The Efficient Particle MCMC Algorithms For Bayesian Estimation Of Nonlinear State Space Models

This thesis focuses on developing particle MCMC algorithms with higher statisti-cal efficiency and lower computational cost for Bayesian estimation of nonlinear/non-Gaussian state space models.The thesis improves the benchmark particle MCMC algo-rithm using multiple techniques and strategies in Monte Carlo computation,for exam-ple multiple-try,delayed acceptance,marginalization and backward sampling.These techniques and strategies broaden the scope of application of particle MCMC and im-prove the statistical and computational efficiency of benchmark algorithms.Specifical-ly,the research content and contribution of this thesis read as follows.Firstly,the thesis proposes the multiple-try particle MH algorithm.The new al-gorithm accelerates the convergence of particle MH chain by multiple-try strategy.Through appropriately use of nonlinear Kalman filter for fast likelihood function ap-proximation,the algorithm admit the true stationary distribution while significantly re-duce the computational cost.The thesis then considers the special case of the algorithm with independent sampling distribution,and combines the algorithm with the delayed acceptance strategy to further improve its computational efficiency.It also proposes a method to calculate marginal likelihood of the model from particle MH outputs.In the numerical experiment,the convergence rate and the computational cost of various algo-rithms are evaluated and compared.In the application section,the proposed algorithm is used to estimate and compare alternative dynamic macroeconomic models and then to analyze China’s monetary policy.Secondly,the thesis proposes the approximate Bayesian Computation(ABC)par-ticle MCMC algorithm.The algorithm is proposed to solve the posterior sampling problem in situation where the conditional distributions of the observed variables are analytically unavailable.The ABC particle filter implements the filtering process by generating pseudo observations to approximates the unavailable conditional distribu-tion.The ABC particle MCMC algorithm is then obtained by embedding the ABC par-ticle filter into the MH algorithm for likelihood function approximation or embedding it into the Gibbs sample for state updating.The thesis then uses the marginalization strategy to improve the accuracy of the ABC particle approximation to the likelihood function,and then use the backward sampling to solve the degeneracy problem in the particle Gibbs algorithm.In the numerical experiment,the two proposed improvement strategies show higher statistics and computational efficiency:The marginalization s-trategy can achieve more accurate likelihood approximation with computational burden unchanged,and and the backward sampling strategy can greatly improve the mixing rate of the state updating whit minor increase in computational cost.Thirdly,the thesis presents an efficient posterior sampling algorithm for Bayesian parameter estimation and model evaluation of Wishart dynamic term structure model.The proposed posterior sampling algorithm updates the state variables and parameters alternately in the framework of Gibbs algorithm.In the state update step,the condi-tional particle filter with backward sampling is performed.In the parameter update step,multiple-try independent MH algorithm is used to update the parameters group by group.Multiple-try strategy is effective to improve the acceptance probability and the mixing rate in parameter updating.Numerical experiments show that the proposed posterior algorithm has higher statistics and computational efficiency.Finally,Bayesian estimation and model evaluation of the Wishart term structure model are implemented based on US data.The effect of stochastic volatility factor on yield curve is studies and the cross-sectional and time series forecasting ability of the model is evaluated.