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- W1702112936 abstract "Study of diffusion limits of the Metropolis-Hastings algorithm in high dimensions yields useful quantificaton of the scaling of the underlying proposal distribution in terms of the dimensionality. Here we consider the recently introduced Transformation-based Markov Chain Monte Carlo (TMCMC) (Dutta and Bhattacharya (2013a)), a methodology that is designed to update all the parameters simultaneously using some simple deterministic transformation of a one-dimensional random variable drawn from some arbitrary distribution on a relevant support. The additive transformation based TMCMC is similar in spirit to random walk Metropolis, except the fact that unlike the latter, additive TMCMC uses a single draw from a one-dimensional proposal distribution to update the high-dimensional parameter. In this paper, we study the diffusion limits of additive TMCMC under various set-ups ranging from the product structure of the target density to the case where the target is absolutely continuous with respect to a Gaussian measure; we also consider the additive TMCMC within Gibbs approach for all the above set-ups. These investigations lead to appropriate scaling of the one-dimensional proposal density. We also show that the optimal acceptance rate of additive TMCMC is 0.439 under all the aforementioned set-ups, in contrast with the well-established 0.234 acceptance rate associated with optimal random walk Metropolis algorithms under the same set-ups. We also elucidate the ramifications of our results and the advantages of additive TMCMC over random walk Metropolis with ample simulation studies. It was found that in all set ups we considered- namely iid component set up, independent scaling components, a wide range of dependent set ups as well as real spatial data application- TMCMC performed much better and converged to the target density much faster than the RWMH algorithm." @default.
- W1702112936 created "2016-06-24" @default.
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- W1702112936 date "2013-07-04" @default.
- W1702112936 modified "2023-09-23" @default.
- W1702112936 title "On Optimal Scaling of Additive Transformation Based Markov Chain Monte Carlo" @default.
- W1702112936 hasPublicationYear "2013" @default.
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