Single chain differential evolution Monte-Carlo for self-tuning Bayesian inference
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1. Bayesian inference is difficult because it often requires time consuming tuning of samplers. Differential evolution Monte-Carlo (DEMC) is a self-tuning multi-chain sampling approach which requires minimal input from the operator as samples are obtained by taking the difference of the current position of multiple randomly selected chains. However, this can also make DEMC more computationally intensive than single chain samplers. 2. We provide a single-chain adaptation of the DEMC algorithm by taking samples according to the difference in previous states of the chain, rather than the current state of multiple chains. This minimises computational costs by requiring only one posterior evaluation per step, while retaining the self-adaptive property of DEMC. We test the algorithm by sampling a bivariate normal distribution and by estimating the posterior distribution of parameters of an ODE model fitted to an artificial prey-predator time series. In both cases we compare the quality of DEMC generated samples to those obtained by a standard adaptive Markov chain Monte-Carlo sampler (AMC). 3. In both case studies, DEMC is as accurate as AMC in estimating posterior distributions, while being an order of magnitude faster due to simpler computations. DEMC also provides a higher effective samples size than AMC, and lower initial samples autocorrelations. 4. Its low computational cost and self-adaptive property make single chain DEMC particularly suitable for fitting models that are costly to evaluate, such as ODE models. The simplicity of the algorithm also makes it easy to implement in base R, hence offering a simple alternative to STAN.
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