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The Expectation Maximisation (EM) algorithm is a popular technique for max- imum likelihood in incomplete data models. In order to overcome its documented limitations, several stochastic variants are proposed in the literature. However,... more
The Expectation Maximisation (EM) algorithm is a popular technique for max- imum likelihood in incomplete data models. In order to overcome its documented limitations, several stochastic variants are proposed in the literature. However, none of these algorithms is guaranteed to provide a global maximizer of the likelihood function. In this paper we introduce the MEM algorithm — a Metropolis version
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ABSTRACT
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We prove a central limit theorem for empirical sums of a condition- ally centred functional of a Markov random field on a non necessarily regular set of sites S. A studentized version of this theorem is also given with a random... more
We prove a central limit theorem for empirical sums of a condition- ally centred functional of a Markov random field on a non necessarily regular set of sites S. A studentized version of this theorem is also given with a random normalisation. Since positive definiteness of the variance of the sums is crucial for these results, we introduce the notion
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This chapter is devoted to the study of second-order random fields, i.e., real-valued random fields where each X s has finite variance. We also study the broader class of intrinsic random fields, that is, random fields with increments of... more
This chapter is devoted to the study of second-order random fields, i.e., real-valued random fields where each X s has finite variance. We also study the broader class of intrinsic random fields, that is, random fields with increments of finite variance. We consider two approaches.
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In this chapter we present the main statistical methods used to deal with the three types of data seen in earlier chapters. As well as general statistical methods that can be applied to various structures (maximum likelihood, minimum... more
In this chapter we present the main statistical methods used to deal with the three types of data seen in earlier chapters. As well as general statistical methods that can be applied to various structures (maximum likelihood, minimum contrast, least squares, estimation of generalized linear models, the method of moments), we have specific techniques for each type of structure: variogram clouds in geostatistics, conditional pseudo-likelihood, Markov random field coding, nearest-neighbor distances, composite likelihood for PPs, etc. We will present each method in turn.
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Being able to simulate probability distributions and random variables is useful whenever we lack an analytic solution to a problem, be it combinatorial (number of ways to put 32 dominoes on an 8 × 8 grid), a search for maxima (Bayesian... more
Being able to simulate probability distributions and random variables is useful whenever we lack an analytic solution to a problem, be it combinatorial (number of ways to put 32 dominoes on an 8 × 8 grid), a search for maxima (Bayesian image reconstruction, cf. §2.2.2) or calculating integrals.
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PPs are used in a variety of situations (Diggle, (62)), in ecology and forestry (spatial distribution of plant species; (154)), spatial epidemiology (pointwise location of sick individuals; (141)), materials science (porosity models;... more
PPs are used in a variety of situations (Diggle, (62)), in ecology and forestry (spatial distribution of plant species; (154)), spatial epidemiology (pointwise location of sick individuals; (141)), materials science (porosity models; (197)), seismology and geophysics (earthquake epicenters and intensities) and astrophysics (locations of stars in nebulae; (163)).
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Nous étudions la modélisation de données spatio-temporelles de nature mixte ; c'est-à-dire que les données sont composées de valeurs discrètes et continues. Dans la plupart des cas, il s'agit de zéros accompagnés de valeurs... more
Nous étudions la modélisation de données spatio-temporelles de nature mixte ; c'est-à-dire que les données sont composées de valeurs discrètes et continues. Dans la plupart des cas, il s'agit de zéros accompagnés de valeurs positives. Ce phénomène est souvent rencontré dans de nombreux domaines. Par exemple en pluviométrie, on mesure la quantité de pluie pendant des périodes, suivies de zéros lorsqu'il ne pleut pas. Nous proposons ici une approche non hiérarchique pour la modélisation de ce type de données.
We prove a CLT for empirical sums of a conditionally centred functional of a MRF on a non necessarly regular set of site. Since positive definiteness of the variance of the sums is crucial, we introduce the notion of conditionally... more
We prove a CLT for empirical sums of a conditionally centred functional of a MRF on a non necessarly regular set of site. Since positive definiteness of the variance of the sums is crucial, we introduce the notion of conditionally separating partition and we give tools to verify such a positive definiteness. Exemples of Ising and gaussian MRF are studied.
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Abstract As well as in the case of independence and by paralleling, in some sense, what happens in time series analysis, in spatial linear models the presence of anomalous observations can badly affect likelihood based inference, both on... more
Abstract As well as in the case of independence and by paralleling, in some sense, what happens in time series analysis, in spatial linear models the presence of anomalous observations can badly affect likelihood based inference, both on the significance of any large scale ...
The Expectation Maximisation (EM) algorithm is a popular technique for max- imum likelihood in incomplete data models. In order to overcome its documented limitations, several stochastic variants are proposed in the literature. However,... more
The Expectation Maximisation (EM) algorithm is a popular technique for max- imum likelihood in incomplete data models. In order to overcome its documented limitations, several stochastic variants are proposed in the literature. However, none of these algorithms is guaranteed to provide a global maximizer of the likelihood function. In this paper we introduce the MEM algorithm — a Metropolis version
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ABSTRACT This paper presents a hierarchical approach to modelling extremes of a stationary time series. The procedure comprises two stages. In the first stage, exceedances over a high threshold are modelled through a generalized Pareto... more
ABSTRACT This paper presents a hierarchical approach to modelling extremes of a stationary time series. The procedure comprises two stages. In the first stage, exceedances over a high threshold are modelled through a generalized Pareto distribution, which is represented as a mixture of an exponential variable with a Gamma distributed rate parameter. In the second stage, a latent Gamma process is embedded inside the exponential distribution in order to induce temporal dependence among exceedances. Unlike other hierarchical extreme-value models, this version has marginal distributions that belong to the generalized Pareto family, so that the classical extreme-value paradigm is respected. In addition, analytical developments show that different choices of the underlying Gamma process can lead to different degrees of temporal dependence of extremes, including asymptotic independence. The model is tested through a simulation study in a Markov chain setting and used for the analysis of two datasets, one environmental and one financial. In both cases, a good flexibility in capturing different types of tail behaviour is obtained.
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ABSTRACT In this paper, we tackle the study of the relationship between daily non accidental deaths and air pollution in the city of Philadelphia in the years 1974 -1988. For modelling the data, we propose to make use of dynamic... more
ABSTRACT In this paper, we tackle the study of the relationship between daily non accidental deaths and air pollution in the city of Philadelphia in the years 1974 -1988. For modelling the data, we propose to make use of dynamic generalized linear models. These models allow to deal with the serial dependence and time-varying effects of the covariates. Inference is performed by using extended Kaiman filter and smoother.
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ABSTRACT In epidemiology, time-series regression models are specially suitable for evaluating short-term effects of time-varying exposures to pollution. To summarize findings from different studies on different cities, the techniques of... more
ABSTRACT In epidemiology, time-series regression models are specially suitable for evaluating short-term effects of time-varying exposures to pollution. To summarize findings from different studies on different cities, the techniques of designed meta-analyses have been employed. In this context, city-specific findings are summarized by an ‘effect size’ measured on a common scale. Such effects are then pooled together on a second hierarchy of analysis. The objective of this article is to exploit exploratory analysis of city-specific time series. In fact, when dealing with many sources of data, that is, many cities, an exploratory analysis becomes almost unaffordable. Our idea is to explore the time series by fitting complete dynamic regression models. These models are easier to fit than models usually employed and allow implementation of very fast automated model selection algorithms. The idea is to highlight the common features across cities through this analysis, which might then be used to design the meta-analysis. The proposal is illustrated by analysing data on the relationship between daily nonaccidental deaths and air pollution in the 20 US largest cities.
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... S In this paper we introduce a new stochastic variant of the algorithm. The algorithm combines the principle of multiple imputation and the theory of simulated annealing to deal with cases where the -step and the -step can... more
... S In this paper we introduce a new stochastic variant of the algorithm. The algorithm combines the principle of multiple imputation and the theory of simulated annealing to deal with cases where the -step and the -step can be intractable or numerically inefficient. ...