Subset models are often useful in the analysis of stationary time series. Although subset autoreg... more Subset models are often useful in the analysis of stationary time series. Although subset autoregressive models have received a lot of attention, the same attention has not been given to subset autoregressive moving-average (ARMA) models, as their identi®cation can be computationally cumbersome. In this paper we propose to overcome this disadvantage by employing a genetic algorithm. After encoding each ARMA model as a binary string, the iterative algorithm attempts to mimic the natural evolution of the population of such strings by allowing strings to reproduce, creating new models that compete for survival in the next population. The success of the proposed procedure is illustrated by showing its ef®ciency in identifying the true model for simulated data. An application to real data is also considered.
Journal of Agricultural Biological and Environmental Statistics, Dec 1, 2007
In this work, we propose a spatial model for analysing rainfall extreme values over the Triveneto... more In this work, we propose a spatial model for analysing rainfall extreme values over the Triveneto region (Italy). The existence of a long term trend in the extremes will be assessed. To integrate data coming from the different stations, we propose a hierarchical model. At the first level, for each monitoring station we model data by making use of a Generalized Extreme Value distribution; at the second level, we combine results from the first stage employing recent advances in modelling non-stationary spatial random fields.
Journal of the American Statistical Association, Mar 1, 2012
In the last years there has been a growing interest in the construction space-time covariance fun... more In the last years there has been a growing interest in the construction space-time covariance functions. However, effective estimation methods for these models are somehow unexplored. In this paper we propose a composite likelihood approach and a weighted variant for the space-time estimation problem.
In this article, we introduce an automatic identification procedure for transfer function models.... more In this article, we introduce an automatic identification procedure for transfer function models. These models are commonplace in time-series analysis, but their identification can be complex. To tackle this problem, we propose to couple a nonlinear conditional least-squares algorithm with a genetic search over the model space. We illustrate the performances of our proposal by examples on simulated and real data.
The Expectation Maximisation (EM) algorithm is a popular technique for max- imum likelihood in in... 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
We prove a central limit theorem for empirical sums of a condition- ally centred functional of a ... 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
This chapter is devoted to the study of second-order random fields, i.e., real-valued random fiel... 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.
In this chapter we present the main statistical methods used to deal with the three types of data... 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.
Being able to simulate probability distributions and random variables is useful whenever we lack ... 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.
PPs are used in a variety of situations (Diggle, (62)), in ecology and forestry (spatial distribu... 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)).
We propose two methods based on composite likelihood that can be used to fit space-time data. We ... more We propose two methods based on composite likelihood that can be used to fit space-time data. We perform an intesive simulation study in order to evaluate the performances of the proposed methods, by keeping a constant comparison with well known methods proposed by the Geostatistical literature. The methods we propose are shown to have considerable computational gains.
Nous étudions la modélisation de données spatio-temporelles de nature mixte ; c'est-à-dire qu... 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.
Subset models are often useful in the analysis of stationary time series. Although subset autoreg... more Subset models are often useful in the analysis of stationary time series. Although subset autoregressive models have received a lot of attention, the same attention has not been given to subset autoregressive moving-average (ARMA) models, as their identi®cation can be computationally cumbersome. In this paper we propose to overcome this disadvantage by employing a genetic algorithm. After encoding each ARMA model as a binary string, the iterative algorithm attempts to mimic the natural evolution of the population of such strings by allowing strings to reproduce, creating new models that compete for survival in the next population. The success of the proposed procedure is illustrated by showing its ef®ciency in identifying the true model for simulated data. An application to real data is also considered.
Journal of Agricultural Biological and Environmental Statistics, Dec 1, 2007
In this work, we propose a spatial model for analysing rainfall extreme values over the Triveneto... more In this work, we propose a spatial model for analysing rainfall extreme values over the Triveneto region (Italy). The existence of a long term trend in the extremes will be assessed. To integrate data coming from the different stations, we propose a hierarchical model. At the first level, for each monitoring station we model data by making use of a Generalized Extreme Value distribution; at the second level, we combine results from the first stage employing recent advances in modelling non-stationary spatial random fields.
Journal of the American Statistical Association, Mar 1, 2012
In the last years there has been a growing interest in the construction space-time covariance fun... more In the last years there has been a growing interest in the construction space-time covariance functions. However, effective estimation methods for these models are somehow unexplored. In this paper we propose a composite likelihood approach and a weighted variant for the space-time estimation problem.
In this article, we introduce an automatic identification procedure for transfer function models.... more In this article, we introduce an automatic identification procedure for transfer function models. These models are commonplace in time-series analysis, but their identification can be complex. To tackle this problem, we propose to couple a nonlinear conditional least-squares algorithm with a genetic search over the model space. We illustrate the performances of our proposal by examples on simulated and real data.
The Expectation Maximisation (EM) algorithm is a popular technique for max- imum likelihood in in... 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
We prove a central limit theorem for empirical sums of a condition- ally centred functional of a ... 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
This chapter is devoted to the study of second-order random fields, i.e., real-valued random fiel... 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.
In this chapter we present the main statistical methods used to deal with the three types of data... 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.
Being able to simulate probability distributions and random variables is useful whenever we lack ... 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.
PPs are used in a variety of situations (Diggle, (62)), in ecology and forestry (spatial distribu... 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)).
We propose two methods based on composite likelihood that can be used to fit space-time data. We ... more We propose two methods based on composite likelihood that can be used to fit space-time data. We perform an intesive simulation study in order to evaluate the performances of the proposed methods, by keeping a constant comparison with well known methods proposed by the Geostatistical literature. The methods we propose are shown to have considerable computational gains.
Nous étudions la modélisation de données spatio-temporelles de nature mixte ; c'est-à-dire qu... 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.
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Papers by Carlo Gaetan