Reliable inference for complex models by discriminative composite likelihood estimation

Composite likelihood estimation has an important role in the analysis of multivariate data for which the full likelihood function is intractable. An important issue in composite likelihood inference is the choice of the weights associated with lower-dimensional data sub-sets, since the presence of incompatible sub-models can deteriorate the accuracy of the resulting estimator. In this paper, we introduce a new approach for simultaneous parameter estimation by tilting, or re-weighting, each sub-likelihood component called discriminative composite likelihood estimation (D-McLE). The data-adaptive weights maximize the composite likelihood function, subject to moving a given distance from uniform weights; then, the resulting weights can be used to rank lower-dimensional likelihoods in terms of their influence in the composite likelihood function. Our analytical findings and numerical examples support the stability of the resulting estimator compared to estimators constructed using standard composition strategies based on uniform weights. The properties of the new method are illustrated through simulated data and real spatial data on multivariate precipitation extremes.Comment: 29 pages, 4 figure

A multiple-imputation-based approach to sensitivity analyses and effectiveness assessments in longitudinal clinical trials.

It is important to understand the effects of a drug as actually taken (effectiveness) and when taken as directed (efficacy). The primary objective of this investigation was to assess the statistical performance of a method referred to as placebo multiple imputation (pMI) as an estimator of effectiveness and as a worst reasonable case sensitivity analysis in assessing efficacy. The pMI method assumes the statistical behavior of placebo- and drug-treated patients after dropout is the statistical behavior of placebo-treated patients. Thus, in the effectiveness context, pMI assumes no pharmacological benefit of the drug after dropout. In the efficacy context, pMI is a specific form of a missing not at random analysis expected to yield a conservative estimate of efficacy. In a simulation study with 18 scenarios, the pMI approach generally provided unbiased estimates of effectiveness and conservative estimates of efficacy. However, the confidence interval coverage was consistently greater than the nominal coverage rate. In contrast, last and baseline observation carried forward (LOCF and BOCF) were conservative in some scenarios and anti-conservative in others with respect to efficacy and effectiveness. As expected, direct likelihood (DL) and standard multiple imputation (MI) yielded unbiased estimates of efficacy and tended to overestimate effectiveness in those scenarios where a drug effect existed. However, in scenarios with no drug effect, and therefore where the true values for both efficacy and effectiveness were zero, DL and MI yielded unbiased estimates of efficacy and effectiveness

A note on predictive densities based on composite likelihood methods

Whenever the computation of data distribution is unfeasible or inconvenient, the classical predictive procedures prove not to be useful. These rely, after all, on the conditional distribution of the future random variable, which is also unavailable. This paper considers a notion of composite likelihood for specifying composite predictive distributions, viewed as surrogates for true unknown predictive distribution. In particular, the focus is on the pairwise likelihood obtained as a weighted product of likelihood factors related to bivariate events associated with both the sample data and future observation. The specification of the weights, andmore generally the evaluation of the frequentist properties of alternative pairwise predictive distributions, is performed by considering the mean square prediction error of the associated predictors and the expected Kullback\u2013Liebler loss of the related predictive densities. Finally, simple examples concerning autoregressive models are presented

Comparing composite likelihood methods based on pairs for spatial Gaussian random fields

In the last years there has been a growing interest in proposing methods for estimating covariance functions for geostatistical data. Among these, maximum likelihood estimators have nice features when we deal with a Gaussian model. However maximum likelihood becomes impractical when the number of observations is very large. In this work we review some solutions and we contrast them in terms of loss of statistical efficiency and computational burden. Specifically we focus on three types of weighted composite likelihood functions based on pairs and we compare them with the method of covariance tapering. Asymptotic properties of the three estimation methods are derived. We illustrate the effectiveness of the methods through theoretical examples, simulation experiments and by analyzing a data set on yearly total precipitation anomalies at weather stations in the United States.In the last years there has been a growing interest in proposing methods for estimating covariance functions for geostatistical data. Among these, maximum likelihood estimators have nice features when we deal with a Gaussian model. However maximum likelihood becomes impractical when the number of observations is very large. In this work we review some solutions and we contrast them in terms of loss of statistical efficiency and computational burden. Specifically we focus on three types of weighted composite likelihood functions based on pairs and we compare them with the method of covariance tapering. Asymptotic properties of the three estimation methods are derived. We illustrate the effectiveness of the methods through theoretical examples, simulation experiments and by analyzing a data set on yearly total precipitation anomalies at weather stations in the United States

Modelling Point Referenced Spatial Count Data: A Poisson Process Approach

Gaussian random field, Gaussian copula, Pairwise likelihood function, Poisson distribution, Renewal proces

Blockwise Euclidean likelihood for spatio-temporal covariance models

A spatio-temporal blockwise Euclidean likelihood method for the estimation of covariance models when dealing with large spatio-temporal Gaussian data is proposed. The method uses moment conditions coming from the score of the pairwise composite likelihood. The blockwise approach guarantees considerable computational improvements over the standard pairwise composite likelihood method. In order to further speed up computation, a general purpose graphics processing unit implementation using OpenCL is implemented. The asymptotic properties of the proposed estimator are derived and the finite sample properties of this methodology by means of a simulation study highlighting the computational gains of the OpenCL graphics processing unit implementation. Finally, there is an application of the estimation method to a wind component data set