The hybrid Monte Carlo (HMC) algorithm is used for Bayesian analysis of the generalized autoregressive conditional heteroscedasticity (GARCH) model. The HMC algorithm is one of Markov chain Monte Carlo (MCMC) algorithms and it updates all parameters at once. We demonstrate that how the HMC reproduces the GARCH parameters correctly. The algorithm is rather general and it can be applied to other ...

This paper introduces the Parallel Hierarchical Sampler (PHS), a class of Markov chain Monte Carlo algorithms using several interacting chains having the same target distribution but different mixing properties. Unlike any single-chain MCMC algorithm, upon reaching stationarity one of the PHS chains, which we call the “mother” chain, attains exact Monte Carlo sampling of the target distribution...

In this paper we develop an original and general framework for automatically optimizing the statistical properties of Markov chain Monte Carlo (MCMC) samples, which are typically used to evaluate complex integrals. The Metropolis-Hastings algorithm is the basic building block of classical MCMC methods and requires the choice of a proposal distribution, which usually belongs to a parametric fami...

We introduce a new Markov chain Monte Carlo (MCMC) sampler for infinite-dimensional inverse problems. Our is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt covariance structure of target distribution. extend this first time function spaces, yielding highly efficient gradient-free MCMC algorithm. Because our does not require gradients or posterior estimat...

Hidden Markov models have proved to be a very exible class of models, with many and diverse applications. Recently Markov chain Monte Carlo (MCMC) techniques have provided powerful computational tools to make inferences about the parameters of hidden Markov models, and about the unobserved Markov chain, when the chain is deened in discrete time. We present a general algorithm, based on reversib...

The following is a simple example to show two important properties of a Markov chain Monte Carlo (MCMC) sampler and to illustrate the basic functionality of the method and issues relating to it’s usage. A Markov chain is a series where the realisation of the next element in the series, Y , is dependent only on the current state, X, and occurs with probability, P (Y |X). So the even number serie...

Fingerprint image segmentation is one key step in Automatic Fingerprint Identification System (AFIS), and how to do it faster, more accurately and more effectively is important for AFIS. This paper introduces the Markov Chain Monte Carlo (MCMC) method and the Genetic Algorithm (GA) into fingerprint image segmentation and brings forward a fingerprint image segmentation method based on Markov Cha...

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...

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...

Markov chain Monte Carlo, or MCMC, is a way to sample probability distributions that cannot be sampled practically using direct samplers. This includes a majority of probability distributions of practical interest. MCMC runs a Markov chain X1, X2, . . ., where Xk+1 is computed from Xk and some other i.i.d. random input. From a coding point of view, a direct solver is X = fSamp();, while the MCM...