2011/06/30 by Sarah Filippi, C. Barnes, Filippi, Sarah +5 · 4 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1106.6280
openalex publication_date 2011/06/30 · openalex created_date 2022/09/19 · openalex updated_date 2026/07/28
Approximate Bayesian computation (ABC) has gained popularity over the past\nfew years for the analysis of complex models arising in population genetic,\nepidemiology and system biology. Sequential Monte Carlo (SMC) approaches have\nbecome work horses in ABC. Here we discuss how to construct the perturbation\nkernels that are required in ABC SMC approaches, in order to construct a set of\ndistributions that start out from a suitably defined prior and converge towards\nthe unknown posterior. We derive optimality criteria for different kernels,\nwhich are based on the Kullback-Leibler divergence between a distribution and\nthe distribution of the perturbed particles. We will show that for many\ncomplicated posterior distributions, locally adapted kernels tend to show the\nbest performance. In cases where it is possible to estimate the Fisher\ninformation we can construct particularly efficient perturbation kernels. We\nfind that the added moderate cost of adapting kernel functions is easily\nregained in terms of the higher acceptance rate. We demonstrate the\ncomputational efficiency gains in a range of toy-examples which illustrate some\nof the challenges faced in real-world applications of ABC, before turning to\ntwo demanding parameter inference problem in molecular biology, which highlight\nthe huge increases in efficiency that can be gained from choice of optimal\nmodels. We conclude with a general discussion of rational choice of\nperturbation kernels in ABC SMC settings.\n
pymc