International Research Journal of Applied and Basic Sciences © 2013 Available online at www.irjabs.com ISSN 2251-838X / Vol, 7 (9): 522-527 Science Explorer Publications Surveying the Characteristics of Population Monte Carlo Ehsan Fayyazi 1* , Gholamhossein Gholami 2 1. Department of Statistics, Science and Research Branch, Islamic Azad University, Fars, Iran. 2. Department of Mathematics, Faculty of sciences, Urmia University, Urmia, Iran. Corresponding Author email: e.fayyazi@fsriau.ac.ir ABSTRACT: The importance sampling method as other Monte Carlo Markov Chain (MCMC) algorithms is iterative while this algorithm i.e. importance sampling does not depend on the initiating point. The Population Monte Carlo method includes the frequent production of importance sampling whose used importance functions depend on the previous produced importance samples. The advantage of this method over the MCMC algorithm is that the framework of this algorithm in each iteration is unbiased, so running this algorithm can stop at any given time. The reason is that the iterations improve running the importance function (i.e. the proposal distribution). Hence, this leads to the improved importance sampling. In this study, we survey this method through diverse examples. Keywords: Population Monte Carlo, Importance sampling, Monte Carlo Markov Chain (MCMC), mixed models, Metropolis-Hastings algorithms. INTRODUCTION This study suggests a method named Population Monte Carlo (PMC) which is the combination of Monte Carlo Chain methods, importance sampling, and importance resampling. The method takes the advantages of every of these methods. In doing so, we describe the extension of importance sampling, andthen suggest the population Monte Carlo. Population Monte Carlo Population Monte Carlo (PMC) algorithm is an iterative importance sampling method which produces in each iteration the stimulated approximate sample from the target distribution and the adaptive algorithm which arranges the proposal distribution with the target distribution throughout the iterations. So, the theoretical basis of this method rootin the importance sampling rather than in MCMC and despite the iterated characteristics (that is, unbiased at least to the order O(1/n)), the estimation of target distribution is valid in each iteration and does not require the convergence times and stopping rules. simulating the sample Considering the MCMC, stationary distribution has been taken into account as a limit distribution from Markovsequenceas{ }, having this experimental result is large enough for X to t. A rather simple expansion of this perspective is that instead of simulating a distribution point of π we embark on simulating the n number sample distributed from π. In other words, one would simulate n number from the following π ⊗ (x ,…,x )= π(x ) The expansion in [4] and [5] accompanied by developed programming for nMCMC parallel running has been argued. In fact, one would use this complete sample int iteration for devising a proposal distribution in +1 iteration. General importance sampling The PMC algorithm can be considered in more general framework: one would assume differentproposal distributions in each iteration and for each particle in this algorithm. In other words, if i is the sample indices and t the iteration indices, then X () can be simulated from q distributions which might depend on the previous samples while being independent from other samples (to be conditioned on other samples) X () ~q (x)