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| We study a diffusion limit for the Random Walk Metropolis algorithm for target measures in non-product form, when the chain is started out of stationarity.
Random Walk Metropolis is a popular Metropolis-Hastings algorithm which samples from a given probability distribution by creating a reversible Markov chain which has the target distribution as unique invariant measure.
When the target measure is in product form, a diffusion limit for the resulting Markov chain has been first studied in the seminal paper by G.O. Roberts et al (1997), assuming the chain is started in stationarity, as a way of understanding the efficiency of the algorithm in high dimensions.
Since then, the overwhelming majority of the literature on the subject has been concerned with the stationary phase of the chain. Recently Jourdain at al (2012) have analysed the transient phase as well, in the case in which the target measure is in product form.
This talk will present a method to extend the results in the literature by considering measures in non-product form, when the chain is started out of stationarity. |
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