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ABSTRACT Approximate Bayesian computation (ABC) methods are applicable to statistical models specified by generative processes with analytically intractable likelihoods. These methods try to approximate the posterior density of a model parameter by comparing the observed data with additional process‐generated simulated data sets. For computational benefit, only the values of certain well‐chosen summary statistics are usually compared, instead of the whole data set. Most ABC procedures are computationally expensive, justified only heuristically, and have poor asymptotic properties. In this article, we introduce a new empirical likelihood‐based approach to the ABC paradigm called ABCel. The proposed procedure is computationally tractable and approximates the target log posterior of the parameter as a sum of two functions of the data—namely, the mean of the optimal log‐empirical likelihood weights and the estimated differential entropy of the summary functions. We rigorously justify the procedure via direct and reverse information projections onto appropriate classes of probability densities. Past applications of empirical likelihood in ABC demanded constraints based on analytically tractable estimating functions that involve both the data and the parameter; although by the nature of the ABC problem such functions may not be available in general. In contrast, we use constraints that are functions of the summary statistics only. Equally importantly, we show that our construction directly connects to the reverse information projection and estimate the relevant differential entropy by a k‐NN estimator. We show that ABCel is posterior consistent and has highly favorable asymptotic properties. Its construction justifies the use of simple summary statistics like moments, quantiles, and so forth, which in practice produce accurate approximation of the posterior density. We illustrate the performance of the proposed procedure in a range of applications.
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Full Bayesian Comparative Phylogeography from Genomic Data
A challenge to understanding biological diversification is accounting for community-scale processes that cause multiple, co-distributed lineages to co-speciate. Such processes predict non-independent, temporally clustered divergences across taxa. Approximate-likelihood Bayesian computation (ABC) approaches to inferring such patterns from comparative genetic data are very sensitive to prior assumptions and often biased toward estimating shared divergences. We introduce a full-likelihood Bayesian approach, ecoevolity, which takes full advantage of information in genomic data. By analytically integrating over gene trees, we are able to directly calculate the likelihood of the population history from genomic data, and efficiently sample the model-averaged posterior via Markov chain Monte Carlo algorithms. Using simulations, we find that the new method is much more accurate and precise at estimating the number and timing of divergence events across pairs of populations than existing approximate-likelihood methods. Our full Bayesian approach also requires several orders of magnitude less computational time than existing ABC approaches. We find that despite assuming unlinked characters (e.g., unlinked single-nucleotide polymorphisms), the new method performs better if this assumption is violated in order to retain the constant characters of whole linked loci. In fact, retaining constant characters allows the new method to robustly estimate the correct number of divergence events with high posterior probability in the face of character-acquisition biases, which commonly plague loci assembled from reduced-representation genomic libraries. We apply our method to genomic data from four pairs of insular populations of Gekko lizards from the Philippines that are not expected to have co-diverged. Despite all four pairs diverging very recently, our method strongly supports that they diverged independently, and these results are robust to very disparate prior assumptions.
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- Award ID(s):
- 1656004
- PAR ID:
- 10092832
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Systematic Biology
- Volume:
- 68
- Issue:
- 3
- ISSN:
- 1063-5157
- Page Range / eLocation ID:
- 371 to 395
- Subject(s) / Keyword(s):
- Bayesian model choice biogeography Dirichlet process prior phylogeography
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/sysbio/syy063
