基于贝叶斯最小错误率决策的分类

基于贝叶斯最小错误率决策的分类

假定某个局部区域细胞识别中正常P(w1)和异常P（w2)两类先验概率分别为P(w1)=0.9, P(w2)=0.1现有一系列待观察的细胞，其观察值为：-2.67 -3.55 -1.24 -0.98 -0.79 -2.85 -2.76 -3.73 -3.54 -2.27 -3.45 -3.08 -1.58 -1.49 -0.74 -0.42 -1.12 4.25 -3.99 2.88 -0.98 0.79 1.19 3.07 两类的类条件概率符合正态分布p(x|w1)=(-2,1.5), p(x|w2)=(2,2).依据最小错误率的贝叶斯决策对观察的结果进行分类。

## 基于贝叶斯最小错误率决策的分类 import numpy as np import math x = [-2.67, -3.55, -1.24, -0.98, -0.79, -2.85, -2.76, -3.73, -3.54, -2.27, -3.45, -3.08, -1.58, -1.49, -0.74, -0.42, -1.12, 4.25, -3.99, 2.88, -0.98, 0.79, 1.19, 3.07] P_w1 = 0.9 P_w2 = 0.1 x_i = 0 mean1 = -2 std1 = np.sqrt(1.5) mean2 = 2 std2 = np.sqrt(2) data_w1 = [] data_w2 = [] for x_i in x: P_x_w1 = 1 / (std1 * pow(2 * math.pi, 0.5)) * np.exp(-((x_i - mean1) ** 2) / (2 * std1 ** 2)) P_x_w2 = 1 / (std2 * pow(2 * math.pi, 0.5)) * np.exp(-((x_i - mean2) ** 2) / (2 * std2 ** 2)) P_x = P_x_w1 * P_w1 + P_x_w2 * P_w2 P_w1_x = (P_x_w1 * P_w1) / P_x P_w2_x = 1 - P_w1_x if P_w1_x > P_w2_x: data_w1 = np.append(data_w1, x_i) if P_w1_x < P_w2_x: data_w2 = np.append(data_w2, x_i) print("data_w1=", data_w1) print("data_w2=", data_w2)