Composite Likelihood Methods Research Articles

Two-Locus Likelihoods Under Variable Population Size and Fine-Scale Recombination Rate Estimation.

Two-locus sampling probabilities have played a central role in devising an efficient composite-likelihood method for estimating fine-scale recombination rates. Due to mathematical and computational challenges, these sampling probabilities are typically computed under the unrealistic assumption of a constant population size, and simulation studies have shown that resulting recombination rate estimates can be severely biased in certain cases of historical population size changes. To alleviate this problem, we develop here new methods to compute the sampling probability for variable population size functions that are piecewise constant. Our main theoretical result, implemented in a new software package called LDpop, is a novel formula for the sampling probability that can be evaluated by numerically exponentiating a large but sparse matrix. This formula can handle moderate sample sizes ([Formula: see text]) and demographic size histories with a large number of epochs ([Formula: see text]). In addition, LDpop implements an approximate formula for the sampling probability that is reasonably accurate and scales to hundreds in sample size ([Formula: see text]). Finally, LDpop includes an importance sampler for the posterior distribution of two-locus genealogies, based on a new result for the optimal proposal distribution in the variable-size setting. Using our methods, we study how a sharp population bottleneck followed by rapid growth affects the correlation between partially linked sites. Then, through an extensive simulation study, we show that accounting for population size changes under such a demographic model leads to substantial improvements in fine-scale recombination rate estimation.

Likelihood-Based Parameter Estimation for High-Dimensional Phylogenetic Comparative Models: Overcoming the Limitations of "Distance-Based" Methods.

Recently, a suite of distance-based multivariate phylogenetic comparative methods has been proposed for studying the evolution of high-dimensional traits, such as morphometric coordinates, gene expression data, and function-valued traits. These methods allow for the statistical comparison of evolutionary rates, assessment of phylogenetic signal, and tests of correlated high-dimensional trait evolution. Simulations reveal that distance-based comparative methods exhibit low statistical power and high Type I error under various evolutionary scenarios. Distance-based methods are also limited to relatively simple model specification (e.g., Brownian motion evolution) due to the lack of a likelihood function for parameter estimation. Here I propose an alternative method for studying high-dimensional trait evolution which overcomes some of the statistical limitations associated with distance-based methods. This framework, based on parametric bootstrapping and maximum pseudolikelihood parameter estimation, opens up the ability to estimate alternative evolutionary models, combine multiple evolutionary hypotheses, and potentially allow missing data and within-species variation. Simulations reveal that pairwise composite likelihood methods demonstrate appropriate Type I error and high statistical power, thus providing a robust framework for studying high-dimensional trait evolution. These methods are implemented in the R package phylocurve [Covariance; distance; evolutionary rate; function-valued trait; high-dimensional; morphometric; multivariate; pairwise composite likelihood; phylogenetic comparative method; phylogenetic generalized least squares; phylogenetic signal.].

Genomewide ancestry and divergence patterns from low-coverage sequencing data reveal a complex history of admixture in wild baboons.

Naturally occurring admixture has now been documented in every major primate lineage, suggesting its key role in primate evolutionary history. Active primate hybrid zones can provide valuable insight into this process. Here, we investigate the history of admixture in one of the best-studied natural primate hybrid zones, between yellow baboons (Papio cynocephalus) and anubis baboons (Papio anubis) in the Amboseli ecosystem of Kenya. We generated a new genome assembly for yellow baboon and low-coverage genomewide resequencing data from yellow baboons, anubis baboons and known hybrids (n=44). Using a novel composite likelihood method for estimating local ancestry from low-coverage data, we found high levels of genetic diversity and genetic differentiation between the parent taxa, and excellent agreement between genome-scale ancestry estimates and a priori pedigree, life history and morphology-based estimates (r(2) =0.899). However, even putatively unadmixed Amboseli yellow individuals carried a substantial proportion of anubis ancestry, presumably due to historical admixture. Further, the distribution of shared vs. fixed differences between a putatively unadmixed Amboseli yellow baboon and an unadmixed anubis baboon, both sequenced at high coverage, is inconsistent with simple isolation-migration or equilibrium migration models. Our findings suggest a complex process of intermittent contact that has occurred multiple times in baboon evolutionary history, despite no obvious fitness costs to hybrids or major geographic or behavioural barriers. In combination with the extensive phenotypic data available for baboon hybrids, our results provide valuable context for understanding the history of admixture in primates, including in our own lineage.

Differentiation of the Chinese minority medicinal plant genus Berchemia spp. by evaluating three candidate barcodes.

The genus Berchemia comprises important Chinese plants with considerable medicinal value; however, these plants are often misidentified in the herbal medicinal market. To differentiate the various morphotypes of Berchemia species, a proficient method employing the screening of universal DNA barcodes was used in this work. Three candidate barcoding loci, namely, psbA-trnH, rbcL, and the second internal transcribed spacer (ITS2), were used to identify an effective DNA barcode that can differentiate the various Berchemia species. Additionally, PCR amplification, efficient sequencing, intra- and inter-specific divergences, and DNA barcoding gaps were employed to assess the ability of each barcode to identify these diverse Berchemia plants authentically; the species were differentiated using the Kimura two-parameter and maximum composite likelihood methods. Sequence data analysis showed that the ITS2 region was the most suitable candidate barcode and exhibited the highest interspecific divergence among the three DNA-barcoding sequences. A clear differentiation was observed at the species level, in which a maximum distance of 0.264 was exhibited between dissimilar species. Clustal analysis also demonstrated that ITS2 clearly differentiated the test species in a more effective manner than that with the two other barcodes at both the hybrid and variety levels. Results indicate that DNA barcoding is ideal for species-level identification of Berchemia and provides a foundation for further identification at the molecular level of other Rhamnaceae medicinal plants.

Likelihood-based inference for multivariate space-time wrapped-Gaussian fields

ABSTRACTDirectional spatial data, typically represented through angles, are of central importance in many scientific disciplines, such as environmental sciences, oceanography and meteorology, among others. We propose a wrapped-Gaussian field to model directions in a multivariate spatial or spatio-temporal context. The n-dimensional distributions of a wrapped Gaussian field can be written as a sum over the n-dimensional lattice of , making likelihood-based inference impracticable. We adopt a parametric approach and develop composite likelihood methods to estimate the parameters associated with location, as well as the spatial or spatio-temporal dependence. Our approach outperforms the analytical and computational limitations of full likelihood, because it works with the marginal bivariate distributions of the random field. We study the performance of the method through simulation experiments and by analysing a real data set of wave directions from the Adriatic coast of Italy.

A flexible class of non-separable cross-covariance functions for multivariate space–time data

Multivariate space–time data are increasingly available in various scientific disciplines. When analyzing these data, one of the key issues is to describe the multivariate space–time dependences. Under the Gaussian framework, one needs to propose relevant models for multivariate space–time covariance functions, i.e. matrix-valued mappings with the additional requirement of non-negative definiteness. We propose a flexible parametric class of cross-covariance functions for multivariate space–time Gaussian random fields. Space–time components belong to the (univariate) Gneiting class of space–time covariance functions, with Matérn or Cauchy covariance functions in the spatial margins. The smoothness and scale parameters can be different for each variable. We provide sufficient conditions for positive definiteness. A simulation study shows that the parameters of this model can be efficiently estimated using weighted pairwise likelihood, which belongs to the class of composite likelihood methods. We then illustrate the model on a French dataset of weather variables.

Augmented composite likelihood for copula modeling in family studies under biased sampling.

The heritability of chronic diseases can be effectively studied by examining the nature and extent of within-family associations in disease onset times. Families are typically accrued through a biased sampling scheme in which affected individuals are identified and sampled along with their relatives who may provide right-censored or current status data on their disease onset times. We develop likelihood and composite likelihood methods for modeling the within-family association in these times through copula models in which dependencies are characterized by Kendall's [Formula: see text] Auxiliary data from independent individuals are exploited by augmentating composite likelihoods to increase precision of marginal parameter estimates and consequently increase efficiency in dependence parameter estimation. An application to a motivating family study in psoriatic arthritis illustrates the method and provides some evidence of excessive paternal transmission of risk.

Composite Estimating Equation Method for the Accelerated Failure Time Model with Length‐biased Sampling Data

AbstractLength‐biased sampling data are often encountered in the studies of economics, industrial reliability, epidemiology, genetics and cancer screening. The complication of this type of data is due to the fact that the observed lifetimes suffer from left truncation and right censoring, where the left truncation variable has a uniform distribution. In the Cox proportional hazards model, Huang & Qin (Journal of the American Statistical Association, 107, 2012, p. 107) proposed a composite partial likelihood method which not only has the simplicity of the popular partial likelihood estimator, but also can be easily performed by the standard statistical software. The accelerated failure time model has become a useful alternative to the Cox proportional hazards model. In this paper, by using the composite partial likelihood technique, we study this model with length‐biased sampling data. The proposed method has a very simple form and is robust when the assumption that the censoring time is independent of the covariate is violated. To ease the difficulty of calculations when solving the non‐smooth estimating equation, we use a kernel smoothed estimation method (Heller; Journal of the American Statistical Association, 102, 2007, p. 552). Large sample results and a re‐sampling method for the variance estimation are discussed. Some simulation studies are conducted to compare the performance of the proposed method with other existing methods. A real data set is used for illustration.

The distribution of Blastocystis subtypes in isolates from Qatar.

BackgroundBlastocystis is a common single-celled intestinal parasite of humans and other animals comprising at least 17 genetically distinct small subunit ribosomal RNA lineages (subtypes (STs)), nine of which have been found in humans. The geographic distribution of Blastocystis subtypes is variable, but the subtypes present in Qatar are at present unknown.MethodsStool samples were collected from randomly selected, apparently healthy subjects arriving in Qatar for the first time. Blastocystis subtypes were determined by sequencing of the small subunit rRNA gene (SSU rDNA) PCR products. Phylogenetic analyses were done using Maximum Composite Likelihood method.Results71.1 % of samples were positive for Blastocystis infection based on PCR-detection methodology compared to only 6.9 % by microscopy. Prevalence of Blastocystis did not differ between the sexes nor between age classes. However, there was a regional difference in prevalence with subjects arriving from Africa showing the highest (87.6 %), those from Western Asia intermediate (68.6 %) and from Eastern Asia the lowest prevalence (67.6 %). Genetic analysis detected only three STs. ST3 was the most common (69.3 %) and ST2 was the rarest (3.5 %), while ST1 had a prevalence of 27.2 %. ST2 showed a regional variation, being absent from the 64 Western Asian Blastocystis-positive subjects. Both ST1 and ST3 showed significant differences in prevalence between the sexes.ConclusionsThis is the first report exploring the distribution of Blastocystis subtypes in our region. We recommend that stool screening via microscopy for the presence of Blastocystis should be abandoned since it is extremely insensitive. In future, the prevalence of Blastocystis infections should be based on PCR methodology and we predict that in the years ahead diagnostic PCR will become the tool of choice. More work is needed to identify the full range of Blastocystis subtypes that circulate in our region.

Composite likelihood and maximum likelihood methods for joint latent class modeling of disease prevalence and high-dimensional semicontinuous biomarker data

Joint latent class modeling of disease prevalence and high-dimensional semicontinuous biomarker data has been proposed to study the relationship between diseases and their related biomarkers. Howev...

A new generalized heterogeneous data model (GHDM) to jointly model mixed types of dependent variables

This paper formulates a generalized heterogeneous data model (GHDM) that jointly handles mixed types of dependent variables—including multiple nominal outcomes, multiple ordinal variables, and multiple count variables, as well as multiple continuous variables—by representing the covariance relationships among them through a reduced number of latent factors. Sufficiency conditions for identification of the GHDM parameters are presented. The maximum approximate composite marginal likelihood (MACML) method is proposed to estimate this jointly mixed model system. This estimation method provides computational time advantages since the dimensionality of integration in the likelihood function is independent of the number of latent factors. The study undertakes a simulation experiment within the virtual context of integrating residential location choice and travel behavior to evaluate the ability of the MACML approach to recover parameters. The simulation results show that the MACML approach effectively recovers underlying parameters, and also that ignoring the multi-dimensional nature of the relationship among mixed types of dependent variables can lead not only to inconsistent parameter estimation, but also have important implications for policy analysis.

A Composite-Likelihood Method for Detecting Incomplete Selective Sweep from Population Genomic Data.

Adaptive evolution occurs as beneficial mutations arise and then increase in frequency by positive natural selection. How, when, and where in the genome such evolutionary events occur is a fundamental question in evolutionary biology. It is possible to detect ongoing positive selection or an incomplete selective sweep in species with sexual reproduction because, when a beneficial mutation is on the way to fixation, homologous chromosomes in the population are divided into two groups: one carrying the beneficial allele with very low polymorphism at nearby linked loci and the other carrying the ancestral allele with a normal pattern of sequence variation. Previous studies developed long-range haplotype tests to capture this difference between two groups as the signal of an incomplete selective sweep. In this study, we propose a composite-likelihood-ratio (CLR) test for detecting incomplete selective sweeps based on the joint sampling probabilities for allele frequencies of two groups as a function of strength of selection and recombination rate. Tested against simulated data, this method yielded statistical power and accuracy in parameter estimation that are higher than the iHS test and comparable to the more recently developed nSL test. This procedure was also applied to African Drosophila melanogaster population genomic data to detect candidate genes under ongoing positive selection. Upon visual inspection of sequence polymorphism, candidates detected by our CLR method exhibited clear haplotype structures predicted under incomplete selective sweeps. Our results suggest that different methods capture different aspects of genetic information regarding incomplete sweeps and thus are partially complementary to each other.

Estimating the relative rate of recombination to mutation in bacteria from single-locus variants using composite likelihood methods

A number of studies have suggested using comparisons between DNA sequences of closely related bacterial isolates to estimate the relative rate of recombination to mutation for that bacterial species. We consider such an approach which uses single-locus variants: pairs of isolates whose DNA differ at a single gene locus. One way of deriving point estimates for the relative rate of recombination to mutation from such data is to use composite likelihood methods. We extend recent work in this area so as to be able to construct confidence intervals for our estimates, without needing to resort to computationally-intensive bootstrap procedures, and to develop a test for whether the relative rate varies across loci. Both our test and method for constructing confidence intervals are obtained by modeling the dependence structure in the data, and then applying asymptotic theory regarding the distribution of estimators obtained using a composite likelihood. We applied these methods to multi-locus sequence typing (MLST) data from eight bacteria, finding strong evidence for considerable rate variation in three of these: Bacillus cereus, Enterococcus faecium and Klebsiella pneumoniae.

Approximate Bayesian computation with composite score functions

Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.

Spatial composite likelihood inference using local C-vines

We present a vine copula based composite likelihood approach to model spatial dependencies, which allows to perform prediction at arbitrary locations. It combines established methods to model (spatial) dependencies. On the one hand spatial differences between the variable locations are utilized to model the degree of spatial dependence. On the other hand the flexible class of C-vine copulas are used to model the spatial dependency structure locally. These local C-vine copulas are parametrized jointly, exploiting a relationship between the copula parameters and the corresponding spatial distances and elevation differences, and are combined in a composite likelihood approach. This spatial local C-vine composite likelihood (S-LCVCL) method benefits from the fact that it is able to capture non-Gaussian dependency structures. The development and validation of the new methodology is illustrated using a data set of daily mean temperatures observed at 73 observation stations spread over Germany. For validation continuous ranked probability scores are utilized. Comparison with another vine copula based approach and a Gaussian approach for spatial dependency modeling shows a preference for vine copula based (spatial) dependency structures.

Demographic inferences using short-read genomic data in an approximate Bayesian computation framework: in silico evaluation of power, biases and proof of concept in Atlantic walrus.

Approximate Bayesian computation (ABC) is a powerful tool for model-based inference of demographic histories from large genetic data sets. For most organisms, its implementation has been hampered by the lack of sufficient genetic data. Genotyping-by-sequencing (GBS) provides cheap genome-scale data to fill this gap, but its potential has not fully been exploited. Here, we explored power, precision and biases of a coalescent-based ABC approach where GBS data were modelled with either a population mutation parameter (θ) or a fixed site (FS) approach, allowing single or several segregating sites per locus. With simulated data ranging from 500 to 50000 loci, a variety of demographic models could be reliably inferred across a range of timescales and migration scenarios. Posterior estimates were informative with 1000 loci for migration and split time in simple population divergence models. In more complex models, posterior distributions were wide and almost reverted to the uninformative prior even with 50000 loci. ABC parameter estimates, however, were generally more accurate than an alternative composite-likelihood method. Bottleneck scenarios proved particularly difficult, and only recent bottlenecks without recovery could be reliably detected and dated. Notably, minor-allele-frequency filters - usual practice for GBS data - negatively affected nearly all estimates. With this in mind, we used a combination of FS and θ approaches on empirical GBS data generated from the Atlantic walrus (Odobenus rosmarus rosmarus), collectively providing support for a population split before the last glacial maximum followed by asymmetrical migration and a high Arctic bottleneck. Overall, this study evaluates the potential and limitations of GBS data in an ABC-coalescence framework and proposes a best-practice approach.

A composite likelihood method for bivariate meta-analysis in diagnostic systematic reviews.

Diagnostic systematic review is a vital step in the evaluation of diagnostic technologies. In many applications, it involves pooling pairs of sensitivity and specificity of a dichotomized diagnostic test from multiple studies. We propose a composite likelihood (CL) method for bivariate meta-analysis in diagnostic systematic reviews. This method provides an alternative way to make inference on diagnostic measures such as sensitivity, specificity, likelihood ratios, and diagnostic odds ratio. Its main advantages over the standard likelihood method are the avoidance of the nonconvergence problem, which is nontrivial when the number of studies is relatively small, the computational simplicity, and some robustness to model misspecifications. Simulation studies show that the CL method maintains high relative efficiency compared to that of the standard likelihood method. We illustrate our method in a diagnostic review of the performance of contemporary diagnostic imaging technologies for detecting metastases in patients with melanoma.

The equine arteritis virus isolate from the 2010 Argentinian outbreak.

A semen sample from a stallion infected during the 2010 equine arteritis virus (EAV) outbreak was received for viral isolation prior to castration of the animal. The virus was identified using a polyclonal antibody immunofluorescence test. Reverse-transcription polymerase chain reaction (RT-PCR) was used to amplify a region of the GP5 gene with primers GL105F and GL673R. The PCR products were purified and sequences of both strands were determined in a MegaBACE™1000 with inner primers CR2 and EAV32. A phylogenetic dataset was built with the previously reported sequences of five strains isolated in Argentina, together with a group of selected sequences obtained from GenBank. The unrooted neighbour-joining tree was constructed using molecular evolutionary genetic analysis (MEGA) and bootstrap analyses were conducted using 1,000 replicate datasets. Evolutionary distances were computed using the maximum composite likelihood method. A NetNGlyc server analysis at the Technical University of Denmark (www.cbs.dtu.dk/services/NetNGlyc/) was used to predict N-glycosylation in GP5 sequences. The phylogenetic analysis revealed that the new strain GLD-LP-ARG), together with other strains previously isolated, belongs to the European group EU-1 but in a different branch. The new strain shows 99% nucleotide identity with strain Al1and 98.1% with the Belgian strain 08P178. Persistently infected stallions and their cryopreserved semen constitute a reservoir of EAV, which ensures its persistence in the horse population around the world. These findings reinforce the importance of careful monitoring of persistently infected stallions, as well as semen straws, by RT-PCR or test mating, in accordance with national regulations.

Functional Principal Component Analysis of Spatiotemporal Point Processes With Applications in Disease Surveillance

In disease surveillance applications, the disease events are modeled by spatiotemporal point processes. We propose a new class of semiparametric generalized linear mixed model for such data, where the event rate is related to some known risk factors and some unknown latent random effects. We model the latent spatiotemporal process as spatially correlated functional data, and propose Poisson maximum likelihood and composite likelihood methods based on spline approximations to estimate the mean and covariance functions of the latent process. By performing functional principal component analysis to the latent process, we can better understand the correlation structure in the point process. We also propose an empirical Bayes method to predict the latent spatial random effects, which can help highlight hot areas with unusually high event rates. Under an increasing domain and increasing knots asymptotic framework, we establish the asymptotic distribution for the parametric components in the model and the asymptotic convergence rates for the functional principal component estimators. We illustrate the methodology through a simulation study and an application to the Connecticut Tumor Registry data. Supplementary materials for this article are available online.

New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels

We develop a new model for the multivariate covariance matrix dynamics based on daily return observations and daily realized covariance matrix kernels based on intraday data. We account for possible fat-failedness of both type of data by assuming a matrix-F distribution for the realized kernels, and a multivariate Student’s t distribution for the returns. Using score dynamics for the unobserved true covariance matrix, our approach automatically corrects for the effect of outliers and incidentally large observations, both in returns and in realized (co)variances. By an appropriate choice of scaling of the conditional score function we retain a convenient matrix formulation for the dynamic updates of the covariance matrix. This makes the model highly computationally efficient. The model performs well for both simulated and empirical data. In our empirical application, we study daily returns and realized kernels from 30 equities over the period 2001-2014 and find that the new model statistically outperforms (recently developed) multivariate volatility models, both in-sample and out-of-sample. We also comment on the possibility of composite likelihood methods for estimation.