutoGFI ’s competitive performance against specialized solutions, highlighting its potential to broaden the application of GFI in practical domains, ultimately enriching the statistical inference toolkit.

Convergence speed and approximation accuracy of numerical MCMC

Abstract When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how the perturbation of MCMC affects the convergence speed and approximation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has fast convergence speed and high approximation accuracy as well. Our convergence analysis is conducted under either the Wasserstein metric or the $\chi^2$ metric, both are widely used in the literature. The results can be extended to obtain non-asymptotic error bounds for MCMC estimators. We demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis, Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally, we present some simple numerical examples to verify our theoretical claims.

Lack of emission lines in the optical spectra of SAX J1808.4–3658 during reflaring of the 2019 outburst

Aims. We present spectroscopy of the accreting X-ray binary and millisecond pulsar SAX J1808.4–3658. These observations are the first to be obtained during a reflaring phase. We collected spectroscopic data during the beginning of the reflaring of the 2019 outburst and compared them to previous datasets taken at different epochs, both of the same outburst and across the years. To this end, we also present spectra of the source taken during quiescence in 2007, one year before the next outburst. Methods. We made use of data taken by the Very Large Telescope (VLT) X-shooter spectrograph on August 31, 2019, three weeks after the outburst peak. For flux calibration, we used photometric data taken during the same night by the 1m telescopes from the Las Cumbres Observatory network that are located in Chile. We compare our spectra to the quiescent data taken by the VLT-FORS1 spectrograph in September, 2007. We inspected the spectral energy distribution by fitting our data with a multicolored accretion-disk model and sampled the posterior probability density function for the model parameters with a Markov chain Monte Carlo (MCMC) algorithm. Results. We find the optical spectra of the 2019 outburst to be unusually featureless, with no emission lines present despite the high resolution of the instrument. Fitting the UV-optical spectral energy distribution with a disk plus irradiated star model results in a very large value for the inner disk radius of ∼5130 ± 240 km, which could suggest that the disk was emptied of material during the outburst, possibly accounting for the emission-less spectra. Alternatively, the absence of emission lines could be due to a significant contribution of the jet emission at optical wavelengths.

Parameter recovery of skew multidimensional multiple-group item response models (MGM-MIRT): a comparison of MCMC algorithms and assessment of effects of interest

Multidimensional item response theory (MIRT) models are powerful tools to analyse item response data. Most of them rely on the assumption that the latent traits are normally distributed. However, when such assumption does not hold, the item and the latent traits estimates can be inaccurate. This paper deals, in a very detailed way, through simulation studies, with the utility of the class of the MIRT models developed by Padilla et al. [Multidimensional multiple-group IRT models with skew normal latent trait distributions. J Multivariate Anal 2018;167:250–268], where the multivariate skew-normal distribution under the centred parameterization is employed for modelling the latent traits. The impact of important factors of interest on the parameter recovery is investigated. Such factors are the number of subjects, number of items, number of groups and asymmetry level. In a general way, the results show that our approach outperforms some traditional models when the latent traits follow asymmetric distributions. In addition, different Monte Carlo Markov Chain (MCMC) algorithms for parameter estimation are compared, by considering two schemes of data augmentation and a proposal to speed up their convergence, based on approaches found in the literature, for binary regression models. Guidelines are provided for the correct using of Bayesian inferential methods for the MIRT models.

Multimodal reconstruction of TbCo thin-film structure with Bayesian analysis of polarized neutron reflectivity

Bayesian analysis has been applied to polarized neutron reflectivity data. Reflectivity data from a magnetic TbCo thin-film structure were studied using a combination of a Monte Carlo Markov-chain algorithm, likelihood estimation and error modeling. By utilizing Bayesian analysis, it was possible to investigate the uniqueness of the solution beyond reconstructing the magnetic and structure parameters. The expedience of this approach has been demonstrated, as several probable reconstructions were found (the multimodality case) concerning the isotopic composition of the surface cover layer. Such multimodal reconstruction emphasizes the importance of rigorous data analysis instead of the direct data fitting approach, especially in the case of poor statistically conditioned data typical for neutron reflectivity experiments. This article presents details of the analysis and a discussion of multimodality.

Modeling Supply Air Jet of Split Air Conditioner Based on Abramovich Jet Theory and Bayesian Markov Chain Monte Carlo Algorithm

Aim: This study aims to develop supply air jet models for split air conditioners. Background: Designing and operating an air conditioning system based on the unique characteristics of the supply air jet is essential to control the draft risk. Motivation: Due to the distinct differences in air supply characteristics of the split air conditioners caused by the intermittent operation and the complex design of supply air outlets, the existing supply air jet models designed for central air conditioning systems are unsuitable for split air conditioners. Significant results: In this study, models for the trajectory position, velocity, and temperature of the supply air jet for split air conditioners are established based on the Abramovich jet theory and Bayesian Markov Chain Monte Carlo (MCMC) algorithm. The effectiveness of the proposed models is demonstrated via comparison with the training dataset from the experimentally validated Computational Fluid Dynamics simulation of a split air conditioner. For the model testing dataset, the RMSEs of trajectory position, velocity, and temperature are 0.01 m, 0.09 m/s, and 0.09 °C, respectively, with a low supply air velocity and 0.01 m, 0.25 m/s, and 0.03 °C with a high supply air velocity. The proposed models of velocity and temperature of the supply air jet are general for various supply air conditions, while coefficients in the trajectory position model of the supply air jet need to be recalibrated with the proposed Bayesian MCMC algorithm for different supply air conditions. The proposed models provide valuable guidance for the operation of split air conditioners.

Matter-geometry interplay in new scalar tensor theories of gravity

The paper studies the possible interplay between matter and geometry in scalar tensor theories of gravitation where the energy–momentum tensor is directly coupled with the Einstein tensor. After obtaining the scalar tensor representation of the f(R,GμνTμν)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R, G_{\\mu \ u }T^{\\mu \ u })$$\\end{document} gravity, the analysis continue with an approach based on the thermodynamics of irreversible processes in open systems. To this regard, various thermodynamic properties are directly obtained in this manner, like the matter creation (annihilation) rate and the corresponding creation (annihilation) pressure. In the case of the Roberson–Walker metric several analytic and numerical solutions are found in the asymptotic regime. In the last part of the manuscript a specific parametrization for the Hubble rate is constrained using the Markov Chain Monte Carlo algorithms in the case of cosmic chronometers (CC) and BAO observations, obtaining an approximate numerical solution which can describe the cosmological model. For this model, we have obtained by fine-tuning some numerical solutions which exhibit creation mechanisms in different specific regimes.

Bayesian Clustering via Fusing of Localized Densities

Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to produce samples from the posterior distribution of the component labels. The data are then clustered by minimizing the expectation of a clustering loss function that favors similarity to the component labels. Unfortunately, although these approaches are routinely implemented, clustering results are highly sensitive to kernel misspecification. For example, if Gaussian kernels are used but the true density of data within a cluster is even slightly non-Gaussian, then clusters will be broken into multiple Gaussian components. To address this problem, we develop Fusing of Localized Densities (FOLD), a novel clustering method that melds components together using the posterior of the kernels. FOLD has a fully Bayesian decision theoretic justification, naturally leads to uncertainty quantification, can be easily implemented as an add-on to MCMC algorithms for mixtures, and favors a small number of distinct clusters. We provide theoretical support for FOLD including clustering optimality under kernel misspecification. In simulated experiments and real data, FOLD outperforms competitors by minimizing the number of clusters while inferring meaningful group structure.

Bounding the speedup of the quantum-enhanced Markov-chain Monte Carlo algorithm

Bounding the speedup of the quantum-enhanced Markov-chain Monte Carlo algorithm

Regularized Bayesian algorithms for Q-matrix inference based on saturated cognitive diagnosis modelling.

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

Lifted TASEP: A Solvable Paradigm for Speeding up Many-Particle Markov Chains

Virtually all Markov-chain Monte Carlo algorithms used for sampling a given distribution are reversible, and they satisfy the detailed-balance condition. For local chains, this leads to a slow, diffusive exploration of sample space. Significant speedups can be achieved through nonreversible algorithms with the given distribution as a targeted steady state. However, nonreversible algorithms for sampling are difficult to set up and to analyze, and exact speedup results for interacting many-particle systems are very rare. Here, we introduce the “lifted” totally asymmetric simple exclusion process (TASEP) as an exactly solvable paradigm for nonreversible many-particle Markov chains. It samples the same hard-sphere distribution as the Metropolis algorithm for symmetrically diffusing hard-core particles on a one-dimensional lattice. We solve the lifted TASEP by an unusual kind of coordinate Bethe ansatz and show that it exhibits polynomial (in particle number) speedups in the relaxation time for the asymptotic approach of the steady state, as well as the nonasymptotic mixing time, compared to both Metropolis and Kardar-Parisi-Zhang-based dynamics. The lifted TASEP is the reduction onto the one-dimensional lattice of the successful hard-sphere event-chain Monte Carlo algorithm, and we discuss that it can likewise be generalized to soft interaction potentials. Published by the American Physical Society 2024

A hybrid inversion algorithm to obtain the resistivity of the uninvaded zone based on the array induction log

This study investigates the impact of the drilling mud invasion on the borehole-measured resistivity. The primary objective is to retrieve the true resistivity of the formation, which helps in identifying different fluids in the reservoir. To achieve this goal, We proposed a hybrid inversion approach integrating the Levenberg-Marquardt and Markov Chain Monte Carlo algorithms with a five-parameter formation resistivity model. Synthetic and real-world data are utilized to assess the method's robustness and reliability. The simulated result indicated that the method is reliable when the data noise level is less than 5%.The method applied to real-world data revealed that the resistivity profile on the water zone showed a slight increase in the inverted resistivity from measured resistivity. Meanwhile, in the oil zone, the calculated resistivity revealed a high deviation from the measured resistivity, indicating the effects of mud invasion. The introduced methods are only applicable when the invasions of mud occur within the range of the logging tool's depth of investigation. Moreover, the method may give no reliable result when the invasion exceeds the tool's investigation depth. It indicates its limitation.

Generation of root zone soil moisture from the integration of an all-weather satellite surface soil moisture estimates and an analytical model: A preliminary result in China

In addition to surface soil moisture (SSM) data, root zone soil moisture (RZSM) is particularly significant for irrigation decision-making and agricultural drought warnings since water uptake generally occurs through the root systems of plants. In this study, a daily/0.05° RZSM dataset covering the major land areas of China was generated from the synergistic use of satellite-derived SSM estimates and a RZSM-SSM analytical model. First, based on the SSM and RZSM datasets generated from the fifth generation of atmospheric reanalysis (ERA5-Land), the Markov Chain Monte Carlo algorithm was applied to optimize the soil moisture analytical relationship (SMAR) model to determine four essential parameters pixel-to-pixel over the study area. In addition, the optimized SMAR parameters were integrated with satellite-derived daily/0.05° SSM to predict the daily/0.05° RZSM in China. Finally, due to the lack of in situ RZSM measurements ground truth at a spatial resolution of 0.05°, two RZSM products, namely the Soil Moisture Active Passive (SMAP)-based RZSM and the China Meteorological Administration Land Data Assimilation System (CLDAS)-based RZSM, were used as references to preliminarily assess the estimated data. The results showed overall fair correlations between SMAP_RZSM and estimated RZSM (correlation coefficient R varying from 0.557 to 0.655), and between CLDAS_RZSM and estimated RZSM (correlation coefficient R varying from 0.496 to 0.596) over four typical days representing spring, summer, autumn, and winter in 2019. Although the proposed approach may overestimate or underestimate RZSM compared to the two referenced products in different seasons, an overall acceptable accuracy with unbiased root mean square error of ∼ 0.070–0.090 cm3/cm3 was obtained.

Heterogeneous Mediation Analysis for Cox Proportional Hazards Model With Multiple Mediators.

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

Sampling random graphs with specified degree sequences

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

Statistical analysis for progressive stress accelerated life test with transmutation Weibull distribution

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

Bayesian estimation of stochastic volatility jump diffusion model parameters using S&P 500 and VIX data

The Stochastic Volatility Jump Diffusion (SVJD) model is a common tool used for option pricing. Existing literature has employed many techniques in order to estimate the parameters of this model, including both Bayesian and frequentist approaches. In 2010, Duan and Yeh [Jump and volatility risk premiums implied by VIX. J Econ Dyn Control. 2010;34(11):2232–2244] used a frequentist approach with maximum likelihood estimation that included the VIX, the Chicago Board Options Exchange (CBOE) Volatility Index, which carries real time S&P 500 option price information in addition to the S&P 500 data. In this paper, we combine the previous Bayesian approach in Cape et al. [Estimating Heston's and Bates' models parameters using Markov Chain Monte Carlo simulation. J Stat Comput Simul. 2015;85(11):2295–2314] with the inclusion of VIX by Duan and Yeh. We provide the derivations of the conditional posterior distributions of the SVJD model's parameters and a guide to a Markov Chain Monte Carlo (MCMC) algorithm used to estimate the parameters. We apply the algorithm to the historical S&P 500 and VIX data and provide the subsequent parameter estimates. We offer these tools for others performing similar research with our R code available upon request.

2D Transdimensional Joint Inversion of Radio Magnetotelluric and Electrical Resistivity Tomography Data

Summary The joint inversion of radio magnetotelluric and electrical resistivity tomography data has the potential to reduce the uncertainties in the subsurface conductivity model. This is particularly beneficial when the datasets offer complementary information about the subsurface. However, the traditional gradient-based inversion methods pose challenges in quantifying uncertainty, as they yield a single model with limited appraisal of parameter uncertainty. The Bayesian inversion approach stands out for its capacity to provide quantitative assessments of uncertainty in the inverted model parameters. This is accomplished by generating an ensemble of models, leading to a posterior distribution that encapsulates both prior information concerning model parameters and the dataset information. We have implemented a transdimensional Markov chain Monte Carlo algorithm to perform the joint inversion of radio magnetotelluric and electrical resistivity tomography data. Through synthetic data studies, we illustrate how the inclusion of two complementary datasets can effectively reduce uncertainties in model parameters and how the model parameter uncertainties can be quantified. Subsequently, the developed algorithm is tested using exemplary field data from a waste site near Roorkee, India. Intensive prior geoelectric and transient electromagnetic as well as radio magnetotelluric studies investigated possible waste water seepage with a potential to contaminate the shallow aquifers. The derived subsurface structure from our transdimensional Bayesian results compare well with the deterministic results for the exemplary profile, but in addition provide comprehensive uncertainty estimates.

Analysis of dependent complementary competing risks data from a generalized inverted family of lifetime distributions under a maximum ranked set sampling procedure with unequal samples

This paper explores analysis of a dependent complementary competing risks model when the failure causes are distributed by the proposed generalized inverted family of lifetime distributions. Under maximum ranked set sampling with unequal samples (MRSSU), statistical inference of model parameters and reliability indices is discussed under classical frequentist and Bayesian approaches, respectively. Maximum likelihood estimators along with their existence and uniqueness are obtained for model parameters, and associated approximate confidence intervals are constructed in consequence. Bayesian estimation is also performed with respect to general flexible priors, and the Markov Chain Monte Carlo (MCMC) algorithm is proposed for complex posterior computation. The study further examines classical and Bayesian estimations with order restriction of parameters when additional historical information is available in the MRSSU scenario. Finally, the performance of different results is evaluated through numerical simulations and a real data example is presented for demonstrating the application of our methods.