Composite Likelihood Methods Research Articles

Truncated pair-wise likelihood for the Brown-Resnick process with applications to maximum temperature data

Max-stable processes are a natural extension of multivariate extreme value theory important for modeling the spatial dependence of environmental extremes. Inference for max-stable processes observed at several spatial locations is challenging due to the intractability of the full likelihood function. Composite likelihood methods avoid these difficulties by combining a number of low-dimensional likelihood objects, typically defined on pairs or triplets of spatial locations. This work develops a new truncation procedure based on ℓ1-penalty to reduce the complexity and computational cost associated with the composite likelihood function. The new method is shown to achieve a favorable trade-off between computational burden and statistical efficiency by dropping a number of noisy sub-likelihoods. The properties of the new method are illustrated through numerical simulations and an application to real extreme temperature data.

Efficiency assessment of approximated spatial predictions for large datasets

Due to the well-known computational showstopper of the exact Maximum Likelihood Estimation (MLE) for large geospatial observations, a variety of approximation methods have been proposed in the literature, which usually require tuning certain inputs. For example, the recently developed Tile Low-Rank approximation (TLR) method involves many tuning parameters, including numerical accuracy. To properly choose the tuning parameters, it is crucial to adopt a meaningful criterion for the assessment of the prediction efficiency with different inputs. Unfortunately, the most commonly-used Mean Square Prediction Error (MSPE) criterion cannot directly assess the loss of efficiency when the spatial covariance model is approximated. Though the Kullback–Leibler Divergence criterion can provide the information loss of the approximated model, it cannot give more detailed information that one may be interested in, e.g., the accuracy of the computed MSE. In this paper, we present three other criteria, the Mean Loss of Efficiency (MLOE), Mean Misspecification of the Mean Square Error (MMOM), and Root mean square MOM (RMOM), and show numerically that, in comparison with the common MSPE criterion and the Kullback–Leibler Divergence criterion, our criteria are more informative, and thus more adequate to assess the loss of the prediction efficiency by using the approximated or misspecified covariance models. Hence, our suggested criteria are more useful for the determination of tuning parameters for sophisticated approximation methods of spatial model fitting. To illustrate this, we investigate the trade-off between the execution time, estimation accuracy, and prediction efficiency for the TLR method with extensive simulation studies and suggest proper settings of the TLR tuning parameters. We then apply the TLR method to a large spatial dataset of soil moisture in the area of the Mississippi River basin, and compare the TLR with the Gaussian predictive process and the composite likelihood method, showing that our suggested criteria can successfully be used to choose the tuning parameters that can keep the estimation or the prediction accuracy in applications.

Inference in cylindrical models having latent Markovian classes—With an application to ocean current data

Spatial direction vector data can be represented cylindrically by linear magnitudes and circular angles. We analyze such data by using a hierarchical Markov random field model with latent discrete classes and conditionally independent cylindrical data given the classes. The structure of a Potts model segments the spatial domain, and each class defines a cylindrical density that represents a specific structure. We consider two types of cylindrical distributions; the Weibull sine-skewed von Mises distribution, which is skewed in the circular part, and the generalized Pareto-type wrapped Cauchy distribution, which is heavy-tailed in the linear part. In this setting, we develop a statistically efficient block composite likelihood method for parameter estimation. The method is shown to provide much faster convergence than an expectation–maximization approach. However, the convergence is less stable for the block composite likelihood method, and we suggest a hybrid estimation approach for practical use. We apply the approach to study ocean surface currents in the Norwegian Sea. The models are able to describe the currents in terms of interpretable local regimes of two–three classes. Scoring rules are used to measure predictive performance of the two cylindrical densities. Results indicate that there is clearly skew angular components, and possibly also some heavy tails in magnitude.

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.

Neyman–Scott process with alpha-skew-normal clusters

The Neyman–Scott processes introduced so far assume a symmetric distribution for the positions of the offspring points and this makes them inappropriate for modelling the skewed and bimodal clustered patterns and is a hindrance in fitting them to data that exhibit skewness or bimodality. In this paper, we apply the bivariate alpha-skew-normal distribution to the locations of the offspring points and introduce a Neyman–Scott process that regulates skewness and bimodality shapes in clustered point patterns. For this process, we obtain closed forms of the pair correlation function and the third-order intensity reweighted product density function and by use of the composite likelihood method, we fit the model to data. To examine the goodness-of-fit of the presented model, we use a statistical test based on the combined global scaled MAD envelopes. The use of the introduced process to model a clustered point pattern is illustrated by application to the locations of a species of trees in a rainforest dataset.

Composite likelihood methods for large Bayesian VARs with stochastic volatility

SummaryAdding multivariate stochastic volatility of a flexible form to large vector autoregressions (VARs) involving over 100 variables has proved challenging owing to computational considerations and overparametrization concerns. The existing literature works with either homoskedastic models or smaller models with restrictive forms for the stochastic volatility. In this paper, we develop composite likelihood methods for large VARs with multivariate stochastic volatility. These involve estimating large numbers of parsimonious models and then taking a weighted average across these models. We discuss various schemes for choosing the weights. In our empirical work involving VARs of up to 196 variables, we show that composite likelihood methods forecast much better than the most popular large VAR approach, which is computationally practical in very high dimensions: the homoskedastic VAR with Minnesota prior. We also compare our methods to various popular approaches that allow for stochastic volatility using medium and small VARs involving up to 20 variables. We find our methods to forecast appreciably better than these as well.

Multivariate Mixed Response Model with Pairwise Composite-Likelihood Method

In clinical research, study outcomes usually consist of various patients’ information corresponding to the treatment. To have a better understanding of the effects of different treatments, one often needs to analyze multiple clinical outcomes simultaneously, while the data are usually mixed with both continuous and discrete variables. We propose the multivariate mixed response model to implement statistical inference based on the conditional grouped continuous model through a pairwise composite-likelihood approach. It can simplify the multivariate model by dealing with three types of bivariate models and incorporating the asymptotical properties of the composite likelihood via the Godambe information. We demonstrate the validity and the statistic power of the multivariate mixed response model through simulation studies and clinical applications. This composite-likelihood method is advantageous for statistical inference on correlated multivariate mixed outcomes.

Composite likelihood methods for histogram-valued random variables

Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions—such as random rectangles or histograms—each describing a portion of the larger dataset. Recent work has developed likelihood-based methods that permit fitting models for the underlying data while only observing the distributional summaries. However, while powerful, when working with random histograms this approach rapidly becomes computationally intractable as the dimension of the underlying data increases. We introduce a composite-likelihood variation of this likelihood-based approach for the analysis of random histograms in K dimensions, through the construction of lower-dimensional marginal histograms. The performance of this approach is examined through simulated and real data analysis of max-stable models for spatial extremes using millions of observed datapoints in more than $$K=100$$ dimensions. Large computational savings are available compared to existing model fitting approaches.

Convergence of the Euler–Maruyama method for CIR model with Markovian switching

In this paper, we focus on the convergence of stochastic differential equations with Markovian switching and 1∕2-Hölder continuous diffusion coefficients. We give the convergence between numerical solutions and explicit solutions at a rate of 1∕logn by the Euler–Maruyama method. Parameter estimations for CIR model with Markovian switching are obtained by the quadratic variation method and composite likelihood method.

A model with space-varying regression coefficients for clustering multivariate spatial count data.

Multivariate spatial count data are often segmented by unobserved space-varying factors that vary across space. In this setting, regression models that assume space-constant covariate effects could be too restrictive. Motivated by the analysis of cause-specific mortality data, we propose to estimate space-varying effects by exploiting a multivariate hidden Markov field. It models the data by a battery of Poisson regressions with spatially correlated regression coefficients, which are driven by an unobserved spatial multinomial process. It parsimoniously describes multivariate count data by means of a finite number of latent classes. Parameter estimation is carried out by composite likelihood methods, that we specifically develop for the proposed model. In a case study of cause-specific mortality data in Italy, the model was capable to capture the spatial variation of gender differences and ageeffects.

A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel

In multinomial response models, idiosyncratic variations in the indirect utility are generally modeled using Gumbel or normal distributions. This study makes a strong case to substitute these thin-tailed distributions with a t-distribution. First, we demonstrate that a model with a t-distributed error kernel better estimates and predicts preferences, especially in class-imbalanced datasets. Our proposed specification also implicitly accounts for decision-uncertainty behavior, i.e. the degree of certainty that decision-makers hold in their choices relative to the variation in the indirect utility of any alternative. Second – after applying a t-distributed error kernel in a multinomial response model for the first time – we extend this specification to a generalized continuous-multinomial (GCM) model and derive its full-information maximum likelihood estimation procedure. The likelihood involves an open-form expression of the cumulative density function of the multivariate t-distribution, which we propose to compute using a combination of the composite marginal likelihood method and the separation-of-variables approach. Third, we establish finite sample properties of the GCM model with a t-distributed error kernel (GCM-t) and highlight its superiority over the GCM model with a normally-distributed error kernel (GCM-N) in a Monte Carlo study. Finally, we compare GCM-t and GCM-N in an empirical setting related to preferences for electric vehicles (EVs). We observe that accounting for decision-uncertainty behavior in GCM-t results in lower elasticity estimates and a higher willingness to pay for improving the EV attributes than those of the GCM-N model. These differences are relevant in making policies to expedite the adoption of EVs.

Bioinformatic analysis of chickpea acetohydroxyacid synthase gene

Aim. Analysis of homologues of chickpea gene encoding acetohydroxyacid synthase, by bioinformatics methods. Methods. Alignment of nucleotide sequences, UPGMA method, Maximum Composite Likelihood method, homologous modeling of three-dimensional structure of enzyme. Results. Homologues of the acetohydroxyacid syntase gene (AHAS) of chickpea were found among representatives of different families. A certain level of conservativeness of mRNA homologues sequences of AHAS gene within the families was noted, including legumes. The distribution of clusters corresponds to the taxonomic position of the investigated plant species. The single nucleotide polymorphism C / T at position 581, potentially associated with herbicide resistance, was detected. Based on the homologous modeling results, two models of the enzyme AHAS were constructed. The replacement of C / T, which leads to the replacement of the amino acids of alanine with valine, leads to a change in the conformation in the A chain of protein. Conclusions. Marker screening of the source breeding material by «real-time» polymerase chain reaction with the developed primers and the TaqMan probe to the polymorphic region of the AHAS gene will allow differentiating the herbicide «resistant» and «tolerant» alleles of the gene for the selection of target genotypes.
 Keywords: chickpea, acetohydroxyacid syntase gene, single nucleotide polymorphism, resistance to herbicides.

Composite likelihood methods: Rao-type tests based on composite minimum density power divergence estimator

This paper is aimed to present a robust extension of the classical Rao test statistic, in the context of composite likelihood ideas and methods. The Rao-type test statistics are defined on the basis of the composite minimum power divergence estimators instead of the composite maximum likelihood estimator. These Rao-type test statistics are used to test simple and composite null hypotheses. Their performance is evaluated in terms of a simulation study which concentrates to the robustness and the comparison of the Rao-type tests with the respective Wald-type tests considered in Castilla et al. (Entropy 20:18, 2018). The proposed here procedures are developed on the basis of the restricted composite minimum density power divergence estimators which are also discussed for the sake of completeness.

Composite likelihood estimation method for hierarchical Archimedean copulas defined with multivariate compound distributions

We consider the family of hierarchical Archimedean copulas obtained from multivariate exponential mixture distribution through compounding, as introduced by Cossette et al. (2017). We investigate ways of determining the structure of these copulas and estimating their parameters. An agglomerative clustering technique based on the matrix of Spearman’s rhos, combined with a bootstrap procedure, is used to identify the tree structure. Parameters are estimated through a top-down composite likelihood. The validity of the approach is illustrated through two simulation studies in which the procedure is explained step by step. The composite likelihood method is also compared to the full likelihood method in a simple case where the latter is computable.

Variable selection via the composite likelihood method for multilevel longitudinal data with missing responses and covariates

Longitudinal data with multilevel structures are commonly collected when following up subjects in clusters over a period of time. Missing values and variable selection issues are common for such data. Biased results may be produced if incompleteness of data is ignored in the analysis. On the other hand, incorporating a large number of irrelevant covariates into inferential procedures may lead to difficulty in computation and interpretation. A unified penalized composite likelihood framework is developed to handle data with missingness and variable selection issues. It is flexible to handle the situation where responses and covariates are missing not simultaneously under the assumption of missing not at random. The method is justified both rigorously with theoretical results and numerically with simulation studies. The method is also applied to the Waterloo Smoking Prevention Project data.

Comparison of IncL/M Plasmids Using the Neighbor-Joining Method on Basis repA and excA Genes

The aim of this study is to make comparison of IncL/M groups on basis of two genes candidates’ repA and excA genes. The sequences of 27 plasmids were compared using the neighbor-joining method. This method was used to construct a phylogenetic tree for the nucleotide sequences of two genes (repA and excA), using the program MEGA X software. The evolutionary distances were computed using the maximum composite likelihood method. The neighbor-joining method analysis showed different results based on the gene used for comparison. The repA gene was more accurate than excA gene to distinguish between different incL/M plasmids. This study suggested that IncL/M plasmids harboring different antibiotic resistance genes have evolved differently.

Bovine Leukemia Virus in Bovine Aborted Fetuses

We investigated the infection of Bovine Leukemia Virus (BLV) related to other pathogens [Neospora caninum, Bovine Herpesvirus-1 (BoHV-1), Bovine Viral Diarrhea Virus (BVDV), and pathogenic bacteria] in 80 bovine aborted fetuses. The materials comprised whole fetuses, fetal organs, and placenta. The BLV was diagnosed by nested-PCR (env gp51 BLV gene), the identification of viral genotypes by sequencing, and the phylogenetic analysis by neighborjoining and maximum composite likelihood methods. The other pathogens and diagnoses were, respectively: Neospora caninum (nested-PCR), BoHV-1 (nested-PCR), BVDV (PCR), Brucella spp. (isolation and identification), Leptospira spp. (PCR), aerobic bacteria [Enterobacteriaceae, Gram positive cocci, Trueperella (Arcanobacterium) pyogenes] and micro-aerophilic (Campylobacter spp., Histophilus somni, and Listeria monocytogenes) by isolation and identification. BLV fetal antibodies were identified by ELISA kit. Thirteen (16.25%) fetuses were positive by BLV nested-PCR. Phylogenetic analysis revealed BLV genotypes 1, 5, and 6, which are frequently found in cattle in Brazil, Argentina, and Uruguay. No fetuses were positive for BLV antibodies by ELISA. A single case of coinfection with BLV was found for each of the pathogens Trueperella (Arcanobacterium) pyogenes, Klebsiella spp., and Streptococcus spp. were isolated as a pure or representing the preponderance of bacteria in a pooled culture. In the 67 BLV-negative fetuses, pathogens identified were single cases of Trueperella (Arcanobacterium) pyogenes, Staphylococcus aureus, and Brucella abortus; 2 of Escherichia coli; 3 of bovine viral diarrhea virus; and 4 of Neospora caninum. No pathogens were found in 55 fetuses. The low number of BLV positive samples infected or no by other pathogens didn´t allow performing statistical analysis for understanding if there were significative differences among not infected and infected BLV fetuses. Because BLV is an immunosuppressive agent and predisposes the cow to other pathogens, its connection with Leukemia or abortions need additional studies with bigger sampling, for elucidating pathogenesis in the pregnant cow and in the fetus. The rates of BLV transplacental transmission show the necessity of prophylactic measures in Brazilian cattle herds, in order to avoid infection in utero.

Non‐stationary intensity‐duration‐frequency curves integrating information concerning teleconnections and climate change

Rainfall intensity‐duration‐frequency (IDF) curves are commonly used for the design of water resources infrastructure. Numerous studies reported non‐stationarity in meteorological time series. Neglecting to incorporate non‐stationarities in hydrological models may lead to inaccurate results. The present work focuses on the development of a general methodology that copes with non‐stationarities that may exist in rainfall, by making the parameters of the IDF relationship dependent on the covariates of time and climate oscillations. In the recent literature, non‐stationary models are generally fit on data series of specific durations. In the approach proposed here, a single model with a separate functional relation with the return period and the rainfall duration is instead defined. This model has the advantage of being simpler and extending the effective sample size. Its parameters are estimated with the maximum composite likelihood method. Two sites in Ontario, Canada and one site in California, USA, exhibiting non‐stationary behaviours are used as case studies to illustrate the proposed method. For these case studies, the time and the climate indices Atlantic Multi‐decadal Oscillation (AMO) and Western Hemisphere Warm Pool (WHWP) for the stations in Canada, and the time and the climate indices Southern Oscillation Index (SOI) and Pacific Decadal Oscillation (PDO) for the stations in United States are used as covariates. The Gumbel and the generalized extreme value distributions are used as the time‐dependent functions in the numerator of the general IDF relationship. Results show that the non‐stationary framework for IDF modelling provides a better fit to the data than its stationary counterpart according to the Akaike information criterion. Results indicate also that the proposed generalized approach is more robust than the common approach especially for stations with short rainfall records (e.g., R2 of 0.98 compared to 0.69 for duration of 30 min and a sample size of 27 years).

ABLE: blockwise site frequency spectra for inferring complex population histories and recombination

We introduce ABLE (Approximate Blockwise Likelihood Estimation), a novel simulation-based composite likelihood method that uses the blockwise site frequency spectrum to jointly infer past demography and recombination. ABLE is explicitly designed for a wide variety of data from unphased diploid genomes to genome-wide multi-locus data (for example, RADSeq) and can also accommodate arbitrarily large samples. We use simulations to demonstrate the accuracy of this method to infer complex histories of divergence and gene flow and reanalyze whole genome data from two species of orangutan. ABLE is available for download at https://github.com/champost/ABLE.

Independence, successive and conditional likelihood for time series of counts

Serial correlation and overdispersion must be handled properly in analyses of time series of counts, and parameter-driven models combine an underlying latent process with a conditional log-linear Poisson model (given the latent process) for that purpose. Regression coefficients have direct interpretations, but likelihood inference is not straight-forward. We consider a two-step procedure for estimation: First regression parameters are estimated from the marginal distribution; second parameters concerning the latent process are estimated with composite likelihood methods, based on low-order simultaneous or conditional distributions. Confidence intervals are computed by bootstrap. Properties of estimators are examined and compared to other methods in three simulation studies, and the methods are applied to two datasets from the literature concerning hospital admission related to asthma and traffic deaths.