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The adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223-242] uses the estimated covariance of the target distribution in the proposal distribution. This paper introduces a new robust adaptive Metropolis algorithm estimating the shape of the target distribution and simultaneously coercing the acceptance rate. The(More)
Preface First of all, I would like to thank Datactica Ltd for providing me the opportunity to write this thesis. It has been a highly therapeutic experience to dig deeper into the theoretical aspects of some problems that I have previously faced. Althgough this thesis is primarily a partial requirement for an academic degree, I hope that other people find(More)
This paper introduces two approximations of the Kullback-Leibler divergence for hidden Markov models (HMMs). The first one is a generalization of an approximation originally presented for HMMs with discrete observation densities. In that case, the HMMs are assumed to be ergodic and the topologies similar. The second one is a modification of the first one.(More)
Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on graphical models for directed acyclic graphs. The implemented algorithms include the seminal Adaptive Metropolis algorithm(More)
The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step n + 1 that is, the sample covariance matrix of the history of the chain plus a (small) constant ǫ > 0 multiple of the identity matrix I. The lower bound on the eigenvalues of(More)