Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain

The School Improvement Partnership Programme: Using Collaboration and Enquiry to tackle Educational Inequity

No abstract available

Exploiting multi-core architectures for reduced-variance estimation with intractable likelihoods

© 2016 International Society for Bayesian Analysis. Many popular statistical models for complex phenomena are intractable, in the sense that the likelihood function cannot easily be evaluated. Bayesian estimation in this setting remains challenging, with a lack of computational methodology to fully exploit modern processing capabilities. In this paper we introduce novel control variates for intractable likelihoods that can dramatically reduce the Monte Carlo variance of Bayesian estimators. We prove that our control variates are well-defined and provide a positive variance reduction. Furthermore, we show how to optimise these control variates for variance reduction. The methodology is highly parallel and offers a route to exploit multi-core processing architectures that complements recent research in this direction. Indeed, our work shows that it may not be necessary to parallelise the sampling process itself in order to harness the potential of massively multi-core architectures. Simulation results presented on the Ising model, exponential random graph models and non-linear stochastic differential equation models support our theoretical findings

Computational inference in systems biology

Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem. The computational costs associated with repeatedly solving the ODEs are often high. Aimed at reducing this cost, new concepts using gradient matching have been proposed. This paper combines current adaptive gradient matching approaches, using Gaussian processes, with a parallel tempering scheme, and conducts a comparative evaluation with current methods used for parameter inference in ODEs

Classification using distance nearest neighbours

This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label should depend more on class labels which are closer in the feature space, than those which are further away. Our approach builds on previous work by Holmes and Adams (2002, 2003) and Cucala et al. (2008). Our work shares many of the advantages of these approaches in providing a probabilistic basis for the statistical inference. In comparison to previous work, we present a more efficient computational algorithm to overcome the intractability of the Markov random field model. The results of our algorithm are encouraging in comparison to the k-nearest neighbour algorithm.Comment: 12 pages, 2 figures. To appear in Statistics and Computin

A comparison of inferential analysis methods for multilevel studies: implications for drawing conclusions in animal welfare science

Investigations comparing the behaviour and welfare of animals in different environments have led to mixed and often conflicting results. These could arise from genuine differences in welfare, poor validity of indicators, low statistical power, publication bias, or inappropriate statistical analysis. Our aim was to investigate the effects of using four approaches for inferential analysis of datasets of varying size on model outcomes and potential conclusions. We considered aggression in 864 growing pigs over six weeks as measured by ear and body injury score and relationships with: less and more enriched environments, pig's relative weight, and sex. Pigs were housed in groups of 18 in one of four pens, replicating the experiment 12 times. We applied four inferential models that either used a summary statistic approach, or else fully or partially accounted for complexities in study design. We tested models using both the full dataset (n = 864) and also using small sample sizes (n = 72). The most appropriate inferential model was a mixed effects, repeated measures model to compare ear and body score. Statistical models that did not acco unt for the correlation between repeated measures and/or the random effects from replications and pens led to spurious associations between environmental factors and indicators of aggression, which were not supported by the initial exploratory analysis. For analyses on smaller datasets (n = 72), due to the effect size and number of independent factors, there was insufficient power to determine statistically significant associations. Based on the mixed effects, repeated measures models, higher body injury scores were associated with more enrichment (coef. est. = 0.09, p = 0.02); weight (coef. est. = 0.05, p < 0.001); pen location on the right side (coef. est. = 0.08, p = 0.03) and at the front of the experimental room (coef. est. = 0.11, p = 0.003). By comparison, lower ear injury scores were associated with more enrichment (coef. est. = -0.51, p = 0.005) and pen location at the front of the experimental room (coef. est. = -0.4, p = 0.02). These observed differences support the hypothesis that injuries to the body and ears arise from different risk factors. Although calculation of the minimum required sample size prior to conducting an experiment and selection of the inferential analysis method will contribute to the validity of the study results, conflict between the outcomes will require further investigation via different methods such as sensitivity and specificity analysis

A catalogue of [Fe/H] determinations : 1996 edition

The Catalogue of [Fe/H] determinations has been updated and now includes 5946 determinations for 3247 stars (with 751 stars in 84 associations, clusters or galaxies). The 700 bibliographical references are complete up to December 1995 and refer only to [Fe/H] determinations obtained from high-resolution spectroscopic observations. The Catalogue also gives the spectral type, the object type, the visual magnitude and colour, as well as determinations of the effective temperature and gravity for each star, when available. In this paper, we comment on the Catalogue, the parameters listed in it, its stellar content,and the precautions that should be observed when using it. The full Catalogue is only available in electronic form at the CDS or upon request ([email protected]).Comment: 7 pages (Latex, A&A style), 4 PostScript figures, to be published in A&A Supplement Series in jul

Transport behavior of holes in boron delta-doped diamond structures

Boron delta-doped diamond structures have been synthesized using microwave plasma chemical vapor deposition and fabricated into FET and gated Hall bar devices for assessment of the electrical characteristics. A detailed study of variable temperature Hall, conductivity, and field-effect mobility measurements was completed. This was supported by Schr€dinger-Poisson and relaxation time o calculations based upon application of Fermi’s golden rule. A two carrier-type model was developed with an activation energy of $0.2 eV between the delta layer lowest subband with mobility$1 cm2/Vs and the bulk valence band with high mobility. This new understanding of the transport of holes in such boron delta-doped structures has shown that although Hall mobility as high as 900 cm2/Vs was measured at room temperature, this dramatically overstates the actual useful performance of the device