Chain Monte Carlo Approach Research Articles

Quantification of Precipitation and Evapotranspiration Uncertainty in Rainfall-Runoff Modeling

Mountainous watersheds have always been a challenge for modelers due to large variability and insufficient ground observations, which cause forcing data, model structure, and parameter uncertainty. This study employed Differential Evolution Adaptive Metropolis (DREAM) algorithm which utilizes Markov Chain Monte Carlo (MCMC) approach to account for forcing data uncertainty. A conceptual degree day snowmelt model, MIKE 11 NAM (Nedbor Afstromnings Model), was used to simulate snowmelt runoff from Ilgaz basin, with an area of 28.4 km2 area, located in the northern part of Turkey. The mean elevation is around 1700 m and the basin is covered with broadleaf forest and has mainly brown soil with a high water holding capacity. Precipitation and evapotranspiration (ET) values were optimized in combination with model parameters conditioned on observed discharges and corrected values of input data were utilized for calibration and validation. Results showed that the observed precipitation was over-estimated by almost 10%, while evapotranspiration calculated by Penman–Monteith method was underestimated. The mean values of storm and ET multipliers were obtained as 1.14 and 0.84, respectively. When only parameter uncertainty was considered, calibration did not yield Nash–Sutcliffe Efficiency (NSE) greater than 0.64. However, when forcing data uncertainty was incorporated in the DREAM approach, an improved value of NSE (0.84) was obtained. After calibration and treatment of forcing data errors, the model yielded reasonable prediction uncertainty bounds and well-defined posterior distributions of NAM model parameters. Main objectives of the study are to assess the applicability of MIKE 11 NAM model to the selected catchment. In addition, the importance of errors in the input forcing variables to the model is demonstrated.

A Fast and Efficient Markov Chain Monte Carlo Method for Market Microstructure Model

The non-linear market microstructure (MM) model for financial time series modeling is a flexible stochastic volatility model with demand surplus and market liquidity. The estimation of the model is difficult, since the unobservable surplus demand is a time-varying stochastic variable in the return equation, and the market liquidity arises both in the mean term and in the variance term of the return equation in the MM model. A fast and efficient Markov Chain Monte Carlo (MCMC) approach based on an efficient simulation smoother algorithm and an acceptance-rejection Metropolis–Hastings algorithm is designed to estimate the non-linear MM model. Since the simulation smoother algorithm makes use of the band diagonal structure and positive definition of Hessian matrix of the logarithmic density, it can quickly draw the market liquidity. In addition, we discuss the MM model with Student-t heavy tail distribution that can be utilized to address the presence of outliers in typical financial time series. Using the presented modeling method to make analysis of daily income of the S&P 500 index through the point forecast and the density forecast, we find clear support for time-varying volatility, volatility feedback effect, market microstructure theory, and Student-t heavy tails in the financial time series. Through this method, one can use the estimated market liquidity and surplus demand which is much smoother than the strong stochastic return process to assist the transaction decision making in the financial market.

Bayesian Estimation of the Polynomial Time Trend AR(1) Model through Spline Function

In this paper, we develop an estimation procedure for an autoregressive model with polynomial time trend approximated by a spline function. Spline function has the advantage of approximating the non-linear time series in an appropriate degree of polynomial time trend model. For Bayesian parameter estimation, the conditional posterior distribution is obtained under two symmetric loss functions. Due to the complex form of the conditional posterior distribution, Markov Chain Monte Carlo (MCMC) approach is used to estimate the Bayes estimators. The performance of Bayes estimators is compared with that of the corresponding maximum likelihood estimators (MLEs) in terms of mean squared error (MSE) and average absolute bias (AB) via a simulation study. To illustrate the proposed study, import series of Brazil, Russia, India, China, and South Africa (BRICS) countries are analyzed.

The application of minimum discrepancy estimation in implementation of cognitive diagnostic models

There has been an increasing interest in implementing cognitive diagnostic models (CDMs) in operational assessments among researchers and practitioners. Operational CDMs require accurate and efficient parameter estimations. In this paper, we introduce two parameter estimation methods—the minimum discrepancy (MD) and the minimum discrepancy maximum likelihood (MDML)—in the context of CDMs. Both methods were proposed in the knowledge space theory, but have not been applied to CDMs. We then compare the performance of the two methods with the other three estimation methods used in CDMs—the joint maximum likelihood estimation (JMLE), the marginal maximum likelihood estimation (MMLE) via the expectation–maximization, and the Markov Chain Monte Carlo (MCMC) approach with Gibbs Sampling—on parameter estimation accuracy and efficiency. Results indicate the potential of applying MD and MDML in CDM parameter estimations, especially when the sample size is small. Practical applications with respect to the selection of a method among MD, MDML, MMLE, JMLE, and MCMC for specific purposes and conditions are also provided.

Thermodynamic integration via differential evolution: A method for estimating marginal likelihoods

A typical goal in cognitive psychology is to select the model that provides the best explanation of the observed behavioral data. The Bayes factor provides a principled approach for making these selections, though the integral required to calculate the marginal likelihood for each model is intractable for most cognitive models. In these cases, Monte Carlo techniques must be used to approximate the marginal likelihood, such as thermodynamic integration (TI; Friel & Pettitt, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(3), 589–607 2008; Lartillot & Philippe, Systematic Biology, 55(2), 195–207 2006), which relies on sampling from the posterior at different powers (called power posteriors). TI can become computationally expensive when using population Markov chain Monte Carlo (MCMC) approaches such as differential evolution MCMC (DE-MCMC; Turner et al., Psychological Methods, 18(3), 368 2013) that require several interacting chains per power posterior. Here, we propose a method called thermodynamic integration via differential evolution (TIDE), which aims to reduce the computational burden associated with TI by using a single chain per power posterior (R code available at https://osf.io/ntmgw/). We show that when applied to non-hierarchical models, TIDE produces an approximation of the marginal likelihood that closely matches TI. When extended to hierarchical models, we find that certain assumptions about the dependence between the individual- and group-level parameters samples (i.e., dependent/independent) have sizable effects on the TI approximated marginal likelihood. We propose two possible extensions of TIDE to hierarchical models, which closely match the marginal likelihoods obtained through TI with dependent/independent sampling in many, but not all, situations. Based on these findings, we believe that TIDE provides a promising method for estimating marginal likelihoods, though future research should focus on a detailed comparison between the methods of estimating marginal likelihoods for cognitive models.

MCMC-Based Detection for Random Access With Preambles in MTC

Random access has been considered for machine-type communication (MTC). In particular, a random access scheme with a pool of preambles is widely studied, which is similar to multichannel ALOHA, to support a number of MTC devices. In this paper, we study optimal approaches for user activity detection in random access with preambles over fading channels. Since the computational complexity grows exponentially with the number of preambles, a low-complexity detector is derived using Markov chain Monte Carlo (MCMC) approaches that can approximately solve an optimal maximum a posteriori detection problem. The resulting MCMC detector can enjoy a trade-off between performance and complexity, while its complexity to obtain a sample is linearly proportional to the number of preambles. A performance analysis for optimal detection is also studied to see the optimal performance. Simulation results confirm that the MCMC detector performs better than compressive sensing-based approaches and can provide a near optimal performance under certain conditions with a reasonable computational complexity.

Gradient-Based Sequential Markov Chain Monte Carlo for Multitarget Tracking With Correlated Measurements

Measurements in wireless sensor networks (WSNs) are often correlated both in space and in time. This paper focuses on tracking multiple targets in WSNs by taking into consideration these measurement correlations. A sequential Markov Chain Monte Carlo (SMCMC) approach is proposed in which a Metropolis within Gibbs refinement step and a likelihood gradient proposal are introduced. This SMCMC filter is applied to case studies with cellular network received signal strength data in which the shadowing component correlations in space and time are estimated. The efficiency of the SMCMC approach compared to particle filtering, as well as the gradient proposal compared to a basic prior proposal, are demonstrated through numerical simulations. The accuracy improvement with the gradient-based SMCMC is above $90\%$ when using a low number of particles. Thanks to its sequential nature, the proposed approach can be applied to various WSN applications, including traffic mobility monitoring and prediction.

A Markov Chain Monte Carlo-Metropolis Hastings Approach for the Simultaneous Estimation of Heat Generation and Heat Transfer Coefficient from a Teflon Cylinder

ABSTRACTThis paper reports the use of Markov Chain Monte Carlo (MCMC) and Metropolis Hastings (MH) approach, to solve an inverse heat transfer problem. Three-dimensional, steady state, conjugate heat transfer from a Teflon cylinder of dimensions 100 mm diameter and 100 mm length with uniform volumetric internal heat generation is considered. The goal is to estimate volumetric heat generation and heat transfer coefficient, given the temperature data at certain fixed location on the surface of the cylinder. The internal volumetric heat generation is specified as input and the temperature and heat transfer coefficient values are obtained by a numerical solution to the governing equation. The temperature values also depend on heat transfer coefficient which is obtained by solving Navier–Stokes equation to obtain flow information. In order to reduce the computational cost, a neural network is trained from the computational fluid dynamics simulations. This is posed as an inverse problem wherein volumetric heat generation and heat transfer coefficient are unknown but the temperature data is known by conducting experiments. The novelty of the paper is the simultaneous determination of volumetric heat generation and heat transfer coefficient for the experimentally measured steady-state temperatures from a Teflon cylinder using MCMC-MH as an inverse model in a Bayesian framework and finally, the estimates are reported in terms of mean, maximum a posteriori, and the standard deviation which is the uncertainty associated with the estimated parameters.

Bayesian comparison of protein structures using partial Procrustes distance.

An important topic in bioinformatics is the protein structure alignment. Some statistical methods have been proposed for this problem, but most of them align two protein structures based on the global geometric information without considering the effect of neighbourhood in the structures. In this paper, we provide a Bayesian model to align protein structures, by considering the effect of both local and global geometric information of protein structures. Local geometric information is incorporated to the model through the partial Procrustes distance of small substructures. These substructures are composed of β-carbon atoms from the side chains. Parameters are estimated using a Markov chain Monte Carlo (MCMC) approach. We evaluate the performance of our model through some simulation studies. Furthermore, we apply our model to a real dataset and assess the accuracy and convergence rate. Results show that our model is much more efficient than previous approaches.

A Bayesian Approach to Diagnostics for Multivariate Control Charts

When a multivariate control chart raises an out-of-control signal, several diagnostic questions arise. When did the change occur? Which components or quality characteristics changed? For those components for which the mean shifted, what are the new values for the mean? While methods exist for addressing these questions individually, we present a Bayesian approach that addresses all three questions in a single model. We employ Markov chain Monte Carlo (MCMC) methods in a Bayesian analysis that can be used in a unified approach to the diagnostics questions for multivariate charts. We demonstrate how a reversible jump Markov chain Monte Carlo (RJMCMC) approach can be used to infer (1) the change point, (2) the change model (i.e., which components changed), and (3) post-change estimates of the mean.

Reciprocal Sliding Friction Model for an Electro-Deposited Coating and Its Parameter Estimation Using Markov Chain Monte Carlo Method.

This paper describes a sliding friction model for an electro-deposited coating. Reciprocating sliding tests using ball-on-flat plate test apparatus are performed to determine an evolution of the kinetic friction coefficient. The evolution of the friction coefficient is classified into the initial running-in period, steady-state sliding, and transition to higher friction. The friction coefficient during the initial running-in period and steady-state sliding is expressed as a simple linear function. The friction coefficient in the transition to higher friction is described with a mathematical model derived from Kachanov-type damage law. The model parameters are then estimated using the Markov Chain Monte Carlo (MCMC) approach. It is identified that estimated friction coefficients obtained by MCMC approach are in good agreement with measured ones.

A Markov Chain Monte Carlo Approach to Nonlinear Parametric System Identification

Nonlinear system identification is discussed in a mixed set-membership and statistical setting. A Markov chain Monte Carlo (MCMC) approach is proposed that estimates the feasible parameter set, the minimum volume outer-bounding ellipsoid and the minimum variance estimate. The proposed algorithm is proved to be convergent and enjoys some desirable properties. Further, its computational complexity and numerical accuracy are studied.

An Integrated Procedure for Bayesian Reliability Inference Using MCMC

The recent proliferation of Markov chain Monte Carlo (MCMC) approaches has led to the use of the Bayesian inference in a wide variety of fields. To facilitate MCMC applications, this paper proposes an integrated procedure for Bayesian inference using MCMC methods, from a reliability perspective. The goal is to build a framework for related academic research and engineering applications to implement modern computational-based Bayesian approaches, especially for reliability inferences. The procedure developed here is a continuous improvement process with four stages (Plan, Do, Study, and Action) and 11 steps, including: (1) data preparation; (2) prior inspection and integration; (3) prior selection; (4) model selection; (5) posterior sampling; (6) MCMC convergence diagnostic; (7) Monte Carlo error diagnostic; (8) model improvement; (9) model comparison; (10) inference making; (11) data updating and inference improvement. The paper illustrates the proposed procedure using a case study.

Modeling of Inverse Gaussian Frailty Model for Bivariate Survival Data

Shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor (frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this article, we consider inverse Gaussian distribution as frailty distribution and three different baseline distributions namely, Weibull, generalized exponential, and exponential power distribution. With these three baseline distributions, we propose three different inverse Gaussian shared frailty models. To estimate the parameters involved in these models we adopt Markov Chain Monte Carlo (MCMC) approach. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply these three models to a real life bivariate survival data set of McGilchrist and Aisbett (1991) related to kidney infection and a better model is suggested for the data.

Using the Reversible Jump MCMC Procedure for Identifying and Estimating Univariate TAR Models

One way that has been used for identifying and estimating threshold autoregressive (TAR) models for nonlinear time series follows the Markov chain Monte Carlo (MCMC) approach via the Gibbs sampler. This route has major computational difficulties, specifically, in getting convergence to the parameter distributions. In this article, a new procedure for identifying a TAR model and for estimating its parameters is developed by following the reversible jump MCMC procedure. It is found that the proposed procedure conveys a Markov chain with convergence properties.

Gene genealogies for genetic association mapping, with application to Crohn's disease

A gene genealogy describes relationships among haplotypes sampled from a population. Knowledge of the gene genealogy for a set of haplotypes is useful for estimation of population genetic parameters and it also has potential application in finding disease-predisposing genetic variants. As the true gene genealogy is unknown, Markov chain Monte Carlo (MCMC) approaches have been used to sample genealogies conditional on data at multiple genetic markers. We previously implemented an MCMC algorithm to sample from an approximation to the distribution of the gene genealogy conditional on haplotype data. Our approach samples ancestral trees, recombination and mutation rates at a genomic focal point. In this work, we describe how our sampler can be used to find disease-predisposing genetic variants in samples of cases and controls. We use a tree-based association statistic that quantifies the degree to which case haplotypes are more closely related to each other around the focal point than control haplotypes, without relying on a disease model. As the ancestral tree is a latent variable, so is the tree-based association statistic. We show how the sampler can be used to estimate the posterior distribution of the latent test statistic and corresponding latent p-values, which together comprise a fuzzy p-value. We illustrate the approach on a publicly-available dataset from a study of Crohn's disease that consists of genotypes at multiple SNP markers in a small genomic region. We estimate the posterior distribution of the tree-based association statistic and the recombination rate at multiple focal points in the region. Reassuringly, the posterior mean recombination rates estimated at the different focal points are consistent with previously published estimates. The tree-based association approach finds multiple sub-regions where the case haplotypes are more genetically related than the control haplotypes, and that there may be one or multiple disease-predisposing loci.

A Computationally Efficient MCMC Approach to Estimating Structural Models of Aggregate Demand

This paper develops a computationally efficient approach to structural estimation of random coefficients logit models of consumer demand using product-level data. The conventional GMM estimation approach relies on two computationally intensive fixed point algorithms developed by Rust (1987) and Berry, Levinsohn, and Pakes (1995). We transform the GMM estimator into a quasi-Bayesian (Laplace type) framework and develop a new Markov Chain Monte Carlo (MCMC) approach that solves the fixed point problems incrementally with Markov chain simulation. The proposed approach has two main advantages. First, it reduces the computational burden involved with the nested fixed point approach. In doing so, the proposed algorithm does not sacrifice the rich consumer heterogeneity. Second, our proposed estimation approach requires only moment condition as the GMM estimator, therefore avoiding the risk of misspecification bias in equilibrium frameworks. This contrasts with alternative approaches such as simulated maximum likelihood, control function, and Bayesian methods that require explicitly specified likelihood model.

Population dynamics and ORF3 gene evolution of porcine circovirus type 2 circulating in Korea

This study was conducted to investigate the status and population dynamics of porcine circovirus type 2(PCV2) in Korea and to assess the molecular evolutionary pattern of the two biologically important, overlapping open reading frames, the ORF1 and ORF3 genes. A wide range of PCV2 genomic sequences (entire genome, ORF1, ORF2 and ORF3) collected between 2001 and 2010 were analyzed using the Bayesian Markov chain Monte Carlo and maximum-likelihood approaches. These techniques identified the PCV2d genotype and the 2Ek cluster of PCV2a in Korea for the first time. Second, the genotypic shift of PCV2b dominating over PCV2a likely occurred between 2002 and 2004 due to a population expansion of PCV2b. In the context of positive Darwinian selection, the results uncovered independent evolutionary patterns in the ORF3 gene compared to the overlapping ORF1 gene and new sites in the viral ORFs/proteins that might relate to differences in the biological properties of the PCV2 groups.

Bayesian method for NLOS mitigation in single moving sensor Geo-location

The problem of locating mobile sensors has received considerable attention, particularly in the field of wireless communications. It is well-known that the presence of non-line-of-sight (NLOS) errors in the geo-location problem leads to severe degradation in the localization performance. In this paper, we propose a robust Bayesian method to mitigate the NLOS errors in location estimation of a single moving sensor, whereby the localization is performed using time-of-arrival (TOA) measurements. This method is based on the Markov chain Monte Carlo (MCMC) approach. Numerical simulations results illustrate the promising results of our method in a mixed line-of-sight (LOS) and NLOS environment.

Multitarget state and track estimation for the probability hypotheses density filter

The particle Probability Hypotheses Density (particle-PHD) filter is a tractable approach for Random Finite Set (RFS) Bayes estimation, but the particle-PHD filter can not directly derive the target track. Most existing approaches combine the data association step to solve this problem. This paper proposes an algorithm which does not need the association step. Our basic ideal is based on the clustering algorithm of Finite Mixture Models (FMM). The intensity distribution is first derived by the particle-PHD filter, and then the clustering algorithm is applied to estimate the multitarget states and tracks jointly. The clustering process includes two steps: the prediction and update. The key to the proposed algorithm is to use the prediction as the initial points and the convergent points as the estimates. Besides, Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC) approaches are used for the FMM parameter estimation.