bayesian statistics abc algorithm mcmc methods abc mcmc simulation bayesian model choice summary statistics bayes factor monte carlo statistical methods statistics bayesian inference foundations sufficiency empirical likelihood model choice mixture models gibbs sampling importance sampling r bayesian random forests metropolis hastings algorithm approximate bayesian inference prior selection particles evidence mixtures model bayesian consistency improper priors intractable likelihood population genetics rao-blackwellisation bridge sampling sampling likelihood-free methods misspecified models wasserstein distance hamiltonian monte carlo bayesian statisics testing statistical hypotheses bayesian tests bootstrap nested choice cirm generative model speed of convergence consistency markov chains estimation noninformative priors bayesian nonparametrics big data reversibility empirical bayes methods unbiasedness adaptivity read paper label switching frequentist statistics harmonic mean warwick 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