Adaptive approximate Bayesian computation for complex models

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 figure

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin

Choosing summary statistics by least angle regression for approximate Bayesian computation

YesBayesian statistical inference relies on the posterior distribution. Depending on the model, the posterior can be more or less difficult to derive. In recent years, there has been a lot of interest in complex settings where the likelihood is analytically intractable. In such situations, approximate Bayesian computation (ABC) provides an attractive way of carrying out Bayesian inference. For obtaining reliable posterior estimates however, it is important to keep the approximation errors small in ABC. The choice of an appropriate set of summary statistics plays a crucial role in this effort. Here, we report the development of a new algorithm that is based on least angle regression for choosing summary statistics. In two population genetic examples, the performance of the new algorithm is better than a previously proposed approach that uses partial least squares.Higher Education Commission (HEC), College Deanship of Scientific Research, King Saud University, Riyadh Saudi Arabia - research group project RGP-VPP-280

Methods for detecting associations between phenotype and aggregations of rare variants

Although genome-wide association studies have uncovered variants associated with more than 150 traits, the percentage of phenotypic variation explained by these associations remains small. This has led to the search for the dark matter that explains this missing genetic component of heritability. One potential explanation for dark matter is rare variants, and several statistics have been devised to detect associations resulting from aggregations of rare variants in relatively short regions of interest, such as candidate genes. In this paper we investigate the feasibility of extending this approach in an agnostic way, in which we consider all variants within a much broader region of interest, such as an entire chromosome or even the entire exome. Our method searches for subsets of variant sites using either Markov chain Monte Carlo or genetic algorithms. The analysis was performed with knowledge of the Genetic Analysis Workshop 17 answers

Simulation-based model selection for dynamical systems in systems and population biology

Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not straightforward. We therefore require suitable statistical tools that allow us to choose rationally between different mechanistic models of e.g. signal transduction or gene regulation networks. This is particularly challenging in systems biology where only a small number of molecular species can be assayed at any given time and all measurements are subject to measurement uncertainty. Here we develop such a model selection framework based on approximate Bayesian computation and employing sequential Monte Carlo sampling. We show that our approach can be applied across a wide range of biological scenarios, and we illustrate its use on real data describing influenza dynamics and the JAK-STAT signalling pathway. Bayesian model selection strikes a balance between the complexity of the simulation models and their ability to describe observed data. The present approach enables us to employ the whole formal apparatus to any system that can be (efficiently) simulated, even when exact likelihoods are computationally intractable.Comment: This article is in press in Bioinformatics, 2009. Advance Access is available on Bioinformatics webpag

Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.Comment: 26 pages, 2 figures, accepted in Journal of Computational and Graphical Statistics (http://www.amstat.org/publications/jcgs.cfm

MSMC and MSMC2: the multiple sequentially markovian coalescent

The Multiple Sequentially Markovian Coalescent (MSMC) is a population genetic method and software for inferring demographic history and population structure through time from genome sequences. Here we describe the main program MSMC and its successor MSMC2. We go through all the necessary steps of processing genomic data from BAM files all the way to generating plots of inferred population size and separation histories. Some background on the methodology itself is provided, as well as bash scripts and python source code to run the necessary programs. The reader is also referred to community resources such as a mailing list and github repositories for further advice

ABCtoolbox: a versatile toolkit for approximate Bayesian computations

BACKGROUND: The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. RESULTS: Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females. CONCLUSION: ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results

Using DNA Methylation Patterns to Infer Tumor Ancestry

Background: Exactly how human tumors grow is uncertain because serial observations are impractical. One approach to reconstruct the histories of individual human cancers is to analyze the current genomic variation between its cells. The greater the variations, on average, the greater the time since the last clonal evolution cycle (‘‘a molecular clock hypothesis’’). Here we analyze passenger DNA methylation patterns from opposite sides of 12 primary human colorectal cancers (CRCs) to evaluate whether the variation (pairwise distances between epialleles) is consistent with a single clonal expansion after transformation. Methodology/Principal Findings: Data from 12 primary CRCs are compared to epigenomic data simulated under a single clonal expansion for a variety of possible growth scenarios. We find that for many different growth rates, a single clonal expansion can explain the population variation in 11 out of 12 CRCs. In eight CRCs, the cells from different glands are all equally distantly related, and cells sampled from the same tumor half appear no more closely related than cells sampled from opposite tumor halves. In these tumors, growth appears consistent with a single ‘‘symmetric’ ’ clonal expansion. In three CRCs, the variation in epigenetic distances was different between sides, but this asymmetry could be explained by a single clonal expansion with one region of a tumor having undergone more cell division than the other. The variation in one CRC was complex and inconsistent with a simple single clonal expansion

A Simulated Annealing Approach to Approximate Bayes Computations

Approximate Bayes Computations (ABC) are used for parameter inference when the likelihood function of the model is expensive to evaluate but relatively cheap to sample from. In particle ABC, an ensemble of particles in the product space of model outputs and parameters is propagated in such a way that its output marginal approaches a delta function at the data and its parameter marginal approaches the posterior distribution. Inspired by Simulated Annealing, we present a new class of particle algorithms for ABC, based on a sequence of Metropolis kernels, associated with a decreasing sequence of tolerances w.r.t. the data. Unlike other algorithms, our class of algorithms is not based on importance sampling. Hence, it does not suffer from a loss of effective sample size due to re-sampling. We prove convergence under a condition on the speed at which the tolerance is decreased. Furthermore, we present a scheme that adapts the tolerance and the jump distribution in parameter space according to some mean-fields of the ensemble, which preserves the statistical independence of the particles, in the limit of infinite sample size. This adaptive scheme aims at converging as close as possible to the correct result with as few system updates as possible via minimizing the entropy production in the system. The performance of this new class of algorithms is compared against two other recent algorithms on two toy examples.Comment: 20 pages, 2 figure