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- Matti Vihola
- 2006

This article introduces a RaoBlackwellised particle filtering (RBPF) approach in the finite set statistics (FISST) multitarget tracking framework. The RBPF approach is proposed in such a case, where each sensor is assumed to produce a sequence of detection reports each containing either one single-target measurement, or a “no detection” report. The tests… (More)

- Eero Saksman, Matti Vihola
- 2008

This paper describes sufficient conditions to ensure the correct ergodicity of the Adaptive Metropolis (AM) algorithm of Haario, Saksman, and Tamminen [8], for target distributions with a non-compact support. The conditions ensuring a strong law of large numbers and a central limit theorem require that the tails of the target density decay… (More)

- Matti Vihola
- Statistics and Computing
- 2012

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)

- Matti Vihola
- 2009

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 Sn induced by the factor ǫI is theoretically convenient, but practically cumbersome, as a good value for the parameter ǫ may not always be easy to choose. This article considers variants of… (More)

- Matti Vihola
- 2004

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- Matti Vihola, Mikko Harju, Petri Salmela, Janne Suontausta, Janne Savela
- 2002 IEEE International Conference on Acoustics…
- 2002

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)

Abstract. Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be unstable without additional stabilisation techniques. We study a stochastic approximation procedure with… (More)

- Matti Vihola
- Computational Statistics & Data Analysis
- 2010

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)

- Matti Vihola
- 2009

The stability and ergodicity properties of an adaptive random walk Metropolis algorithm are considered. The algorithm adjusts the scale of the symmetric proposal distribution continuously based on the observed acceptance probability. Unlike the previously proposed forms of this algorithm, the adapted scaling parameter is not constrained within a predefined… (More)

- Gersende Fort, Eric Moulines, Amandine Schreck, Matti Vihola
- SIAM J. Control and Optimization
- 2016

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)