A Research Of Hidden State Estimation And Parameter Estimation Problem For HMM Based On ABC

Hidden Markov Model(HMM) is a very important statistical models,which widely used in speech recognition, biological statistics, error diagnosis etc. In real life, there are a lot of phenomenon can be described by Double Chain Markov Model(DCMM). In order to understand and use DCMM better. In this paper, first of all, we study DCMM based on HMM. Secondly, when the likelihood function of the HMM without analytic form, In order to study its hidden state estimation and parameter estimation problem. We introduce the Approximate Bayesian computation(ABC) methods.This thesis is divided into six chapters. In chapter1, we introduce the research back-ground、value、Research Actuality、main content and innovation points of of our study. In chapter2, we introduce the concepts and algorithm associated with HMM, and then on the basis of the literature Berchtold(1999a),we use the difference between DCMM and HMM’s definition,proposed a derived relationship from basic algorithm of HMM to the basic algorithm of DCMM.The derived relationship are analyzed. At last,we obtain the concepts and algortihm of DCMM derived from the concepts and algorithm of HMM. when the likelihood function of HMM without analytic form In order to solve its hidden s-tate estimation and parameter estimation problem, In chapter3,we summarize the content of the ABC,and analyzed thinking of ABC method by a numerical example.In chapter4, under optimal principle of single point, we view the HMM hidden state estimation prob-lem as a optimal bayesian filtering problem, we introduces the hidden state estimation based on particle filter. And then based on literature chengwen et al.(2012)、Jasra et al.(2012),we proposed hidden state estimation method of ABC. Finally we carried on the numerical simulation, compares the merits of the four methods EKF, UKF, PF, ABCSMC.we analyze the relation between efficiency and precision of the algorithm and particle number N.In chapter5, on the basis of literature Elena et al.(2012)、Elena et al.(2014) and Del Moral et al.(2012), we proposed an adaptive ABC-HMM pa-rameter estimation method based on SMC and SPSA, At last a numerical simulation was carried out.we analyze the influence the particle number N、pseudo observed val-ue numberM、quality control parater a on algorithm、the tolerance level changes with time, etc.In chapter6,the whole article are summarized.