Embarrassingly parallel sequential Markov-chain Monte Carlo for large sets of time series

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Bayesian computation crucially relies on Markov chain Monte Carlo (MCMC) algorithms. In the case of massive data sets, running the Metropolis-Hastings sampler to draw from the posterior distribution becomes prohibitive due to the large number of likelihood terms that need to be calculated at each iteration. In order to perform Bayesian inference for a large set of time series, we consider an algorithm that combines “divide and conquer” ideas previously used to design MCMC algorithms for big data with a sequential MCMC strategy. The performance of the method is illustrated using a large set of financial data.