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Analytic Convergence Rates and Parameterization Issues for the Gibbs Sampler Applied to State Space Models
Author(s) -
Pitt Michael K.,
Shephard Neil
Publication year - 1999
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00126
Subject(s) - gibbs sampling , mathematics , stochastic volatility , markov chain monte carlo , state space , markov chain , rate of convergence , monte carlo method , autoregressive model , state space representation , volatility (finance) , convergence (economics) , econometrics , statistical physics , statistics , algorithm , computer science , bayesian probability , computer network , channel (broadcasting) , physics , economics , economic growth
In this paper we obtain a closed form expression for the convergence rate of the Gibbs sampler applied to the unobserved states of a first‐order autoregression plus noise model. The rate is expressed in terms of the parameters of the model, which are regarded as fixed. For the case where the unconditional mean of the states is a parameter of interest we provide evidence that a ‘centred’ parameterization of a state space model is preferable for the performance of the Gibbs sampler. These two results provide guidance when the Gaussianity or linearity of the state space form is lost. We illustrate this by examining the performance of a Markov chain Monte Carlo sampler for the stochastic volatility model.