70 citations · 315 across the 30 of their papers we have counts for
11 papers · 1 filter
An invitation to adaptive Markov chain Monte Carlo convergence theory
Pietari Laitinen, Matti Vihola
Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mech…
On the Forgetting of Particle Filters
Joona Karjalainen, Anthony Lee, Sumeetpal S. Singh +1
We study the forgetting properties of the particle filter when its state - the collection of particles - is regarded as a Markov chain. Under a strong mixing assumption on the part…
Conditional convex orders and measurable martingale couplings
Lasse Leskelä, Matti Vihola
Strassen's classical martingale coupling theorem states that two real-valued random variables are ordered in the convex (resp.\ increasing convex) stochastic order if and only if t…
Uniform Ergodicity of the Iterated Conditional SMC and Geometric Ergodicity of Particle Gibbs samplers
Christophe Andrieu, Anthony Lee, Matti Vihola
We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gi…
Quantitative convergence rates for sub-geometric Markov chains
Christophe Andrieu, Gersende Fort, Matti Vihola
We provide explicit expressions for the constants involved in the characterisation of ergodicity of sub-geometric Markov chains. The constants are determined in terms of those appe…
Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms
Christophe Andrieu, Matti Vihola
We study convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (Andrieu and Roberts [Ann. Statist. 37 (2009) 697-725]). We find that the asymptotic variance…
Markovian stochastic approximation with expanding projections
Christophe Andrieu, Matti Vihola
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 v…
Stochastic order characterization of uniform integrability and tightness
Lasse Leskelä, Matti Vihola
We show that a family of random variables is uniformly integrable if and only if it is stochastically bounded in the increasing convex order by an integrable random variable. This…
Can the Adaptive Metropolis Algorithm Collapse Without the Covariance Lower Bound?
Matti Vihola
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 s…
On the stability and ergodicity of adaptive scaling Metropolis algorithms
Matti Vihola
The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. The both algorithms adjust the scaling of the proposal distribution contin…
On the ergodicity of the adaptive Metropolis algorithm on unbounded domains
Eero Saksman, Matti Vihola
This paper describes sufficient conditions to ensure the correct ergodicity of the Adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223--242]…