Chain Monte Carlo Sampling Research Articles

Probabilistic Assessment of the Dynamic Viscosity of Self-Compacting Steel-Fiber Reinforced Concrete through a Micromechanical Model.

This article develops a probabilistic approach to a micromechanical model to calculate the dynamic viscosity in self-compacting steel-fiber reinforced concrete (SCSFRC), which implies a paradigm shift in the approach of the deterministic models used. It builds on a previous work by the authors in which Bayesian analysis is applied to rheological micromechanical models in cement paste, self-compacting mortar, and self-compacting concrete. As a consequence of the varied characteristics of the particles in these suspensions (in terms of materials, shapes, size distributions, etc.), as well as their random nature, it seems appropriate to study these systems with probabilistic models. The Bayesian analysis, thorough Markov Chain Monte Carlo and Gibbs Sampling methods, allows the conversion of parametric-deterministic models into parametric-probabilistic models, which results in enrichment in engineering and science. The incorporation of steel fibers requires a new term in the model to account for their effect on the dynamic viscosity of SCSFRC, and this new term is also treated here with the Bayesian approach. The paper uses an extensive collection of experimental data to obtain the probability density functions of the parameters for assessing the dynamic viscosity in SCSFRC. The results obtained with these parameters’ distributions are much better than those calculated with the theoretical values of the parameters, which indicates that Bayesian methods are appropriated to respond to questions in complex systems with complex models.

The Analysis of the Aftershock Sequences of the Recent Mainshocks in Alaska

The forecasting of the evolution of natural hazards is an important and critical problem in natural sciences and engineering. Earthquake forecasting is one such example and is a difficult task due to the complexity of the occurrence of earthquakes. Since earthquake forecasting is typically based on the seismic history of a given region, the analysis of the past seismicity plays a critical role in modern statistical seismology. In this respect, the recent three significant mainshocks that occurred in Alaska (the 2002, Mw 7.9 Denali; the 2018, Mw 7.9 Kodiak; and the 2018, Mw 7.1 Anchorage earthquakes) presented an opportunity to analyze these sequences in detail. This included the modelling of the frequency-magnitude statistics of the corresponding aftershock sequences. In addition, the aftershock occurrence rates were modelled using the Omori–Utsu (OU) law and the Epidemic Type Aftershock Sequence (ETAS) model. For each sequence, the calculation of the probability to have the largest expected aftershock during a given forecasting time interval was performed using both the extreme value theory and the Bayesian predictive framework. For the Bayesian approach, the Markov Chain Monte Carlo (MCMC) sampling of the posterior distribution was performed to generate the chains of the model parameters. These MCMC chains were used to simulate the models forward in time to compute the predictive distributions. The calculation of the probabilities to have the largest expected aftershock to be above a certain magnitude after a mainshock using the Bayesian predictive framework fully takes into account the uncertainties of the model parameters. Moreover, in order to investigate the credibility of the obtained forecasts, several statistical tests were conducted to compare the performance of the earthquake rate models based on the OU formula and the ETAS model. The results indicate that the Bayesian approach combined with the ETAS model produced more robust results than the standard approach based on the extreme value distribution and the OU law.

Evaluating Stan’s Variational Bayes Algorithm for Estimating Multidimensional IRT Models

Bayesian estimation of multidimensional item response theory (IRT) models in large data sets may come with impractical computational burdens when general-purpose Markov chain Monte Carlo (MCMC) samplers are employed. Variational Bayes (VB)—a method for approximating the posterior distribution—poses a potential remedy. Stan’s general-purpose VB algorithms have drastically improved the accessibility of VB methods for a wide psychometric audience. Using marginal maximum likelihood (MML) and MCMC as benchmarks, the present simulation study investigates the utility of Stan’s built-in VB function for estimating multidimensional IRT models with between-item dimensionality. VB yielded a marked speed-up in comparison to MCMC, but did not generally outperform MML in terms of run time. VB estimates were trustworthy only for item difficulties, while bias in item discriminations depended on the model’s dimensionality. Under realistic conditions of non-zero correlations between dimensions, VB correlation estimates were subject to severe bias. The practical relevance of performance differences is illustrated with data from PISA 2018. We conclude that in its current form, Stan’s built-in VB algorithm does not pose a viable alternative for estimating multidimensional IRT models.

Accelerated Bayesian inference-based history matching of petroleum reservoirs using polynomial chaos expansions

The forecast for oil production from an oil reservoir is made with the aid of reservoir simulations. The model parameters in reservoir simulations are uncertain whose values are estimated by matching the simulation predictions with production history. Bayesian inference (BI) provides a convenient way of estimating parameters of a mathematical model, starting from a probable distribution of parameter values and knowing the production history. BI techniques for history matching require Markov chain Monte Carlo (MCMC) sampling methods, which involve large number of reservoir simulations. This limits the application of BI for history matching in petroleum reservoir engineering, where each reservoir simulation can be computationally expensive. To overcome this limitation, we use polynomial chaos expansions (PCEs), which represent the uncertainty in production forecasts due to the uncertainty in model parameters, to construct proxy models for model predictions. As an application of the method, we present history matching in simulations based on the black-oil model to estimate model parameters such as porosity, permeability, and exponents of the relative permeability curves. Solutions to these history matching problems show that the PCE-based method enables accurate estimation of model parameters with two orders of magnitude less number of reservoir simulations compared with MCMC method.

Maximum—A Posteriori Estimation of Linear Time-Invariant State-Space Models via Efficient Monte-Carlo Sampling

Abstract This article addresses maximum-a-posteriori (MAP) estimation of linear time-invariant state-space (LTI-SS) models. The joint posterior distribution of the model matrices and the unknown state sequence is approximated by using Rao-Blackwellized Monte-Carlo sampling algorithms. Specifically, the conditional distribution of the state sequence given the model parameters is derived analytically, while only the marginal posterior distribution of the model matrices is approximated using a Metropolis-Hastings Markov Chain Monte-Carlo sampler. From the joint distribution, MAP estimates of the unknown model matrices as well as the state sequence are computed. The performance of the proposed algorithm is demonstrated on a numerical example and on a real laboratory benchmark dataset of a hair dryer process.

Validation of MCMC-Based Travel Simulation Framework Using Mobile Phone Data

An essential step in agent-based travel demand models is the characterization of the population, including transport-related attributes. This study looks deep into various mobility data in the province of Liège, Belgium. Based on the data stemming from the 2010 Belgian HTS, that is, BELDAM, a Markov chain Monte Carlo (MCMC) sampling method combined with a cross-validation process is used to generate sociodemographic attributes and trip-based variables. Besides, representative micro-samples are calibrated using data about the population structure. As a critical part of travel demand modeling for practical applications in the real-world context, validation using various data sources can contribute to the modeling framework in different ways. The innovation in this study lies in the comparison of outputs of MCMC with mobile phone data. The difference between modeled and observed trip length distributions is studied to validate the simulation framework. The proposed framework infers trips with multiple attributes while preserving the traveler’s sociodemographics. We show that the framework effectively captures the behavioral complexity of travel choices. Moreover, we demonstrate mobile phone data’s potential to contribute to the reliability of travel demand models.

Bayesian estimation and uncertainty quantification in models of urea hydrolysis by E. coli biofilms

ABSTRACT Urea-hydrolysing biofilms are crucial to applications in medicine, engineering, and science. Quantitative information about ureolysis rates in biofilms is required to model these applications. We formulate a novel model of urea consumption in a biofilm that allows different kinetics, for example either first order or Michaelis–Menten. The model is fit to synthetic data to validate and compare two approaches, Bayesian and nonlinear least squares (NLS), commonly used by biofilm practitioners. The shortcomings of NLS motivate the Bayesian approach where a simple Markov Chain Monte Carlo (MCMC) sampler is applied. The model is then fit to real data of influent and effluent urea concentrations from experiments with biofilms of Escherichia coli. Results from synthetic data aid in interpreting results from real data, where first-order and Michaelis–Menten kinetic models are compared. The method shows potential for general applications requiring biofilm kinetic information.

The origin and spread of CRF85_BC, driven by heterosexual transmission among older people in Sichuan, China

BackgroundCRF_BC recombinants, including CRF07_BC and CRF08_BC, were considered the predominant subtypes in China. Since the discovery of HIV-1 circulating recombinant form CRF 85_BC in Southwest China in 2016, this BC recombinant forms had been reported in different regions of China. However, the history and magnitude of CRF85_BC transmission were still to be investigated.MethodWe conducted the most recent molecular epidemiology of HIV-1 among newly reported HIV-1 infected patients in Sichuan in 2019 by sequencing and phylogenetic analysis of 1291 pol sequences. Then, we used maximum likelihood approach and the Bayesian Markov chain Monte Carlo (MCMC) sampling of pol sequences to reconstruct the phylogeographic and demographic dynamics of the CRF85_BC.ResultsHIV-1 CRF85_BC (68/1291, 5.27%) became the fourth most prevalent strain revealing a significant increase in local population. CRF85_BC were only found in heterosexually infected individuals and the majority of CRF85_BC (95.45%) were circulating among the people living with HIV aged 50 years and over (PLHIV50+), suggesting a unique prevalent pattern. The founder lineages of CRF85_BC were likely to have first emerged in Yunnan, a province of Southwest China bordering Sichuan, in the early 2000s. It then spread exponentially to various places (including Guangxi, Sichuan, et al) and became endemic around 2008.6 (2006.7–2010.2) in Sichuan.ConclusionTaken together, our findings on HIV-1 subtype CRF85_BC infections provided new insights into the spread of this virus and extended the understanding of the HIV epidemic in China.

FastMM: an efficient toolbox for personalized constraint-based metabolic modeling

BackgroundConstraint-based metabolic modeling has been applied to understand metabolism related disease mechanisms, to predict potential new drug targets and anti-metabolites, and to identify biomarkers of complex diseases. Although the state-of-art modeling toolbox, COBRA 3.0, is powerful, it requires substantial computing time conducting flux balance analysis, knockout analysis, and Markov Chain Monte Carlo (MCMC) sampling, which may limit its application in large scale genome-wide analysis.ResultsHere, we rewrote the underlying code of COBRA 3.0 using C/C++, and developed a toolbox, termed FastMM, to effectively conduct constraint-based metabolic modeling. The results showed that FastMM is 2~400 times faster than COBRA 3.0 in performing flux balance analysis and knockout analysis and returns consistent outputs. When applied to MCMC sampling, FastMM is 8 times faster than COBRA 3.0. FastMM is also faster than some efficient metabolic modeling applications, such as Cobrapy and Fast-SL. In addition, we developed a Matlab/Octave interface for fast metabolic modeling. This interface was fully compatible with COBRA 3.0, enabling users to easily perform complex applications for metabolic modeling. For example, users who do not have deep constraint-based metabolic model knowledge can just type one command in Matlab/Octave to perform personalized metabolic modeling. Users can also use the advance and multiple threading parameters for complex metabolic modeling. Thus, we provided an efficient and user-friendly solution to perform large scale genome-wide metabolic modeling. For example, FastMM can be applied to the modeling of individual cancer metabolic profiles of hundreds to thousands of samples in the Cancer Genome Atlas (TCGA).ConclusionFastMM is an efficient and user-friendly toolbox for large-scale personalized constraint-based metabolic modeling. It can serve as a complementary and invaluable improvement to the existing functionalities in COBRA 3.0. FastMM is under GPL license and can be freely available at GitHub site: https://github.com/GonghuaLi/FastMM.

Space Product Reliability Evaluation in Two-stage Development Based on Scaling Factor

Space products have high reliability and will experience multi-stage development with respective tests after each stage. Due to the limit of budget and time-to-market, the tests usually have small sample sizes and short durations. A few or no failures are more likely to appear in such tests for high-reliability products. In practical engineering, reliability assessment will not be satisfactory if only depending on data from the current test. And this problem will be improved if multi-stage data is included. In this paper, a scaling factor method is adopted to deal with the conversion problem of the data in the previous stage. Then the Bayesian posteriori estimations of the reliability parameters are obtained by the Markov Chain Monte Carlo (MCMC) sampling method. After two-dimensional integral is calculated, the confidence lower limit of reliability can be given accurately. A case study is carried out to illustrate the effectiveness of the proposed method.

Inflated density ratio and its variation and generalization for computing marginal likelihoods

In the Bayesian framework, the marginal likelihood plays an important role in variable selection and model comparison. The marginal likelihood is the marginal density of the data after integrating out the parameters over the parameter space. However, this quantity is often analytically intractable due to the complexity of the model. In this paper, we first examine the properties of the inflated density ratio (IDR) method, which is a Monte Carlo method for computing the marginal likelihood using a single MC or Markov chain Monte Carlo (MCMC) sample. We then develop a variation of the IDR estimator, called the dimension reduced inflated density ratio (Dr.IDR) estimator. We further propose a more general identity and then obtain a general dimension reduced (GDr) estimator. Simulation studies are conducted to examine empirical performance of the IDR estimator as well as the Dr.IDR and GDr estimators. We further demonstrate the usefulness of the GDr estimator for computing the normalizing constants in a case study on the inequality-constrained analysis of variance.

Structural modelling and Bayesian inference for model validation and confidence extrapolation

ABSTRACTThe hierarchical validation is recommended for assessing the confidence of the large-scale simulation model, through comparing the model predictions with experimental observations at each level. However, the system-level experimental observations may be scarce in the full-scale testing. A new structural modelling approach is proposed to implement the higher-level model validation using lower-level data. The proposed approach relates the computation model to corresponding system responses and lower-level outputs to higher-level responses. Bayesian network with Markov chain Monte Carlo (MCMC) sampling is used to represent the relationship sets and estimate the structural modelling parameters and input variables. Highest posterior density (HPD) confidence range is employed to quantify the model credibility, the confidence intervals of model errors, and the effect of lower-level data on the higher-level model assessment. The proposed methodology is implemented for hierarchical model validation and confidence extrapolation of a guidance model on a flight vehicle using time series data.

Stochastic search variable selection for split-plot and blocked screening designs

Split-plot definitive screening and blocked definitive screening designs have been developed for detecting active main effects and second-order effects in screening experiments when split-plot and block structures exist. In the literature, multistage regression and forward stepwise regression methods were proposed for data analysis on the two types of designs. However, classical regression approaches present limitations and potential problems. First, the degrees of freedom may not be large enough to estimate all active effects. Second, the restricted maximum-likelihood estimates for variances of whole-plot and block errors can be zero. To solve these problems and enhance detection capability, we propose a stochastic search variable selection (SSVS) method based on Bayesian theory. Different from the existing Bayesian approaches for split-plot and blocked designs, the proposed SSVS method can perform variable selections and choose models that follow the effect heredity principle. Markov chain Monte Carlo and Gibbs sampling are applied and a general WinBUGS code, which can be used for any split-plot and blocked screening design, is provided. Simulation studies are conducted and their results show that the proposed SSVS method effectively controls the false discovery rate and has higher detection capability than the two regression methods.

Meta analysis of binary data with excessive zeros in two-arm trials

We present a novel Bayesian approach to random effects meta analysis of binary data with excessive zeros in two-arm trials. We discuss the development of likelihood accounting for excessive zeros, the prior, and the posterior distributions of parameters of interest. Dirichlet process prior is used to account for the heterogeneity among studies. A zero inflated binomial model with excessive zero parameters were used to account for excessive zeros in treatment and control arms. We then define a modified unconditional odds ratio accounting for excessive zeros in two arms. The Bayesian inference is carried out using Markov chain Monte Carlo (MCMC) sampling techniques. We illustrate the approach using data available in published literature on myocardial infarction and death from cardiovascular causes. Bayesian approaches presented here use all the data, including the studies with zero events and capture heterogeneity among study effects, and produce interpretable estimates of overall and study-level odds-ratios, over the commonly used frequentist’s approaches. Results from the data analysis and the model selection also indicate that the proposed Bayesian method, while accounting for zero events, adjusts for excessive zeros and provides better fit to the data resulting in the estimates of overall odds-ratio and study-level odds-ratios that are based on the totality of the information.

Bayesian variable selection in a finite mixture of linear mixed-effects models

ABSTRACTMixture of linear mixed-effects models has received considerable attention in longitudinal studies, including medical research, social science and economics. The inferential question of interest is often the identification of critical factors that affect the responses. We consider a Bayesian approach to select the important fixed and random effects in the finite mixture of linear mixed-effects models. To accomplish our goal, latent variables are introduced to facilitate the identification of influential fixed and random components and to classify the membership of observations in the longitudinal data. A spike-and-slab prior for the regression coefficients is adopted to sidestep the potential complications of highly collinear covariates and to handle large p and small n issues in the variable selection problems. Here we employ Markov chain Monte Carlo (MCMC) sampling techniques for posterior inferences and explore the performance of the proposed method in simulation studies, followed by an actual psychiatric data analysis concerning depressive disorder.

Reliability estimation under type-II censored data from the generalized Bilal distribution

The main object of this article is the estimation of the unknown population parameters and the reliability function for the generalized Bilal model under type-II censored data. Both maximum likelihood and Bayesian estimates are considered. In the Bayesian framework, although we have discussed mainly the squared error loss function, any other loss function can easily be considered. Gibb’s sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples, which have been used to compute the Bayes estimates and also to construct their corresponding credible intervals with the help of two different importance sampling techniques. A simulation study is carried out to examine the accuracy of the resulting Bayesian estimates and compare them with their corresponding maximum likelihood estimates. Application to a real data set is considered for the sake of illustration.

Intuition for an Old Curiosity and an Implication for MCMC

ABSTRACT Morris and Ebey reported the following curiosity. “The unweighted sample mean is examined as an estimator of the population mean in a first-order autoregressive model. It is demonstrated that the precision of this estimator deteriorates as the number of equally spaced observations taken within a fixed time interval increases.” Morris and Ebey proved their result but gave no intuition for it. We provide some intuition, then examine an implication: that the usual practice of estimating posterior expectations by taking the unweighted average of consecutive Markov chain Monte Carlo (MCMC) samples may not be optimal.

Estimating the Volume of the Solution Space of SMT(LIA) Constraints by a Flat Histogram Method

The satisfiability modulo theories (SMT) problem is to decide the satisfiability of a logical formula with respect to a given background theory. This work studies the counting version of SMT with respect to linear integer arithmetic (LIA), termed SMT(LIA). Specifically, the purpose of this paper is to count the number of solutions (volume) of a SMT(LIA) formula, which has many important applications and is computationally hard. To solve the counting problem, an approximate method that employs a recent Markov Chain Monte Carlo (MCMC) sampling strategy called “flat histogram” is proposed. Furthermore, two refinement strategies are proposed for the sampling process and result in two algorithms, MCMC-Flat1/2 and MCMC-Flat1/t, respectively. In MCMC-Flat1/t, a pseudo sampling strategy is introduced to evaluate the flatness of histograms. Experimental results show that our MCMC-Flat1/t method can achieve good accuracy on both structured and random instances, and our MCMC-Flat1/2 is scalable for instances of convex bodies with up to 7 variables.

Geoacoustic inversion of the pressure gradient data using a single vector sensor

A vector sensor has the capability of obtaining the acoustic field involving the sound pressure and three-dimensional particle velocities simultaneously, which means that there exists a potential to extract deep information for further applications like direction of arrival (DOA), positioning, classification, geoacoustic inversion, etc. This paper applies a nonlinear Bayesian approach to the pressure gradient data for geoacoustic properties of South China Sea, about which the experiment took place in July of 2013 in South China Sea of nearly 90 m depth. Recorded linear frequency modulation (LFM) signals of the pressure and vertical particle velocity are windowed and processed together to estimate the pressure gradient in the vertical direction at multiple frequencies as the observation data. After the optimal sediment model is selected based on BIC (Bayesian Information Criterion) using adaptive simplex simulated annealing (ASSA), delayed rejection adaptive Metropolis (DRAM), a Markov chain Monte Carlo (MCMC) sampling method, is used not only to provide a maximum a-posteriori (MAP) parameters estimates but also to quantify the parameters uncertainties and inter-parameter relationships. [Work supported by the National Natural Science Foundation (Grant No. 61531012).]

Applying bayesian population assessment models to artisanal, multispecies fisheries in the Northern Mokran Sea, Iran

Small-scale fisheries substantially contribute to the reduction of poverty, local economies and food safety in many countries. However, limited and low-quality catches and effort data for small-scale fisheries complicate the stock assessment and management. Bayesian modelling has been advocated when assessing fisheries with limited data. Specifically, Bayesian models can incorporate information of the multiple sources, improve precision in the stock assessments and provide specific levels of uncertainty for estimating the relevant parameters. In this study, therefore, the state-space Bayesian generalised surplus production models will be used in order to estimate the stock status of fourteen Demersal fish species targeted by small-scale fisheries in Sistan and Baluchestan, Iran. The model was estimated using Markov chain Monte Carlo (MCMC) and Gibbs Sampling. Model parameter estimates were evaluated by the formal convergence and stationarity diagnostic tests, indicating convergence and accuracy. They were also aligned with existing parameter estimates for fourteen species of the other locations. This suggests model reliability and demonstrates the utility of Bayesian models. According to estimated fisheries’ management reference points, all assessed fish stocks appear to be overfished. Overfishing considered, the current fisheries management strategies for the small-scale fisheries may need some adjustments to warrant the long-term viability of the fisheries.