Matti Vihola

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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)
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)
This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form θn+1 = θn + γn+1Hθn (Xn+1), where {θn, n ∈ N} is an Rd-valued sequence, {γn, n ∈ N} is a deterministic stepsize sequence, and {Xn, n ∈ N} is a controlled Markov chain. We study the convergence under weak assumptions on smoothness-in-θ of the function θ 7→(More)