Bayesian estimation has played a pivotal role in the understanding of individual differences. However, for many models in psychology, Bayesian estimation of model parameters can be difficult. One reason for this difficulty is that conventional sampling algorithms, such as Markov chain Monte Carlo (MCMC), can be inefficient and impractical when little is known about the target distribution--part...

The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain convergence. Model comparison and fit issues in the ...

Markov chain Monte Carlo (MCMC) is a popular class of algorithms to sample from a complex distribution. A key issue in the design of MCMC algorithms is to improve the proposal mechanism and the mixing behaviour. This has led some authors to propose the use of a population of MCMC chains, while others go even further by integrating techniques from evolutionary computation (EC) into the MCMC fram...

Sequential Monte Carlo (SMC) methods are not only a popular tool in the analysis of state–space models, but offer an alternative to Markov chain Monte Carlo (MCMC) in situations where Bayesian inference must proceed via simulation. This paper introduces a new SMC method that uses adaptive MCMC kernels for particle dynamics. The proposed algorithm features an online stochastic optimization proce...

Probability distributions over many variables occur frequently in Bayesian inference, statistical physics and simulation studies. Samples from distributions give insight into their typical behavior and can allow approximation of any quantity of interest, such as expectations or normalizing constants. Markov chain Monte Carlo (MCMC), introduced by Metropolis et al. (1953), allows sampling from d...

We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the MCMC method itself. It turns out that autocorrelations between the data generated with our adaptive proposal density are greatly reduced. Thus it is concluded t...

The MCMC procedure, first released in SAS/STAT® 9.2, provides a flexible environment for fitting a wide range of Bayesian statistical models. Key enhancements in SAS/STAT 9.22 and 9.3 offer additional functionality and improved performance. The RANDOM statement provides a convenient way to specify linear and nonlinear random-effects models along with substantially improved performance. The MCMC...

We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simu­ lation. Naive algorithms that use the vari­ ational approximation as proposal distribu­ tion can perform poorly because this approx­ imation tends to underestimate the true vari­ ance and other features of the data. We solve this problem by introducing more so­ phistic...

To improve the accuracy of coal and gas prominence prediction, an improved sparrow search algorithm (ISSA) optimized support vector machine (SVM) based on Markov chain Monte Carlo (MCMC) filling prediction model were proposed. The mean value data after in missing values using MCMC was 2.282, with a standard deviation 0.193. Compared fill method (Mean), random forest (random forest, RF), K-neare...