相关软件（R代码）

# HMM在R中的实现
# install.packages("HMM")
library(HMM)
# 定义HMM
# 3个隐藏状态：健康、轻度疾病、重度疾病
# 3个观测状态：无症状、轻微症状、严重症状
states <- c("健康", "轻度", "重度")
symbols <- c("无症状", "轻微", "严重")
# 初始概率
start_probs <- c(0.7, 0.2, 0.1)
# 转移概率矩阵
trans_probs <- matrix(c(
  0.7, 0.2, 0.1,
  0.1, 0.6, 0.3,
  0.05, 0.15, 0.8
), nrow = 3, byrow = TRUE)
# 观测概率矩阵
emission_probs <- matrix(c(
  0.9, 0.08, 0.02,
  0.05, 0.9, 0.05,
  0.01, 0.2, 0.79
), nrow = 3, byrow = TRUE)
hmm_model <- initHMM(States = states, Symbols = symbols,
                     startProbs = start_probs,
                     transProbs = trans_probs,
                     emissionProbs = emission_probs)
# 观测序列：无症状、轻微、无症状、轻微、严重
observation <- c("无症状", "轻微", "无症状", "轻微", "严重")
# Viterbi算法：解码最可能的状态序列
viterbi_result <- viterbi(hmm_model, observation)
print(viterbi_result)
# 前向算法：计算观测序列的概率
forward_result <- forward(hmm_model, observation)
print(exp(forward_result[, ncol(forward_result)]))  # 最终概率
# Baum-Welch算法：从数据中学习参数
# 需要多个观测序列来训练
train_obs <- list(
  c("无症状", "轻微", "无症状"),
  c("无症状", "无症状", "轻微", "严重"),
  c("轻微", "严重", "严重", "严重")
)
# baumWelch(hmm_model, train_obs)  # 需要足够的数据

2.3.8 贝叶斯统计基础