We give an FPRAS for Holant problems with parity constraints and not-all-equal constraints, a generalisation of the problem of counting sink-free-orientations. The approach combines a sampler for near-assignments of “windable” functions – using the cycle-unwinding canonical paths technique of Jerrum and Sinclair – with a bound on the weight of nearassignments. The proof generalises to a larger ...

A Bayesian Prediction using the Elliptical Processes (EP) and the Skew Gaussian Processes (SGP) is proposed, motivated by a Bayesian model for heavy, light tailed or skewed real data. We define weak third order stationary for the Skew Gaussian Processes. Sometimes the family of distributions have dimensional coherency (consistency) property which is important for prediction. We use a Markov Cha...

It is proposed to jointly estimate the parameters of nonGaussian autoregressive (AR) processes in a Bayesian context using the Gibbs sampler. Using the Markov chains produced by the sampler an approximation to the vector MAP estimator is implemented. The results reported here used AR(4) models driven by noise sequences where each sample is iid as a two component Gaussian sum mixture. The result...

Boltzmann samplers are a kind of random samplers; in 2004, Duchon, Flajolet, Louchard and Schaeffer showed that given a combinatorial class and a combinatorial specification for that class, one can automatically build a Boltzmann sampler. In this paper, we introduce a Boltzmann sampler for Motzkin trees built from a holonomic specification, that is, a specification that uses the pointing operat...

The DA-T Gibbs sampler is proposed by Maris and Maris (2002) as a Bayesian estimation method for a wide variety of Item Response Theory (IRT) models. The present paper provides an expository account of the DAT Gibbs sampler for the 2PL model. However, the scope is not limited to the 2PL model. It is demonstrated how the DA-T Gibbs sampler for the 2PL may be used to build, quite easily, Gibbs sa...

Abstract: We explore two strategies that resample from previously sampled observations in a Markov Chain Monte Carlo algorithm. In one strategy the MCMC sampler reuses its own past. We show that in general this strategy generates a sampler with slower mixing. We propose another strategy based on multiple chains where some of the chains reuse past samples generated by other chains. This latter a...

A sampling device based on a telephone headset was developed and used to support a sampler close to the mouth during personal exposure monitoring of solder fume. In a field trial, it was compared with the established method of mounting the sampler on the arm of a pair of spectacles, and a linear correlation was evident between the two positions (slope 1.56 +/- 0.05, r(2) = 0.98). Although the h...

In a prototype of a new personal dust sampling system (PDS) the speed of air sampling in the breathing zone is related to the pulmonary ventilation rate of the wearer, using the correlation between pulmonary ventilation and pulse rate that is monitored by electrodes fastened on the sampler wearer's chest. The method of calibration and the results of dust chamber and field measurements are prese...

We study the slice sampler, a method of constructing a reversible Markov chain with a speciied invariant distribution. Given an independence Metropolis-Hastings algorithm it is always possible to construct a slice sampler that dominates it in the Peskun sense. This means that the resulting Markov chain produces estimates with a smaller asymptotic variance. Furthermore the slice sampler has a sm...

In Bayesian statistical inference and computationally intensive frequentist inference, one is interested in obtaining samples from a high dimensional, and possibly multi-modal target density. The challenge is to obtain samples from this target without any knowledge of the normalizing constant. Several approaches to this problem rely on Monte Carlo methods. One of the simplest such methods is th...