§11.1 计算积分的Monte Carlo方法 §11.2 Markov链Monte Carlo方法简介 §11.3 Metropolis-Hastings算法 §11.4 Gibbs抽样 §11.5 贝叶斯MCMC估计方法

1 Markov Chain Monte Carlo Methods 1.4 The Gibbs Sampler 1.4.1 The Slice Gibbs Sampler 1.5 Monitoring Convergence 1.5.1 Convergence diagnostics plots 1.5.2 Monte Carlo Error 1.5.3 The Gelman-Rubin Method 1.6 WinBUGS Introduction 1.6.1 Building Bayesian models in WinBUGS 1.6.2 Model specification in WinBUGS 1.6.3 Data and initial value specification 1.6.4 Compiling model and simulating values

Assumptions of the classical Linear Model (Clm) e So far, we know that given the Gauss Markov assumptions, OLS IS BLUE e In order to do classical hypothesis testing we need to add another assumption(beyond the Gauss-Markov assumptions) Assume that u is independent of x,x2…,xk and u is normally distributed with zero mean and variance 0: u- Normal(0, 02) Economics 20- Prof anderson

• Models – HMM: Hidden Markov Model – maximum entropy Markov model – CRFs: Conditional Random Fields • Tasks – Chinese word segmentation – part-of-speech tagging – named entity recognition

Application of MR2T2 algorithm in statistical mechanics Canonical ensemble: Distribution function: p(rN)=exp(-E(rN)/KT)/Q Q= JdrN exp(-E(rN)/kT) Different states of the Markov chain: In the application of Metropolis algorithm to a simulation of molecular system, the states of the Markov chain correspond to different configurations of the molecular system

Foundations of state Estimation Topics: Bayes Filters Kalman filters Hidden markov models Additional readins G. Welch and G. Bishop. An Introduction to the Kalman Filter \. University of North Carolina at Chapel Hill

Estimation · Summary Examine correlations -Process noise · White noise · Random walk First-order Gauss Markov Processes Kalman filters Estimation in which the parameters to be estimated are changing with time

定义:设C是状态空间S的一个子集,如果从C内任何一个状 态i不能到达C外的任何状态,则称C是一个闭集。如果单个状 态i构成的集l}是闭集,则称状态是吸收态。如果闭集C中不 再含有任何非空闭的真子集则称C是不可约的闭集是存在的

（一）纯不连续马氏过程的

Introduction Speech recognition based on HMM • Acoustic processing • Acoustic modeling: Hidden Markov Model • Language modeling