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- Title
Scaling limits for the transient phase of local Metropolis–Hastings algorithms.
- Authors
Christensen, Ole F.; Roberts, Gareth O.; Rosenthal, Jeffrey S.
- Abstract
The paper considers high dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well understood and it is now well known how to scale their proposal distribution variances. For the random-walk Metropolis algorithm, convergence during the transient phase is extremely regular—to the extent that the algo-rithm's sample path actually resembles a deterministic trajectory. In contrast, the Langevin algorithm with variance scaled to be optimal for stationarity performs rather erratically. We give weak convergence results which explain both of these types of behaviour and practical guidance on implementation based on our theory.
- Subjects
MARKOV processes; STOCHASTIC processes; MONTE Carlo method; MATHEMATICAL models; NUMERICAL analysis
- Publication
Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2005, Vol 67, Issue 2, p253
- ISSN
1369-7412
- Publication type
Article
- DOI
10.1111/j.1467-9868.2005.00500.x