Showing papers in "Statistics and Computing in 2009"
TL;DR: Finite mixtures of the normal inverse Gaussian distribution (and its multivariate extensions) are proposed, which start from a density that allows for skewness and fat tails, generalize the existing models, are tractable and have desirable properties.
Abstract: The majority of the existing literature on model-based clustering deals with symmetric components. In some cases, especially when dealing with skewed subpopulations, the estimate of the number of groups can be misleading; if symmetric components are assumed we need more than one component to describe an asymmetric group. Existing mixture models, based on multivariate normal distributions and multivariate t distributions, try to fit symmetric distributions, i.e. they fit symmetric clusters. In the present paper, we propose the use of finite mixtures of the normal inverse Gaussian distribution (and its multivariate extensions). Such finite mixture models start from a density that allows for skewness and fat tails, generalize the existing models, are tractable and have desirable properties. We examine both the univariate case, to gain insight, and the multivariate case, which is more useful in real applications. EM type algorithms are described for fitting the models. Real data examples are used to demonstrate the potential of the new model in comparison with existing ones.
127 citations
TL;DR: A class of widely applicable trans-dimensional TD models that can be represented by a generic graphical model, which may be incorporated into arbitrary other graphical structures without significantly affecting the mechanism of inference is described.
Abstract: Markov chain Monte Carlo techniques have revolutionized the field of Bayesian statistics. Their power is so great that they can even accommodate situations in which the structure of the statistical model itself is uncertain. However, the analysis of such trans-dimensional (TD) models is not easy and available software may lack the flexibility required for dealing with the complexities of real data, often because it does not allow the TD model to be simply part of some bigger model. In this paper we describe a class of widely applicable TD models that can be represented by a generic graphical model, which may be incorporated into arbitrary other graphical structures without significantly affecting the mechanism of inference. We also present a decomposition of the reversible jump algorithm into abstract and problem-specific components, which provides infrastructure for applying the method to all models in the class considered. These developments represent a first step towards a context-free method for implementing TD models that will facilitate their use by applied scientists for the practical exploration of model uncertainty. Our approach makes use of the popular WinBUGS framework as a sampling engine and we illustrate its use via two simple examples in which model uncertainty is a key feature.
105 citations
TL;DR: An improved method of auxiliary mixture sampling that uses a bounded number of latent variables per observation leads to a substantial increase in efficiency of Auxiliary mixture sampling for highly structured models.
Abstract: The article considers Bayesian analysis of hierarchical models for count, binomial and multinomial data using efficient MCMC sampling procedures. To this end, an improved method of auxiliary mixture sampling is proposed. In contrast to previously proposed samplers the method uses a bounded number of latent variables per observation, independent of the intensity of the underlying Poisson process in the case of count data, or of the number of experiments in the case of binomial and multinomial data. The bounded number of latent variables results in a more general error distribution, which is a negative log-Gamma distribution with arbitrary integer shape parameter. The required approximations of these distributions by Gaussian mixtures have been computed. Overall, the improvement leads to a substantial increase in efficiency of auxiliary mixture sampling for highly structured models. The method is illustrated for finite mixtures of generalized linear models and an epidemiological case study.
98 citations
TL;DR: A new regularization method for regression models which contains a penalty term which explicitly links strength of penalization to the correlation between predictors, and which compares well to competing regularization techniques.
Abstract: A new regularization method for regression models is proposed. The criterion to be minimized contains a penalty term which explicitly links strength of penalization to the correlation between predictors. Like the elastic net, the method encourages a grouping effect where strongly correlated predictors tend to be in or out of the model together. A boosted version of the penalized estimator, which is based on a new boosting method, allows to select variables. Real world data and simulations show that the method compares well to competing regularization techniques. In settings where the number of predictors is smaller than the number of observations it frequently performs better than competitors, in high dimensional settings prediction measures favor the elastic net while accuracy of estimation and stability of variable selection favors the newly proposed method.
84 citations
TL;DR: Approximate Bayesian computation provides an alternative approach requiring only a sampling scheme for the distribution of interest, enabling easier use of quantile distributions under the Bayesian framework.
Abstract: Use of Bayesian modelling and analysis has become commonplace in many disciplines (finance, genetics and image analysis, for example). Many complex data sets are collected which do not readily admit standard distributions, and often comprise skew and kurtotic data. Such data is well-modelled by the very flexibly-shaped distributions of the quantile distribution family, whose members are defined by the inverse of their cumulative distribution functions and rarely have analytical likelihood functions defined. Without explicit likelihood functions, Bayesian methodologies such as Gibbs sampling cannot be applied to parameter estimation for this valuable class of distributions without resorting to numerical inversion. Approximate Bayesian computation provides an alternative approach requiring only a sampling scheme for the distribution of interest, enabling easier use of quantile distributions under the Bayesian framework. Parameter estimates for simulated and experimental data are presented.
82 citations
TL;DR: This work shows that the variational Bayesian analyses can be carried out much faster than the MCMC analyses and produce good estimates of model parameters, and found that the reduced dependence approximation of the normalisation constant outperformed the pseudo-likelihood approximation in the analysis of real and synthetic datasets.
Abstract: Hidden Markov random field models provide an appealing representation of images and other spatial problems. The drawback is that inference is not straightforward for these models as the normalisation constant for the likelihood is generally intractable except for very small observation sets. Variational methods are an emerging tool for Bayesian inference and they have already been successfully applied in other contexts. Focusing on the particular case of a hidden Potts model with Gaussian noise, we show how variational Bayesian methods can be applied to hidden Markov random field inference. To tackle the obstacle of the intractable normalising constant for the likelihood, we explore alternative estimation approaches for incorporation into the variational Bayes algorithm. We consider a pseudo-likelihood approach as well as the more recent reduced dependence approximation of the normalisation constant. To illustrate the effectiveness of these approaches we present empirical results from the analysis of simulated datasets. We also analyse a real dataset and compare results with those of previous analyses as well as those obtained from the recently developed auxiliary variable MCMC method and the recursive MCMC method. Our results show that the variational Bayesian analyses can be carried out much faster than the MCMC analyses and produce good estimates of model parameters. We also found that the reduced dependence approximation of the normalisation constant outperformed the pseudo-likelihood approximation in our analysis of real and synthetic datasets.
70 citations
TL;DR: This paper advocates simulation by the inversion method using a modified Newton-Raphson method, with values of the distribution and density functions obtained by numerical transform inversion, and shows that this algorithm performs well in a series of increasingly complex examples.
Abstract: This paper discusses simulation from an absolutely continuous distribution on the positive real line when the Laplace transform of the distribution is known but its density and distribution functions may not be available. We advocate simulation by the inversion method using a modified Newton-Raphson method, with values of the distribution and density functions obtained by numerical transform inversion. We show that this algorithm performs well in a series of increasingly complex examples. Caution is needed in some situations when the numerical Laplace transform inversion becomes unreliable. In particular the algorithm should not be used for distributions with finite range. But otherwise, except for rather pathological distributions, the approach offers a rapid way of generating random samples with minimal user effort. We contrast our approach with an alternative algorithm due to Devroye (Comput. Math. Appl. 7, 547---552, 1981).
63 citations
TL;DR: A hidden Markov model for longitudinal count data where sources of unobserved heterogeneity arise, making data overdispersed is proposed, using a more flexible approach based on the Expectation Maximization (EM) algorithm.
Abstract: We propose a hidden Markov model for longitudinal count data where sources of unobserved heterogeneity arise, making data overdispersed The observed process, conditionally on the hidden states, is assumed to follow an inhomogeneous Poisson kernel, where the unobserved heterogeneity is modeled in a generalized linear model (GLM) framework by adding individual-specific random effects in the link function
Due to the complexity of the likelihood within the GLM framework, model parameters may be estimated by numerical maximization of the log-likelihood function or by simulation methods; we propose a more flexible approach based on the Expectation Maximization (EM) algorithm Parameter estimation is carried out using a non-parametric maximum likelihood (NPML) approach in a finite mixture context Simulation results and two empirical examples are provided
53 citations
TL;DR: This work provides the range of values of λ1,j that will ensure convergence of the sparse principal components algorithm and consequently achieve sparsity of component loadings for nonstationary time series data.
Abstract: The effect of nonstationarity in time series columns of input data in principal components analysis is examined. Nonstationarity are very common among economic indicators collected over time. They are subsequently summarized into fewer indices for purposes of monitoring. Due to the simultaneous drifting of the nonstationary time series usually caused by the trend, the first component averages all the variables without necessarily reducing dimensionality. Sparse principal components analysis can be used, but attainment of sparsity among the loadings (hence, dimension-reduction is achieved) is influenced by the choice of parameter(s) (λ1,i). Simulated data with more variables than the number of observations and with different patterns of cross-correlations and autocorrelations were used to illustrate the advantages of sparse principal components analysis over ordinary principal components analysis. Sparse component loadings for nonstationary time series data can be achieved provided that appropriate values of λ1,j are used. We provide the range of values of λ1,j that will ensure convergence of the sparse principal components algorithm and consequently achieve sparsity of component loadings.
47 citations
TL;DR: New dependence measures for two real random variables not necessarily linearly related are proposed and are expressed in terms of principal components and are generalized for variables distributed along a curve.
Abstract: We propose new dependence measures for two real random variables not necessarily linearly related. Covariance and linear correlation are expressed in terms of principal components and are generalized for variables distributed along a curve. Properties of these measures are discussed. The new measures are estimated using principal curves and are computed for simulated and real data sets. Finally, we present several statistical applications for the new dependence measures.
44 citations
TL;DR: In this article, a Gaussian prior distribution on the unknown parameters of the inverse regression problem is proposed to regularize their estimation, which is based on the Fisher Lecture given by RD Cook.
Abstract: Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems The original method, however, requires the inversion of the predictors covariance matrix In case of collinearity between these predictors or small sample sizes compared to the dimension, the inversion is not possible and a regularization technique has to be used Our approach is based on a Fisher Lecture given by RD Cook where it is shown that SIR axes can be interpreted as solutions of an inverse regression problem We propose to introduce a Gaussian prior distribution on the unknown parameters of the inverse regression problem in order to regularize their estimation We show that some existing SIR regularizations can enter our framework, which permits a global understanding of these methods Three new priors are proposed leading to new regularizations of the SIR method A comparison on simulated data as well as an application to the estimation of Mars surface physical properties from hyperspectral images are provided
TL;DR: In this paper, a Bayesian approach to estimating a covariance matrix by using a prior that is a mixture over all decomposable graphs, with the probability of each graph size specified by the user and graphs of equal size assigned equal probability, is presented.
Abstract: We present a Bayesian approach to estimating a covariance matrix by using a prior that is a mixture over all decomposable graphs, with the probability of each graph size specified by the user and graphs of equal size assigned equal probability. Most previous approaches assume that all graphs are equally probable. We show empirically that the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs in more efficiently estimating the covariance matrix. The prior requires knowing the number of decomposable graphs for each graph size and we give a simulation method for estimating these counts. We also present a Markov chain Monte Carlo method for estimating the posterior distribution of the covariance matrix that is much more efficient than current methods. Both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.
TL;DR: A new class of nonparametric tests, based on random projections, is proposed, which can be used for several null hypotheses of practical interest, including uniformity for spherical and compositional data, sphericity of the underlying distribution and homogeneity in two-sample problems on the sphere or the simplex.
Abstract: A new class of nonparametric tests, based on random projections, is proposed. They can be used for several null hypotheses of practical interest, including uniformity for spherical (directional) and compositional data, sphericity of the underlying distribution and homogeneity in two-sample problems on the sphere or the simplex.
The proposed procedures have a number of advantages, mostly associated with their flexibility (for example, they also work to test "partial uniformity" in a subset of the sphere), computational simplicity and ease of application even in high-dimensional cases.
This paper includes some theoretical results concerning the behaviour of these tests, as well as a simulation study and a detailed discussion of a real data problem in astronomy.
TL;DR: This paper proposes a new calibration method for obtaining reliable cut-off points of distances derived from the MCD estimator of scatter based on a more accurate estimate of the extreme tail of the distribution of robust distances.
Abstract: Multivariate outlier detection requires computation of robust distances to be compared with appropriate cut-off points. In this paper we propose a new calibration method for obtaining reliable cut-off points of distances derived from the MCD estimator of scatter. These cut-off points are based on a more accurate estimate of the extreme tail of the distribution of robust distances. We show that our procedure gives reliable tests of outlyingness in almost all situations of practical interest, provided that the sample size is not much smaller than 50. Therefore, it is a considerable improvement over all the available MCD procedures, which are unable to provide good control over the size of multiple outlier tests for the data structures considered in this paper.
TL;DR: A new Gaussian proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method for solving non-linear filtering problems and is characterized by the exact moments obtained from the dynamical system.
Abstract: In this article we introduce a new Gaussian proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method for solving non-linear filtering problems. The proposal, in line with the recent trend, incorporates the current observation. The introduced proposal is characterized by the exact moments obtained from the dynamical system. This is in contrast with recent works where the moments are approximated either numerically or by linearizing the observation model. We show further that the newly introduced proposal performs better than other similar proposal functions which also incorporate both state and observations.
TL;DR: The novelty of the paper is the combination of the two techniques, tapering and backfitting, to model and analyze spatial datasets several orders of magnitude larger than those datasets typically analyzed with conventional approaches.
Abstract: Many problems in the environmental and biological sciences involve the analysis of large quantities of data. Further, the data in these problems are often subject to various types of structure and, in particular, spatial dependence. Traditional model fitting often fails due to the size of the datasets since it is difficult to not only specify but also to compute with the full covariance matrix describing the spatial dependence. We propose a very general type of mixed model that has a random spatial component. Recognizing that spatial covariance matrices often exhibit a large number of zero or near-zero entries, covariance tapering is used to force near-zero entries to zero. Then, taking advantage of the sparse nature of such tapered covariance matrices, backfitting is used to estimate the fixed and random model parameters. The novelty of the paper is the combination of the two techniques, tapering and backfitting, to model and analyze spatial datasets several orders of magnitude larger than those datasets typically analyzed with conventional approaches. Results will be demonstrated with two datasets. The first consists of regional climate model output that is based on an experiment with two regional and two driver models arranged in a two-by-two layout. The second is microarray data used to build a profile of differentially expressed genes relating to cerebral vascular malformations, an important cause of hemorrhagic stroke and seizures.
TL;DR: This work proposes the use of a marginal density estimator to construct between-model proposal distributions and compares the performance of this approach to well established alternatives in both time series and mixture model examples.
Abstract: The reversible jump Markov chain Monte Carlo (MCMC) sampler (Green in Biometrika 82:711---732, 1995) has become an invaluable device for Bayesian practitioners. However, the primary difficulty with the sampler lies with the efficient construction of transitions between competing models of possibly differing dimensionality and interpretation. We propose the use of a marginal density estimator to construct between-model proposal distributions. This provides both a step towards black-box simulation for reversible jump samplers, and a tool to examine the utility of common between-model mapping strategies. We compare the performance of our approach to well established alternatives in both time series and mixture model examples.
TL;DR: This paper uses regression quantiles to create Markov chains for the estimation of the quantile curves and uses approximate Bayesian factor in the inference, which extends the work in automatic Bayesian mean curve fitting to quantile regression.
Abstract: Quantile regression, including median regression, as a more completed statistical model than mean regression, is now well known with its wide spread applications. Bayesian inference on quantile regression or Bayesian quantile regression has attracted much interest recently. Most of the existing researches in Bayesian quantile regression focus on parametric quantile regression, though there are discussions on different ways of modeling the model error by a parametric distribution named asymmetric Laplace distribution or by a nonparametric alternative named scale mixture asymmetric Laplace distribution. This paper discusses Bayesian inference for nonparametric quantile regression. This general approach fits quantile regression curves using piecewise polynomial functions with an unknown number of knots at unknown locations, all treated as parameters to be inferred through reversible jump Markov chain Monte Carlo (RJMCMC) of Green (Biometrika 82:711---732, 1995). Instead of drawing samples from the posterior, we use regression quantiles to create Markov chains for the estimation of the quantile curves. We also use approximate Bayesian factor in the inference. This method extends the work in automatic Bayesian mean curve fitting to quantile regression. Numerical results show that this Bayesian quantile smoothing technique is competitive with quantile regression/smoothing splines of He and Ng (Comput. Stat. 14:315---337, 1999) and P-splines (penalized splines) of Eilers and de Menezes (Bioinformatics 21(7):1146---1153, 2005).
TL;DR: A novel ensemble classifier generation method by integrating the ideas of bootstrap aggregation and Principal Component Analysis (PCA), which performs better than or as well as several other ensemble methods on some benchmark data sets publicly available from the UCI repository.
Abstract: This paper presents a novel ensemble classifier generation method by integrating the ideas of bootstrap aggregation and Principal Component Analysis (PCA). To create each individual member of an ensemble classifier, PCA is applied to every out-of-bag sample and the computed coefficients of all principal components are stored, and then the principal components calculated on the corresponding bootstrap sample are taken as additional elements of the original feature set. A classifier is trained with the bootstrap sample and some features randomly selected from the new feature set. The final ensemble classifier is constructed by majority voting of the trained base classifiers. The results obtained by empirical experiments and statistical tests demonstrate that the proposed method performs better than or as well as several other ensemble methods on some benchmark data sets publicly available from the UCI repository. Furthermore, the diversity-accuracy patterns of the ensemble classifiers are investigated by kappa-error diagrams.
TL;DR: The cornerstone of the procedures here introduced is the connection between cumulants of a random variable and a suitable compound Poisson random variable, which holds also for multivariate random variables.
Abstract: We propose new algorithms for generating k-statistics, multivariate k-statistics, polykays and multivariate polykays. The resulting computational times are very fast compared with procedures existing in the literature. Such speeding up is obtained by means of a symbolic method arising from the classical umbral calculus. The classical umbral calculus is a light syntax that involves only elementary rules to managing sequences of numbers or polynomials. The cornerstone of the procedures here introduced is the connection between cumulants of a random variable and a suitable compound Poisson random variable. Such a connection holds also for multivariate random variables.
TL;DR: A statistical framework in which the observed images are defined as noisy realizations of a randomly deformed template image and the Markovian properties of deformations are used to build an efficient simulation strategy based on a Metropolis-Hasting-Within-Gibbs sampler.
Abstract: This paper is about object deformations observed throughout a sequence of images. We present a statistical framework in which the observed images are defined as noisy realizations of a randomly deformed template image. In this framework, we focus on the problem of the estimation of parameters related to the template and deformations. Our main motivation is the construction of estimation framework and algorithm which can be applied to short sequences of complex and highly-dimensional images. The originality of our approach lies in the representations of the template and deformations, which are defined on a common triangulated domain, adapted to the geometry of the observed images. In this way, we have joint representations of the template and deformations which are compact and parsimonious. Using such representations, we are able to drastically reduce the number of parameters in the model. Besides, we adapt to our framework the Stochastic Approximation EM algorithm combined with a Markov Chain Monte Carlo procedure which was proposed in 2004 by Kuhn and Lavielle. Our implementation of this algorithm takes advantage of some properties which are specific to our framework. More precisely, we use the Markovian properties of deformations to build an efficient simulation strategy based on a Metropolis-Hasting-Within-Gibbs sampler. Finally, we present some experiments on sequences of medical images and synthetic data.
TL;DR: A factored covariance model is proposed for matrix data, and a method for classification using a likelihood ratio criterion is developed, which has previously been used for evaluating the strength of forensic evidence.
Abstract: A dimension reduction technique is proposed for matrix data, with applications to face recognition from images. In particular, we propose a factored covariance model for the data under study, estimate the parameters using maximum likelihood, and then carry out eigendecompositions of the estimated covariance matrix. We call the resulting method factored principal components analysis. We also develop a method for classification using a likelihood ratio criterion, which has previously been used for evaluating the strength of forensic evidence. The methodology is illustrated with applications in face recognition.
TL;DR: Numerical tests suggest that the weighted kernel estimation can lead to tangible improvements in performance over the usual kernel deconvolution estimator, and is free from the problem of negative estimation in the tails that can occur when using modified kernels.
Abstract: Nonparametric density estimation in the presence of measurement error is considered. The usual kernel deconvolution estimator seeks to account for the contamination in the data by employing a modified kernel. In this paper a new approach based on a weighted kernel density estimator is proposed. Theoretical motivation is provided by the existence of a weight vector that perfectly counteracts the bias in density estimation without generating an excessive increase in variance. In practice a data driven method of weight selection is required. Our strategy is to minimize the discrepancy between a standard kernel estimate from the contaminated data on the one hand, and the convolution of the weighted deconvolution estimate with the measurement error density on the other hand. We consider a direct implementation of this approach, in which the weights are optimized subject to sum and non-negativity constraints, and a regularized version in which the objective function includes a ridge-type penalty. Numerical tests suggest that the weighted kernel estimation can lead to tangible improvements in performance over the usual kernel deconvolution estimator. Furthermore, weighted kernel estimates are free from the problem of negative estimation in the tails that can occur when using modified kernels. The weighted kernel approach generalizes to the case of multivariate deconvolution density estimation in a very straightforward manner.
TL;DR: In this article, methodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions are proposed. And both exact values can be derived.
Abstract: For a confidence interval (L(X),U(X)) of a parameter θ in one-parameter discrete distributions, the coverage probability is a variable function of θ. The confidence coefficient is the infimum of the coverage probabilities, infθPθ( θe(L(X), U(X))). Since we do not know which point in the parameter space the infimum coverage probability occurs at, the exact confidence coefficients are unknown. Beside confidence coefficients, evaluation of a confidence intervals can be based on the average coverage probability. Usually, the exact average probability is also unknown and it was approximated by taking the mean of the coverage probabilities at some randomly chosen points in the parameter space. In this article, methodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions are proposed. With these methodologies, both exact values can be derived.
TL;DR: A new acceleration scheme for optimization procedures is defined through geometric considerations and applied to the EM algorithm, and in many cases it is able to circumvent the problem of stagnation.
Abstract: A new acceleration scheme for optimization procedures is defined through geometric considerations and applied to the EM algorithm. In many cases it is able to circumvent the problem of stagnation. No modification of the original algorithm is required. It is simply used as a software component. Thus the new scheme can be easily implemented to accelerate a fixed point algorithm maximizing some objective function. Some practical examples and simulations are presented to show its ability to accelerate EM-type algorithms converging slowly.
TL;DR: An approximate nonparametric solution to this problem has similarities to that of testing for stochastic dominance, that is, of testing under order restrictions, for ordered categorical variables.
Abstract: In many sciences researchers often meet the problem of establishing if the distribution of a categorical variable is more concentrated, or less heterogeneous, in population P 1 than in population P 2. An approximate nonparametric solution to this problem is discussed within the permutation context. Such a solution has similarities to that of testing for stochastic dominance, that is, of testing under order restrictions, for ordered categorical variables. Main properties of given solution and a Monte Carlo simulation in order to evaluate its degree of approximation and its power behaviour are examined. Two application examples are also discussed.
TL;DR: A by-product of this task gave us an infinite mixture representation of the Fisher–Bingham distribution; the mixing distributions being based on the Dirichlet distribution.
Abstract: This paper primarily is concerned with the sampling of the Fisher---Bingham distribution and we describe a slice sampling algorithm for doing this. A by-product of this task gave us an infinite mixture representation of the Fisher---Bingham distribution; the mixing distributions being based on the Dirichlet distribution. Finite numerical approximations are considered and a sampling algorithm based on a finite mixture approximation is compared with the slice sampling algorithm.
TL;DR: This paper proposes a new ‘nondecimated’ lifting transform, based on the lifting algorithm which removes one coefficient at a time, and opens avenues for generating a ‘best’ representation, which will be explored.
Abstract: Classical nondecimated wavelet transforms are attractive for many applications. When the data comes from complex or irregular designs, the use of second generation wavelets in nonparametric regression has proved superior to that of classical wavelets. However, the construction of a nondecimated second generation wavelet transform is not obvious. In this paper we propose a new `nondecimated' lifting transform, based on the lifting algorithm which removes one coefficient at a time, and explore its behavior. Our approach also allows for embedding adaptivity in the transform, i.e. wavelet functions can be constructed such that their smoothness adjusts to the local properties of the signal. We address the problem of nonparametric regression and propose an (averaged) estimator obtained by using our nondecimated lifting technique teamed with empirical Bayes shrinkage. Simulations show that our proposed method has higher performance than competing techniques able to work on irregular data. Our construction also opens avenues for generating a `best' representation, which we shall explore.
TL;DR: A maximum pairwise likelihood approach to estimate the parameters of multivariate mixed Poisson models when the mixing distribution is a multivariate Gamma distribution is studied and the consistency and asymptotic normality of this estimator are derived.
Abstract: Estimating the parameters of multivariate mixed Poisson models is an important problem in image processing applications, especially for active imaging or astronomy. The classical maximum likelihood approach cannot be used for these models since the corresponding masses cannot be expressed in a simple closed form. This paper studies a maximum pairwise likelihood approach to estimate the parameters of multivariate mixed Poisson models when the mixing distribution is a multivariate Gamma distribution. The consistency and asymptotic normality of this estimator are derived. Simulations conducted on synthetic data illustrate these results and show that the proposed estimator outperforms classical estimators based on the method of moments. An application to change detection in low-flux images is also investigated.
TL;DR: A novel spatial-temporal algorithm for generating packing structures of disks and spheres, which not only incorporates all the attractive features of existing algorithms but is also more flexible in defining spatial interactions and other control parameters.
Abstract: We describe a novel spatial-temporal algorithm for generating packing structures of disks and spheres, which not only incorporates all the attractive features of existing algorithms but is also more flexible in defining spatial interactions and other control parameters. The advantage of this approach lies in the ability of marks to exploit to best advantage the space available to them by changing their size in response to the interaction pressure of their neighbours. Allowing particles to move in response to such pressure results in high-intensity packing. Indeed, since particles may temporarily overlap, even under hard-packing scenarios, they possess a greater potential for rearranging themselves, and thereby creating even higher packing intensities than exist under other strategies. Non-overlapping pattern structures are achieved simply by allowing the process to `burn-out' at the end of its development period. A variety of different growth-interaction regimes are explored, both symmetric and asymmetric, and the convergence issues that they raise are examined. We conjecture that not only may this algorithm be easily generalised to cover a large variety of situations across a wide range of disciplines, but that appropriately targeted generalisations may well include established packing algorithms as special cases.