根据贝氏定理为基础.ppt

Chapter 5 Statistical Methods By Jinn-Yi Yeh Ph.D. 4/7/2009 Outline 5.1 STATISTICAL INFERENCE 5.2 ASSESSING DIFFERENCES IN DATA SETS 5.3 BAYESIAN INFERENCE 5.4 PREDICTIVE REGRESSION 5.5 ANALYSIS OF VARIANCE 5.6 LOGISTIC REGRESSION 5.7 LOG-LINEAR MODELS 5.8 LINEAR DISCRIMINANT ANALYSIS 5.1 STATISTICAL INFERENCE Descriptive statistics V.S Statistical inference Population, Sample, Data set Parameter V.S Statistic Inference methods : estimation, and tests of hypotheses 5.1 STATISTICAL INFERENCE (cont.) Estimation: The goal is to gain information from a data set T in order to estimate one or more parameters w belonging to the model of the real-world system f(X, w) 5.1 STATISTICAL INFERENCE (cont.) statistical testing: to decide whether a hypothesis concerning the value of the population characteristic should be accepted or rejected null hypothesis V.S alternative hypothesis 5.2 ASSESSING DIFFERENCES IN DATA SETS central tendency 1 2 3 5.2 ASSESSING DIFFERENCES IN DATA SETS (cont.) data dispersion 1 2 5.2 ASSESSING DIFFERENCES IN DATA SETS (cont.) Boxplot In many statistical software tools, a popularly used visualization tool of descriptive statistical measures for central tendency and dispersion 5.3 BAYESIAN INFERENCE Na?ve Bayesian Classification Process (Simple Bayesian Classified) 根據貝氏定理為基礎，用以判斷未知類別的資料應該最接近哪一個類別 監督式學習方式(需訓練資料) P(H/X):事後機率 P(H):事前機率 5.3 BAYESIAN INFERENCE (cont.) Given an additional data sample X (its class is unknown), it is possible to predict the class for X using the highest conditional probability P(Ci/X) P(X):constant for all classes，only the product P(X/Ci) · P(Ci) needs to be maximized P(Ci):Ci/m (m is total number of training samples) 5.3 BAYESIAN INFERENCE -example 5.3 BAYESIAN INFERENCE –example (cont.) Goal：to predict classification of the new sample X = {1, 2, 2, class = ?} maximize the product P(X/Ci) · P(Ci) for i = 1,2 Step1:compute prior probabilities P(Ci) 5.3 BAYESIAN INFERENCE –example (cont.) Step2:c