一开始用python写的，后来发现要延伸到二维的贝叶斯分类，然后想画一个二元正态分布图就很难....后来改用matlab

基础知识：Bayesian Principle:（查询书《模式分类》第二章

Task 1

According to the above principle and theory in section 2.2, design a Bayesian classifier for the classification of two classes of patterns which are subjected to Gaussian normal distribution and compile the corresponding programme codes.  

What we have: 1. two classes and the data in this two classes; 2. four loss paras 3.prior probability of two classes

    Teacher has given us the data ,the loss parameters and the prior probability. So we just need to calculate the P(x|wi) to get the P(wi|x). I decided to use the normal distribution to calculate the conditional probability(the parameters of the normal distribution were calculated according to the given data).  Here is my code:

import math
import matplotlib.pyplot as plt
import numpy as np

#'''This part is used to define classes which has attributes the average and the variance'''
class w:  
    def __init__(self, data, prob):
        self.mu = 0
        self.sigma = 0
        self.data = data  # a list of data
        self.priProb = prob  # prior probability
        bar = 0
        for i in self.data:
            self.mu += i
        self.mu = self.mu / len(self.data)
        for i in self.data:
            bar += (i - self.mu) ** 2
        self.sigma = math.sqrt(bar / len(self.data))

#'''used to caculate the conditional probability'''
def condProb(mu, sigma, x):   # input the number and return the conditional prob
    condp = 1/(2.5066*sigma) * math.exp(-0.5*(x-mu)**2/sigma**2)
    return condp

#'''calculate the posterior probability'''
def postProb(x, w1, w2):  # input the number and the class, suppose there are two classes
    num = condProb(w1.mu, w1.sigma, x) * w1.priProb
    den = condProb(w1.mu, w1.sigma, x) * w1.priProb + condProb(w2.mu, w2.sigma, x) * w2.priProb
    return num/den

#'''The most important  part: smallest risk Bayesian Classifier'''

def classify(x, cls):  # a list of unclassified object, two classes
    result = []
    for i in x:
        risk = []
        risk.append(condProb(cls[0].mu, cls[0].sigma,i) * cls[0].priProb * 6)
        risk.append(condProb(cls[1].mu, cls[1].sigma,i) * cls[1].priProb * 1)
        if min(risk) == risk[0]:
            result.append(2)
        else:
            result.append(1)
    return result

下次再更二维空间上的贝叶斯分类器设计，比较复杂，我还要去复习复习基础知识....