| Summary: | 碩士 === 國立臺灣大學 === 流行病學與預防醫學研究所 === 100 === Metropolis-Hastings algorithm is established based on a Markov chain method to generate a series of random samples from multivariate distributions. When the distributions are rugged or the number of dimensions in multimodal distributions is high, Metropolis-Hastings algorithm is likely to be trapped locally by a certain unimodal distributions. There are several algorithms proposed to improve Metropolis-Hastings algorithm in literature. For example, parallel tempering is a simulation method which uses auxiliary variables to modify Metropolis-Hastings algorithm. Alternatively, the stochastic approximation Monte Carlo algorithm exploits the past sample information to adapt Metropolis-Hastings algorithm. In this study, a new algorithm is proposed by combing these two methods for using both information from auxiliary variables and past samples. A simulation study is conducted to investigate and compare the performance of the new algorithm and the abovementioned algorithms. The simulation results show that the performance of stochastic approximation Monte Carlo algorithm for the multimodal distribution modes coverage is poor but its performance is better for modes without covering. Parallel tempering performs well for both situations, while performance of the combined method is dependent on the exchange of incidence and proposal function.
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