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چكيده انگليسي :

Slice Sampling Method and Related Topics Azam Arshadipour a arshadipoor@math iut ac ir February 3 2010 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisors Dr Amir Naderi amir@cc iut ac ir 2000 MSC 62G05 Key words Markov chain monte carlo Metropolis Hastings algorithm Gibbs sampling Slice sampling Abstract Statistical simulation is of great importance in Engineering and applied sciences Simu lating random numbers from some distributions however is not an easy task Markov chain monte carlo MCMC is among the most important methods to simulate random numbers in such situations Two of the most applicable algorithms based on the MCMC methods are Metropolis Hastings and Gibbs sampling However to implement Gibbs sampling one may need to devise methods for sampling from non standard univariate distributions and to use the Metropolis algorithm one must nd an appropriate proposal distribution that will lead to e cient sampling The need for such special tailoring limits the routine use of these meth ods and inhibits the development of software that automatically constructs Markov chain samplers from model speci cations Furthermore many common Markov chain samplers are ine cient due to a combination of two aws First they may try to make changes that are not well adapted to the local properties of the density function with the result that changes must be made in small steps Second these small steps take the form of a random walk in which about n2 such steps are needed in order to move a distance that could be traversed in only n steps if these steps moved consistently in one direction Slice sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under the plot of its density function A Markov chain that converges to this uniform distribution can be constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal slice de ned by the current vertical position or more generally with some update that leaves the uniform distribution over this slice invariant Variation on such slice sampling methods are easily implemented for univariate distributions and can be used to sample from a multivari ate distribution by updating each variable in turn This approach is often easier to implement than Gibbs sampling and more e cient than simple Metropolis updates due to the ability of slice sampling to adaptively choose the magnitude of changes made It is therefore attractive for routine and automated use Slice sampling methods that update all variables simultane ously are also possible This methods can adaptively choose the magnitudes of changes made to each variable based on the local properties of the density function More ambitiously such methods could potentially allow the sampling to adapt to dependencies between variables by constructing local quadratic approximations In this work general aspects of the MCMC and slice sampling method are studied and examples and applications are presented 1

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شبيه سازي به روش برشي و مباحث مرتبط

مونت كارلوزنجير ماركفي , الگوريتم متروپوليس-هستينگس , نمونه گيري گيبس , نمونه گيري برشي