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Using Approximate Bayesian Computation to understand the distribution of genetic diversity in eastern massasauga rattlesnakes (Sistrurus catenatus catenatus)

Szenteczki, Mark
Fonte: Quens University Publicador: Quens University
Tipo: Tese de Doutorado
EN
Relevância na Pesquisa
96.33%
My study investigated the extent of genetic structuring within the two largest populations of eastern massasauga rattlesnakes (Sistrurus c. catenatus) in Ontario, and their demographic histories at local levels. With my wider sampling range and larger sample size, I anticipated more extensive genetic structuring within regional populations than has been previously described in the literature. Based on the natural history of massasauga rattlesnakes and studies on a co-distributed species (eastern foxsnakes; Pantherophis gloydi), I also hypothesized that declines in effective population size within individual populations would be the greatest historical influence on contemporary population structure. I used microsatellite data (390 individuals, 10 loci) and Bayesian assignment tests to address my first hypothesis, and compared eight competing demographic scenarios within individual populations using an Approximate Bayesian Computation (ABC) framework to address my second hypothesis. I found evidence of a new distinct genetic cluster corresponding to a previously unstudied island (Cove Island), as well as stronger evidence of further subdivision between the two northernmost areas sampled along the eastern shores of Georgian Bay. I also found that recent (i.e. within the past 200 years)...

Interpreting scratch assays using pair density dynamics and approximate Bayesian computation

Johnston, S.T.; Simpson, M.J.; McElwain, D.L.S.; Binder, B.J.; Ross, J.V.
Fonte: The Royal Society Publicador: The Royal Society
Tipo: Artigo de Revista Científica
Publicado em //2014 EN
Relevância na Pesquisa
96.29%
Quantifying the impact of biochemical compounds on collective cell spreading is an essential element of drug design, with various applications including developing treatments for chronic wounds and cancer. Scratch assays are a technically simple and inexpensive method used to study collective cell spreading; however, most previous interpretations of scratch assays are qualitative and do not provide estimates of the cell diffusivity, D, or the cell proliferation rate, λ. Estimating D and λ is important for investigating the efficacy of a potential treatment and provides insight into the mechanism through which the potential treatment acts. While a few methods for estimating D and λ have been proposed, these previous methods lead to point estimates of D and λ, and provide no insight into the uncertainty in these estimates. Here, we compare various types of information that can be extracted from images of a scratch assay, and quantify D and λ using discrete computational simulations and approximate Bayesian computation. We show that it is possible to robustly recover estimates of D and λ from synthetic data, as well as a new set of experimental data. For the first time, our approach also provides a method to estimate the uncertainty in our estimates of D and λ. We anticipate that our approach can be generalized to deal with more realistic experimental scenarios in which we are interested in estimating D and λ...

Kernel Approximate Bayesian Computation for Population Genetic Inferences

Nakagome, Shigeki; Fukumizu, Kenji; Mano, Shuhei
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
76.29%
Approximate Bayesian computation (ABC) is a likelihood-free approach for Bayesian inferences based on a rejection algorithm method that applies a tolerance of dissimilarity between summary statistics from observed and simulated data. Although several improvements to the algorithm have been proposed, none of these improvements avoid the following two sources of approximation: 1) lack of sufficient statistics: sampling is not from the true posterior density given data but from an approximate posterior density given summary statistics; and 2) non-zero tolerance: sampling from the posterior density given summary statistics is achieved only in the limit of zero tolerance. The first source of approximation can be improved by adding a summary statistic, but an increase in the number of summary statistics could introduce additional variance caused by the low acceptance rate. Consequently, many researchers have attempted to develop techniques to choose informative summary statistics. The present study evaluated the utility of a kernel-based ABC method (Fukumizu et al. 2010, arXiv:1009.5736 and 2011, NIPS 24: 1549-1557) for complex problems that demand many summary statistics. Specifically, kernel ABC was applied to population genetic inference. We demonstrate that...

Accelerating inference for diffusions observed with measurement error and large sample sizes using Approximate Bayesian Computation

Picchini, Umberto; Forman, Julie Lyng
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
76.31%
In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large datasets and complex models. This paper considers a nonlinear stochastic differential equation model observed with correlated measurement errors and an application to protein folding modelling. An Approximate Bayesian Computation (ABC) MCMC algorithm is suggested to allow inference for model parameters within reasonable time constraints. The ABC algorithm uses simulations of "subsamples" from the assumed data generating model as well as a so-called "early rejection" strategy to speed up computations in the ABC-MCMC sampler. Using a considerate amount of subsamples does not seem to degrade the quality of the inferential results for the considered applications. A simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower than ABC-MCMC for the considered setup. Finally the ABC algorithm is applied to a large size protein data. The suggested methodology is fairly general and not limited to the exemplified model and data.; Comment: 22 pages...

Fast Approximate Bayesian Computation for discretely observed Markov models using a factorised posterior distribution

White, Simon R.; Kypraios, Theodore; Preston, Simon P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
76.29%
Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential echniques cannot be used. In such settings, Bayesian inference can be performed using Approximate Bayesian Computation (ABC). However, in spite of many recent developments to ABC methodology, in many applications the computational cost of ABC necessitates the choice of summary statistics and tolerances that can potentially severely bias the estimate of the posterior. We propose a new "piecewise" ABC approach suitable for discretely observed Markov models that involves writing the posterior density of the parameters as a product of factors, each a function of only a subset of the data, and then using ABC within each factor. The approach has the advantage of side-stepping the need to choose a summary statistic and it enables a stringent tolerance to be set, making the posterior "less approximate". We investigate two methods for estimating the posterior density based on ABC samples for each of the factors: the first is to use a Gaussian approximation for each factor, and the second is to use a kernel density estimate. Both methods have their merits. The Gaussian approximation is simple...

Diagnostic tools of approximate Bayesian computation using the coverage property

Prangle, D.; Blum, M. G. B.; Popovic, G.; Sisson, S. A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/01/2013
Relevância na Pesquisa
76.27%
Approximate Bayesian computation (ABC) is an approach for sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model, parameter and dataset triples, (m,\theta,y), from the prior, and then accepting as samples from the approximate posterior, those pairs (m,\theta) for which y, or a summary of y, is "close" to the observed data. Closeness is typically determined though a distance measure and a kernel scale parameter, \epsilon. Appropriate choice of \epsilon is important to producing a good quality approximation. This paper proposes diagnostic tools for the choice of \epsilon based on assessing the coverage property, which asserts that credible intervals have the correct coverage levels. We provide theoretical results on coverage for both model and parameter inference, and adapt these into diagnostics for the ABC context. We re-analyse a study on human demographic history to determine whether the adopted posterior approximation was appropriate. R code implementing the proposed methodology is freely available in the package "abc."; Comment: Figures 8-13 are Supplementary Information Figures S1-S6

Adaptive approximate Bayesian computation for complex models

Lenormand, Maxime; Jabot, Franck; Deffuant, Guillaume
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
76.38%
Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fi t a model to data without relying on the computation of the model likelihood. They instead require to simulate a large number of times the model to be fi tted. A number of re finements to the original rejection-based ABC scheme have been proposed, including the sequential improvement of posterior distributions. This technique allows to de- crease the number of model simulations required, but it still presents several shortcomings which are particu- larly problematic for costly to simulate complex models. We here provide a new algorithm to perform adaptive approximate Bayesian computation, which is shown to perform better on both a toy example and a complex social model.; Comment: 14 pages, 5 figures

Approximate Bayesian Computation: a nonparametric perspective

Blum, Michael
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
76.33%
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics s_obs from the data and simulating summary statistics for different values of the parameter theta. The posterior distribution is then approximated by an estimator of the conditional density g(theta|s_obs). In this paper, we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment. Additionally, we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a fewer number of terms than the estimator with linear adjustment. Although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling, we find that they can achieve better performance when there is a nearly homoscedastic relationship between the summary statistics and the parameter of interest. To make this relationship as homoscedastic as possible, we propose to use transformations of the summary statistics. In different examples borrowed from the population genetics and epidemiological literature...

On Consistency of Approximate Bayesian Computation

Frazier, David T.; Martin, Gael M.; Robert, Christian P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/08/2015
Relevância na Pesquisa
76.27%
Approximate Bayesian computation (ABC) methods have become increasingly prevalent of late, facilitating as they do the analysis of intractable, or challenging, statistical problems. With the initial focus being primarily on the practical import of ABC, exploration of its formal statistical properties has begun to attract more attention. The aim of this paper is to establish general conditions under which ABC methods are Bayesian consistent, in the sense of producing draws that yield a degenerate posterior distribution at the true parameter (vector) asymptotically (in the sample size). We derive conditions under which arbitrary summary statistics yield consistent inference in the Bayesian sense, with these conditions linked to identification of the true parameters. Using simple illustrative examples that have featured in the literature, we demonstrate that identification, and hence consistency, is unlikely to be achieved in many cases, and propose a simple diagnostic procedure that can indicate the presence of this problem. We also formally explore the link between consistency and the use of auxiliary models within ABC, and illustrate the subsequent results in the Lotka-Volterra predator-prey model.

Extending approximate Bayesian computation methods to high dimensions via Gaussian copula

Li, Jingjing; Nott, David J.; Fan, Yanan; Sisson, Scott A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/04/2015
Relevância na Pesquisa
76.29%
Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of dimensionality, and a marginal adjustment strategy was recently introduced in the literature to improve the performance of ABC algorithms in high-dimensional problems. In this article, the marginal adjustment approach is extended using a Gaussian copula approximation. The method first estimates the bivariate posterior for each pair of parameters separately using $2$-dimensional Gaussian copula, and then combines these estimates together to estimate the joint posterior. The approximation works well in large sample settings when the posterior is approximately normal, but also works well in many cases where we are far from that situation due to the nonparametric estimation of the marginal posterior distributions. If each bivariate posterior distribution can be well estimated with a low-dimensional ABC analysis then this Gaussian copula method can extend ABC methods to problems of high dimension. The method also results in an analytic expression for the approximate posterior which is useful for many purposes such as approximation of the likelihood itself. We illustrate this method with several examples.

Approximate Bayesian Computation via Regression Density Estimation

Fan, Y.; Nott, D. J.; Sisson, S. A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 06/12/2012
Relevância na Pesquisa
76.41%
Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior distribution, but an alternative, less common strategy is to approximate the likelihood function. This has several advantages. First, in some problems, it is easier to approximate the likelihood than to approximate the posterior. Second, an approximation to the likelihood allows reference analyses to be constructed based solely on the likelihood. Third, it is straightforward to perform sensitivity analyses for several different choices of prior once an approximation to the likelihood is constructed, which needs to be done only once. The contribution of the present paper is to consider regression density estimation techniques to approximate the likelihood in the ABC setting. Our likelihood approximations build on recently developed marginal adaptation density estimators by extending them for conditional density estimation. Our approach facilitates reference Bayesian inference, as well as frequentist inference. The method is demonstrated via a challenging problem of inference for stereological extremes, where we perform both frequentist and Bayesian inference.

Approximate Bayesian computation and Bayes linear analysis: Towards high-dimensional ABC

Nott, D. J.; Fan, Y.; Marshall, L.; Sisson, S. A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
76.29%
Bayes linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article we connect these ideas by demonstrating that regression-adjustment ABC algorithms produce samples for which first and second order moment summaries approximate adjusted expectation and variance for a Bayes linear analysis. This gives regression-adjustment methods a useful interpretation and role in exploratory analysis in high-dimensional problems. As a result, we propose a new method for combining high-dimensional, regression-adjustment ABC with lower-dimensional approaches (such as using MCMC for ABC). This method first obtains a rough estimate of the joint posterior via regression-adjustment ABC, and then estimates each univariate marginal posterior distribution separately in a lower-dimensional analysis. The marginal distributions of the initial estimate are then modified to equal the separately estimated marginals, thereby providing an improved estimate of the joint posterior. We illustrate this method with several examples. Supplementary materials for this article are available online.; Comment: To appear in Journal of Computational and Graphical Statistics

Sequential Monte Carlo with Adaptive Weights for Approximate Bayesian Computation

Bonassi, Fernando V.; West, Mike
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/03/2015
Relevância na Pesquisa
76.3%
Methods of approximate Bayesian computation (ABC) are increasingly used for analysis of complex models. A major challenge for ABC is over-coming the often inherent problem of high rejection rates in the accept/reject methods based on prior:predictive sampling. A number of recent developments aim to address this with extensions based on sequential Monte Carlo (SMC) strategies. We build on this here, introducing an ABC SMC method that uses data-based adaptive weights. This easily implemented and computationally trivial extension of ABC SMC can very substantially improve acceptance rates, as is demonstrated in a series of examples with simulated and real data sets, including a currently topical example from dynamic modelling in systems biology applications.; Comment: Published at http://dx.doi.org/10.1214/14-BA891 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/)

Adaptive approximate Bayesian computation

Beaumont, Mark A.; Cornuet, Jean-Marie; Marin, Jean-Michel; Robert, Christian P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
76.36%
Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappe et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm.; Comment: 8 pages, 2 figures, one algorithm, third revised resubmission to Biometrika

A comparison of emulation methods for Approximate Bayesian Computation

Jabot, Franck; Lagarrigues, Guillaume; Courbaud, Benoît; Dumoulin, Nicolas
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/12/2014
Relevância na Pesquisa
76.27%
Approximate Bayesian Computation (ABC) is a family of statistical inference techniques, which is increasingly used in biology and other scientific fields. Its main benefit is to be applicable to models for which the computation of the model likelihood is intractable. The basic idea of ABC is to empirically approximate the model likelihood by using intensive realizations of model runs. Due to computing time limitations, ABC has thus been mainly applied to models that are relatively quick to simulate. We here aim at briefly introducing the field of statistical emulation of computer code outputs and to demonstrate its potential for ABC applications. Emulation consists in replacing the costly to simulate model by another (quick to simulate) statistical model called emulator or meta-model. This emulator is fitted to a small number of outputs of the original model, and is subsequently used as a surrogate during the inference procedure. In this contribution, we first detail the principles of model emulation, with a special reference to the ABC context in which the description of the stochasticity of model realizations is as important as the description of the trends linking model parameters and outputs. We then compare several emulation strategies in an ABC context...

Deviance Information Criteria for Model Selection in Approximate Bayesian Computation

Francois, Olivier; Laval, Guillaume
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/05/2011
Relevância na Pesquisa
76.27%
Approximate Bayesian computation (ABC) is a class of algorithmic methods in Bayesian inference using statistical summaries and computer simulations. ABC has become popular in evolutionary genetics and in other branches of biology. However model selection under ABC algorithms has been a subject of intense debate during the recent years. Here we propose novel approaches to model selection based on posterior predictive distributions and approximations of the deviance. We argue that this framework can settle some contradictions between the computation of model probabilities and posterior predictive checks using ABC posterior distributions. A simulation study and an analysis of a resequencing data set of human DNA show that the deviance criteria lead to sensible results in a number of model choice problems of interest to population geneticists.

AABC: approximate approximate Bayesian computation when simulating a large number of data sets is computationally infeasible

Buzbas, Erkan O.; Rosenberg, Noah A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/01/2013
Relevância na Pesquisa
76.42%
Approximate Bayesian computation (ABC) methods perform inference on model-specific parameters of mechanistically motivated parametric statistical models when evaluating likelihoods is difficult. Central to the success of ABC methods is computationally inexpensive simulation of data sets from the parametric model of interest. However, when simulating data sets from a model is so computationally expensive that the posterior distribution of parameters cannot be adequately sampled by ABC, inference is not straightforward. We present approximate approximate Bayesian computation" (AABC), a class of methods that extends simulation-based inference by ABC to models in which simulating data is expensive. In AABC, we first simulate a limited number of data sets that is computationally feasible to simulate from the parametric model. We use these data sets as fixed background information to inform a non-mechanistic statistical model that approximates the correct parametric model and enables efficient simulation of a large number of data sets by Bayesian resampling methods. We show that under mild assumptions, the posterior distribution obtained by AABC converges to the posterior distribution obtained by ABC, as the number of data sets simulated from the parametric model and the sample size of the observed data set increase simultaneously. We illustrate the performance of AABC on a population-genetic model of natural selection...

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Toni, Tina; Welch, David; Strelkowa, Natalja; Ipsen, Andreas; Stumpf, Michael P. H.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/01/2009
Relevância na Pesquisa
76.36%
Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC gives information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.; Comment: 26 pages, 9 figures

Approximate Bayesian Computation for Complex Dynamic Systems

Bonassi, Fernando Vieira
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2013
Relevância na Pesquisa
76.3%

This thesis focuses on the development of ABC methods for statistical modeling in complex dynamic systems. Motivated by real applications in biology, I propose computational strategies for Bayesian inference in contexts where standard Monte Carlo methods cannot be directly applied due to the high complexity of the dynamic model and/or data limitations.

Chapter 2 focuses on stochastic bionetwork models applied to data generated from the marginal distribution of a few network nodes at snapshots in time. I present a Bayesian computational strategy, coupled with an approach to summarizing and numerically characterizing biological phenotypes that are represented in terms of the resulting sample distributions of cellular markers. ABC and mixture modeling are used to define the approach to linking mechanistic mathematical models of network dynamics to snapshot data, using a toggle switch example integrating simulated and real data as context.

Chapter 3 focuses on the application of the methodology presented in Chapter 2 to the Myc/Rb/E2F network. This network involves a relatively high number of parameters and stochastic equations in the model specification and, thus, is substantially more complex than the toggle switch example. The analysis of the Myc/Rb/E2F network is performed with simulated and real data. I demonstrate that the proposed method can indicate which parameters can be learned about using the marginal data.

In Chapter 4...

Topics in Modern Bayesian Computation

Qamar, Shaan
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2015
Relevância na Pesquisa
76.35%

Collections of large volumes of rich and complex data has become ubiquitous in recent years, posing new challenges in methodological and theoretical statistics alike. Today, statisticians are tasked with developing flexible methods capable of adapting to the degree of complexity and noise in increasingly rich data gathered across a variety of disciplines and settings. This has spurred the need for novel multivariate regression techniques that can efficiently capture a wide range of naturally occurring predictor-response relations, identify important predictors and their interactions and do so even when the number of predictors is large but the sample size remains limited.

Meanwhile, efficient model fitting tools must evolve quickly to keep pace with the rapidly growing dimension and complexity of data they are applied to. Aided by the tremendous success of modern computing, Bayesian methods have gained tremendous popularity in recent years. These methods provide a natural probabilistic characterization of uncertainty in the parameters and in predictions. In addition, they provide a practical way of encoding model structure that can lead to large gains in statistical estimation and more interpretable results. However, this flexibility is often hindered in applications to modern data which are increasingly high dimensional...