The Unobserved ARCH model is a good description of the phenomenon of changing volatility that is commonly appeared in the financial time series. We study this model adopting Bayesian inference via Markov Chain Monte Carlo (MCMC). In order to provide an easy to implement MCMC algorithm we adopt some suitable non-linear transformations of the parameter space such that the resulting MCMC algorithm...

We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves ε error (in 2-Wasserstein distance) in O( √ d/ε) steps. This is a significant improvement over the best known rate for overdamped Langevin MCMC, which is O(d/ε) steps under the same smoothness/concav...

Missing data are often a problem in statistical modeling. The Bayesian paradigm offers a natural modelbased solution for this problem by treating missing values as random variables and estimating their posterior distributions. This paper reviews the Bayesian approach and describes how the MCMC procedure implements it. Beginning with SAS/STAT® 12.1, PROC MCMC automatically samples all missing va...

Particle Markov chain Monte Carlo (pMCMC) is now a popular method for performing Bayesian statistical inference on challenging state space models (SSMs) with unknown static parameters. It uses particle filter (PF) at each iteration of an MCMC algorithm to unbiasedly estimate the likelihood given parameter value. However, pMCMC can be computationally intensive when large number particles in PF r...

The theory of learning under the uniform distribution is rich and deep, with connections to cryptography, computational complexity, and the analysis of boolean functions to name a few areas. This theory however is very limited due to the fact that the uniform distribution and the corresponding Fourier basis are rarely encountered as a statistical model. A family of distributions that vastly gen...

This work develops a new functionality in UCODE_2014 to evaluate Bayesian credible intervals using the Markov Chain Monte Carlo (MCMC) method. The MCMC capability in UCODE_2014 is based on the FORTRAN version of the differential evolution adaptive Metropolis (DREAM) algorithm of Vrugt et al. (2009), which estimates the posterior probability density function of model parameters in highdimensiona...

Stochastic gradient MCMC (SG-MCMC) has played an important role in largescale Bayesian learning, with well-developed theoretical convergence properties. In such applications of SG-MCMC, it is becoming increasingly popular to employ distributed systems, where stochastic gradients are computed based on some outdated parameters, yielding what are termed stale gradients. While stale gradients could...

Markov Chain Monte Carlo (MCMC) methods are often used to sample from intractable target distributions. Some MCMC variants aim to improve the performance by running a population of MCMC chains. In this paper, we investigate the use of techniques from Evolutionary Computation (EC) to design population-based MCMC algorithms that exchange useful information between the individual chains. We invest...

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 ...

System identi®cation involves determination of the functional structure of a target system that underlies the observed data. In this paper, we present a probabilistic evolutionary method that optimizes system architectures for the iden-ti®cation of unknown target systems. The method is distinguished from existing evolutionary algorithms (EAs) in that the individuals are generated from a probabi...