Coherent and incoherent inference in phylogeography and human evolution

Templeton, Alan R.

doi:10.1073/pnas.0910647107

Cited by 51 publications

(49 citation statements)

References 31 publications

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“…(2) Set d s ¼ 1. There are two disconnected groups of haplotypes: (1,2,3,4,5,6), and (7,8,9,10,11,12), with closest distance between nodes 1 and 8 which are two mutations apart (step 1). Since there is only one pair of groups, immediately we obtain d min ¼ 2 (step 2).…”

Section: A1 Synthetic Examplementioning

confidence: 99%

A Bayesian approach to phylogeographic clustering

et al. 2011

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Phylogeographic methods have attracted a lot of attention in recent years, stressing the need to provide a solid statistical framework for many existing methodologies so as to draw statistically reliable inferences. Here, we take a flexible fully Bayesian approach by reducing the problem to a clustering framework, whereby the population distribution can be explained by a set of migrations, forming geographically stable population clusters. These clusters are such that they are consistent with a fixed number of migrations on the corresponding (unknown) subdivided coalescent tree. Our methods rely upon a clustered population distribution, and allow for inclusion of various covariates (such as phenotype or climate information) at little additional computational cost. We illustrate our methods with an example from weevil mitochondrial DNA sequences from the Iberian peninsula.

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Section: A1 Synthetic Examplementioning

confidence: 99%

A Bayesian approach to phylogeographic clustering

et al. 2011

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“…For instance, a whole new area of population genetic modeling (8,10) has been explored thanks to the availability of such methods. However, practitioners and theoreticians both show a reluctance in adopting ABC, with some doubt about the validity of the method (11)(12)(13). We propose in this paper to supplement the ABC approach with a generic and convergent likelihood approximation called the empirical likelihood that validates this Bayesian computational technique as a convergent inferential method when the number of observations grows to infinity.…”

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confidence: 99%

Bayesian computation via empirical likelihood

Mengersen

Pudlo

Robert

2013

Proc. Natl. Acad. Sci. U.S.A.

117

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Approximate Bayesian computation has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the approximate Bayesian computation parameters (summary statistics, distance, tolerance), while being convergent in the number of observations. Furthermore, bypassing model simulations may lead to significant time savings in complex models, for instance those found in population genetics. The Bayesian computation with empirical likelihood algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size. The method is illustrated using several examples, including estimation of standard distributions, time series, and population genetics models.autoregressive models | Bayesian statistics | likelihood-free methods | coalescent model B ayesian statistical inference cannot easily operate when the likelihood function associated with the data is not entirely known, or cannot be computed in a manageable time, as is the case in most population genetic models (1-3). The fundamental reason for this difficulty with population genetics is that the statistical model associated with coalescent data needs to integrate over trees of high complexity. Similar computational issues with the likelihood function often occur in hidden Markov and other dynamic models (4). In those settings, traditional approximation tools based on stochastic simulation (5) are unavailable or unreliable. Indeed, the complexity of the latent structure defining the likelihood makes simulation of such structures too unstable to be trusted. Such settings call for alternative and often cruder approximations. The approximate Bayesian computation (ABC) methodology (1, 6) is a popular solution that bypasses the computation of the likelihood function (surveys in refs. 7 and 8); ref. 9 validates a conditional version of ABC that applies to hierarchical Bayes models in a wide generality.The fast and polytomous development of the ABC algorithm is indicated by the rising literature in the domain, at both the methodological and the application levels. For instance, a whole new area of population genetic modeling (8, 10) has been explored thanks to the availability of such methods. However, practitioners and theoreticians both show a reluctance in adopting ABC, with some doubt about the validity of the method (11-13). We propose in this paper to supplement the ABC approach with a generic and convergent likelihood approximation called the empirical likelihood that validates this Bayesian computational technique as a convergent inferential method when the number of observations grows to infinity. The empirical likelihood perspective, introduced by ref. 14, is a robust statistical approach that does not require the specification of the likelihood function. However, although i...

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“…The analysis was has been successfully applied in numerous studies, concerns have been raised that it is highly 241 subjective when applied to complex models (Templeton, 2010 (Csillery et al, 2010).…”

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confidence: 99%