Approximate Bayesian Computation Procedure Research Articles

Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation

AbstractIn this article, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not expressible in closed form but it is easy to simulate realizations under the model. We therefore explain how to use approximate Bayesian computation (ABC) to carry out statistical inference for this model. We suggest a method for model validation based on posterior predictions and global envelopes. We illustrate the ABC procedure and model validation approach using both simulated point patterns and a real data example.

Building an adaptive trait simulator package to infer parametric diffusion model along phylogenetic tree

The development of an adaptive trait simulator package for inferring trait evolution along a phylogenetic tree is shown. Stochastic processes of the continuous type are broadly applied to modeling trait evolution when the evolutionary relationship among species and traits of study interest are present. By including several popular stochastic processes, evolutionary information embedded in a dataset can be revealed. The highlights of the method include:1.The implementation of the popular Cox-Ingersol-Ross process for modeling rate evolution within the package to prevent rates from becoming negative and thus is potentially a useful extension to study adaptive trait evolution in randomly evolved environment.2.The established trait simulator approach along with approximate Bayesian computation procedure provides a feasible statistical inference without model likelihood.3.The procedure proposed for trait simulator along phylogenetic tree can be applied to all established models of trait evolution in literature, thus providing users an alternative option to analyze their data.

An integrated model of population genetics and community ecology

AbstractAimQuantifying abundance distributions is critical for understanding both how communities assemble, and how community structure varies through time and space, yet estimating abundances requires considerable investment in fieldwork. Community‐level population genetic data potentially offer a powerful way to indirectly infer richness, abundance and the history of accumulation of biodiversity within a community. Here we introduce a joint model linking neutral community assembly and comparative phylogeography to generate both community‐level richness, abundance and genetic variation under a neutral model, capturing both equilibrium and non‐equilibrium dynamics.LocationGlobal.MethodsOur model combines a forward‐time individual‐based community assembly process with a rescaled backward‐time neutral coalescent model of multi‐taxa population genetics. We explore general dynamics of genetic and abundance‐based summary statistics and use approximate Bayesian computation (ABC) to estimate parameters underlying the model of island community assembly. Finally, we demonstrate two applications of the model using community‐scale mtDNA sequence data and densely sampled abundances of an arachnid community on La Réunion. First, we use genetic data alone to estimate a summary of the abundance distribution, ground‐truthing this against the observed abundances. Then, we jointly use the observed genetic data and abundances to estimate the proximity of the community to equilibrium.ResultsSimulation experiments of our ABC procedure demonstrate that coupling abundance with genetic data leads to improved accuracy and precision of model parameter estimates compared with using abundance‐only data. We further demonstrate reasonable precision and accuracy in estimating a metric underlying the shape of the abundance distribution, temporal progress towards local equilibrium and several key parameters of the community assembly process. For the insular arachnid assemblage, we find the joint distribution of genetic diversity and abundance approaches equilibrium expectations, and that the Shannon entropy of the observed abundances can be estimated using genetic data alone.Main conclusionsThe framework that we present unifies neutral community assembly and comparative phylogeography to characterize the community‐level distribution of both abundance and genetic variation through time, providing a resource that should greatly enhance understanding of both the processes structuring ecological communities and the associated aggregate demographic histories.

Simultaneous Model Selection and Model Calibration for the Proliferation of Tumor and Normal Cells During In Vitro Chemotherapy Experiments.

In vitro experiments were conducted in this work to analyze the proliferation of tumor (DU-145) and normal (macrophage RAW 264.7) cells under the influence of a chemotherapeutic drug (doxorubicin). Approximate Bayesian Computation (ABC) was used to select among four competing models to represent the number of cells and to estimate the model parameters, based on the experimental data. For one case, the selected model was validated in a replicated experiment, through the solution of a state estimation problem with a particle filter algorithm, thus demonstrating the robustness of the ABC procedure used in this work.

Combining molecular and fossil data to infer demographic history of Quercus cerris: insights on European eastern glacial refugia

AbstractAimPhylogeographical studies of Eastern Mediterranean species are rare. We aim to fill a gap in the current understanding of the role of Eastern Mediterranean glacial refugia, and their connections with other refugia across Europe. To this end, we studied the genetic diversity distribution and genetic structure of the modern population of Quercus cerris in relation to its Quaternary demographic history and to more ancient events.LocationMediterranean Basin; Italian, Balkan, Anatolian peninsulas.MethodsA total of 192 populations were genotyped with six polymorphic chloroplast microsatellites, and the genetic diversity and differentiation of the populations were evaluated. The geographical structure of genetic variation was analysed with a Bayesian clustering method using baps 5.2. The demographic history of Q. cerris was explored by an approximate Bayesian computation procedure using diyabc 2.0. To reconstruct the past distribution of Q. cerris, we also considered the chronology and geographical distribution of fossil records.ResultsThirty‐five haplotypes were found, three of which (together) were found in 71.82% of individuals. Bayesian analysis resulted in three genetically and geographically distinct clusters: a Western group, a Central group, and an Eastern group. The approximate Bayesian computation analysis, together with fossil data, showed a possible bottleneck leading to the divergence of the Eastern and Central populations in the Early Pleistocene (Gelasian). The split into two groups of populations in the Italian and Balkan Peninsulas, respectively, was probably caused by a marked population contraction during a glacial phase of the Middle Pleistocene.Main conclusionsThis study provides information on the potential role of Eastern Europe and the Near East as refugia and as a source for ancient westward range expansions in the Mediterranean region. Our study covers a remarkable gap in European oak phylogeography, showing a putative eastern origin of Q. cerris and the presence of large amounts of genetic diversity in this region.

Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation

ABSTRACTIn this paper, we derive a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach. Simulation approaches to nonlinear system identification have been shown to outperform regression methods under certain conditions, such as non-persistently exciting inputs and fast-sampling. We use the approximate Bayesian computation (ABC) algorithm to perform simulation-based inference of model parameters. The framework has the following main advantages: (1) parameter distributions are intrinsically generated, giving the user a clear description of uncertainty, (2) the simulation approach avoids the difficult problem of estimating signal derivatives as is common with other continuous-time methods, and (3) as noted above, the simulation approach improves identification under conditions of non-persistently exciting inputs and fast-sampling. Term selection is performed by judging parameter significance using parameter distributions that are intrinsically generated as part of the ABC procedure. The results from a numerical example demonstrate that the method performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation.

Genetic and linguistic correlation of the Kra-Dai-speaking groups in Thailand.

The Kra-Dai linguistic family includes Thai and Lao as well as a great number of languages spoken by ethnic minorities in Southeast Asia. In Thailand, a dozen of other Kra-Dai languages are spoken in addition to Thai, the national language. The genetic structure of the Kra-Dai-speaking populations in Thailand has been studied extensively using uniparentally inherited markers. To extend this line of genetic investigation, this study used 15 autosomal microsatellites of 500 individuals from 11 populations, belonging to nine Kra-Dai ethnicities, namely, the Kaleung, Phu Thai, Saek, Nyo, Lao Isan, Yuan, Black Tai, Phuan and Lue. These ethnolinguistic groups are dispersed in three different geographic regions of Thailand, that is, Northern, Northeastern and Central. The results show a very low average of pairwised F(st) (0.0099), as well as no population substructure based on STRUCTURE analysis, indicating genetic homogeneity within the Kra-Dai-speaking group, possibly owing to shared linguistic ancestry. The Mantel test, an analysis of molecular variance, and the approximate Bayesian computation procedure employed to evaluate potential factors for driving genetic diversity revealed that language is the predominant factor affecting genetic variations, whereas geography is not. The result of distance-based clustering analyses and spatial analysis of molecular variance revealed genetic distinctions of some populations, reflecting the effects of genetic drift and gene flow on allele frequency within populations, in concordance with the result of R-matrix regression. The genetic and linguistic affiliations of the contemporary Kra-Dai-speaking groups are consistent with each other despite certain deviation due to various evolutionary factors that may have occurred during their migrations and resettlements.

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.

Evidence for cryptic northern refugia in the last glacial period in Cryptomeria japonica.

Distribution shifts and natural selection during past climatic changes are important factors in determining the genetic structure of forest species. In particular, climatic fluctuations during the Quaternary appear to have caused changes in the distribution ranges of plants, and thus strongly affected their genetic structure. This study was undertaken to identify the responses of the conifer Cryptomeria japonica, endemic to the Japanese Archipelago, to past climatic changes using a combination of phylogeography and species distribution modelling (SDM) methods. Specifically, this study focused on the locations of refugia during the last glacial maximum (LGM). Genetic diversity and structure were examined using 20 microsatellite markers in 37 populations of C. japonica. The locations of glacial refugia were assessed using STRUCTURE analysis, and potential habitats under current and past climate conditions were predicted using SDM. The process of genetic divergence was also examined using the approximate Bayesian computation procedure (ABC) in DIY ABC to test the divergence time between the gene pools detected by the STRUCTURE analysis. STRUCTURE analysis identified four gene pools: northern Tohoku district; from Chubu to Chugoku district; from Tohoku to Shikoku district on the Pacific Ocean side of the Archipelago; and Yakushima Island. DIY ABC analysis indicated that the four gene pools diverged at the same time before the LGM. SDM also indicated potential northern cryptic refugia. The combined evidence from microsatellites and SDM clearly indicates that climatic changes have shaped the genetic structure of C. japonica. The gene pool detected in northern Tohoku district is likely to have been established by cryptic northern refugia on the coast of the Japan Sea to the west of the Archipelago. The gene pool in Yakushima Island can probably be explained simply by long-term isolation from the other gene pools since the LGM. These results are supported by those of SDM and the predicted divergence time determined using ABC analysis.

Approximate Bayesian computation with functional statistics

Functional statistics are commonly used to characterize spatial patterns in general and spatial genetic structures in population genetics in particular. Such functional statistics also enable the estimation of parameters of spatially explicit (and genetic) models. Recently, Approximate Bayesian Computation (ABC) has been proposed to estimate model parameters from functional statistics. However, applying ABC with functional statistics may be cumbersome because of the high dimension of the set of statistics and the dependences among them. To tackle this difficulty, we propose an ABC procedure which relies on an optimized weighted distance between observed and simulated functional statistics. We applied this procedure to a simple step model, a spatial point process characterized by its pair correlation function and a pollen dispersal model characterized by genetic differentiation as a function of distance. These applications showed how the optimized weighted distance improved estimation accuracy. In the discussion, we consider the application of the proposed ABC procedure to functional statistics characterizing non-spatial processes.

Lack of confidence in approximate Bayesian computation model choice

Approximate Bayesian computation (ABC) have become an essential tool for the analysis of complex stochastic models. Grelaud et al. [(2009) Bayesian Anal 3:427-442] advocated the use of ABC for model choice in the specific case of Gibbs random fields, relying on an intermodel sufficiency property to show that the approximation was legitimate. We implemented ABC model choice in a wide range of phylogenetic models in the Do It Yourself-ABC (DIY-ABC) software [Cornuet et al. (2008) Bioinformatics 24:2713-2719]. We now present arguments as to why the theoretical arguments for ABC model choice are missing, because the algorithm involves an unknown loss of information induced by the use of insufficient summary statistics. The approximation error of the posterior probabilities of the models under comparison may thus be unrelated with the computational effort spent in running an ABC algorithm. We then conclude that additional empirical verifications of the performances of the ABC procedure as those available in DIY-ABC are necessary to conduct model choice.