Florian Maire

Comparison of asymptotic variances of inhomogeneous Markov chains with application to Markov chain Monte Carlo methods

In this paper, we study the asymptotic variance of sample path averages for inhomogeneous Markov chains that evolve alternatingly according to two different 7-reversible Markov transition kernels P and Q. More specifically, our main result allows us to compare directly the asymptotic variances of two inhomogeneous Markov chains associated with different kernels Pi and Q(i), i is an element of {0, 1}, as soon as the kernels of each pair (P-0, P-1) and (Q(0), Q(1)) can be ordered in the sense of lag-one autocovariance. As an important application, we use this result for comparing different data-augmentation-type Metropolis Hastings algorithms. In particular, we compare some pseudo-marginal algorithms and propose a novel exact algorithm, referred to as the random refreshment algorithm, which is more efficient, in terms of asymptotic variance, than the Grouped Independence Metropolis Hastings algorithm and has a computational complexity that does not exceed that of the Monte Carlo Within Metropolis algorithm.

Detecting Aircraft With a Low-Resolution Infrared Sensor

We propose a new method, based on level sets, to detect aircraft on low resolution infrared images. Aircraft correspond to hot temperatures at the sensor level. Hence it is natural to rely on a test that considers the hottest pixels in the sensed image. If these pixels are close, they are likely to come from a target (i.e., an aircraft); otherwise they belong to the clutter. Instead of manually testing the neighborhood of each hot pixel, we use level sets; this is the first contribution of the paper (corresponding to eq. 2). The other contribution is the calibration of the resulting test. The method is implemented and tested over a database containing 45 604 simulated aircraft images and provides 98.5% of correct detections.

Efficient Bayesian inference for exponential random graph models by correcting the pseudo-posterior distribution

Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves the calculation of an intractable normalizing constant. This barrier motivates the consideration of tractable approximations to the likelihood function, such as the pseudolikelihood function, which offers an approach to constructing such an approximation. Naive implementation of what we term a pseudo-posterior resulting from replacing the likelihood function in the posterior distribution by the pseudolikelihood is likely to give misleading inferences. We provide practical guidelines to correct a sample from such a pseudo-posterior distribution so that it is approximately distributed from the target posterior distribution and discuss the computational and statistical efficiency that result from this approach. We illustrate our methodology through the analysis of real-world graphs. Comparisons against the approximate exchange algorithm of Caimo and Friel (2011) are provided, followed by concluding remarks.

Aircraft classification with a low resolution infrared sensor

Existing computer simulations of aircraft infrared signature do not account for the dispersion induced by uncertainty on input data, such as aircraft aspect angles and meteorological conditions. As a result, they are of little use to estimate the detection performance of IR optronic systems: in that case, the scenario encompasses a lot of possible situations that must indeed be addressed, but can not be singly simulated. In this paper, we focus on low resolution infrared sensors and we propose a methodological approach for performing a classification of different aircraft on the resulting set of low resolution infrared images. It is based on a maximum likelihood classification which takes advantage of Bayesian dense deformable template models estimation. This method is illustrated in a typical scenario, over a database of 30 000 simulated aircraft images. Assuming a white noise background model, classification performances are very promising, and appear to be more noise-robust than support vector machines ones.

Bayesian Model Selection for Exponential Random Graph Models via Adjusted Pseudolikelihoods

ABSTRACT Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter estimation in these settings is termed a doubly intractable problem because both the likelihood function and the posterior distribution are intractable. The comparison of Bayesian models is often based on the statistical evidence, the integral of the un-normalized posterior distribution over the model parameters which is rarely available in closed form. For doubly intractable models, estimating the evidence adds another layer of difficulty. Consequently, the selection of the model that best describes an observed network among a collection of exponential random graph models for network analysis is a daunting task. Pseudolikelihoods offer a tractable approximation to the likelihood but should be treated with caution because they can lead to an unreasonable inference. This article specifies a method to adjust pseudolikelihoods to obtain a reasonable, yet tractable, approximation to the likelihood. This allows implementation of widely used computational methods for evidence estimation and pursuit of Bayesian model selection of exponential random graph models for the analysis of social networks. Empirical comparisons to existing methods show that our procedure yields similar evidence estimates, but at a lower computational cost. Supplementary material for this article is available online.

On the use of Markov chain Monte Carlo methods for the sampling of mixture models: a statistical perspective

In this paper we study asymptotic properties of different data-augmentation-type Markov chain Monte Carlo algorithms sampling from mixture models comprising discrete as well as continuous random variables. Of particular interest to us is the situation where sampling from the conditional distribution of the continuous component given the discrete component is infeasible. In this context, we advance Carlin & Chib’s pseudo-prior method as an alternative way of infering mixture models and discuss and compare different algorithms based on this scheme. We propose a novel algorithm, the Frozen Carlin & Chib sampler, which is computationally less demanding than any Metropolised Carlin & Chib-type algorithm. The significant gain of computational efficiency is however obtained at the cost of some asymptotic variance. The performance of the algorithm vis-à-vis alternative schemes is, using some recent results obtained in Maire et al. (Ann Stat 42: 1483–1510, 2014) for inhomogeneous Markov chains evolving alternatingly according to two different

Model comparison for Gibbs random fields using noisy reversible jump Markov chain Monte Carlo

\pi ^{*}

Detecting Aircraft in Low-Resolution Multispectral Images: Specification of Relevant IR Wavelength Bands

π∗-reversible Markov transition kernels, investigated theoretically as well as numerically.