馬爾科夫過程描述的是空間狀態(tài)經(jīng)過一個狀態(tài)到另一個狀態(tài)轉(zhuǎn)換的隨機過程。該過程要求具備“無記憶”性質(zhì)，也就是下一狀態(tài)的概率分布只與當前的狀態(tài)有關(guān)，再時間序列中其他前面的事件無關(guān)。

馬爾科夫隨機序列由元組<S,P>表示。 S 代表有限狀態(tài)集，P 是狀態(tài)轉(zhuǎn)移概率矩陣。公式,描述了一個狀態(tài)轉(zhuǎn)移到另一個狀態(tài)發(fā)生的概率。

本文主要以代碼描述MP過程。若要詳細看圖文例子，可參考知乎https://zhuanlan.zhihu.com/p/35124726

import numpy as np
state = ["sleep","icecream","run"]
transitionName =[["ss","si","sr"],["is","ii","ir"],["rs","ri","rr"]]
transitionMatrix =[[0.2,0.6,0.2],[0.1,0.6,0.3],[0.2,0.7,0.1]]

def activity_forecast(days):
    activitytoday= "sleep"
    print("start state",activitytoday)
    activityList = [activitytoday]
    i =0
    prob =1
    while i < days :
        if activitytoday =="sleep":
            change = np.random.choice(transitionName[0],replace=True,p=transitionMatrix[0])
            if change =='ss':
                prob *= transitionMatrix[0][0]
                activityList.append("sleep")

            elif change == 'si':
                prob *= transitionMatrix[0][1]
                activityList.append("icecream")
                activitytoday ='icecream'
            else :
                prob *= transitionMatrix[0][2]
                activityList.append("run")
                activitytoday='run'

        elif activitytoday == "icecream":
            change = np.random.choice(transitionName[1], replace=True, p=transitionMatrix[1])
            if change == 'is':
                prob *= transitionMatrix[1][0]
                activityList.append("sleep")
                activitytoday = 'sleep'
            elif change == 'ii':
                prob *= transitionMatrix[1][1]
                activityList.append("icecream")
            else:
                prob *= transitionMatrix[1][2]
                activityList.append("run")
                activitytoday = 'run'

        else:
            change = np.random.choice(transitionName[2], replace=True, p=transitionMatrix[2])
            if change == 'rs':
                prob *= transitionMatrix[2][0]
                activityList.append("sleep")
                activitytoday = 'sleep'
            elif change == 'ri':
                prob *= transitionMatrix[2][1]
                activityList.append("icecream")
                activitytoday = 'icecream'
            else:
                prob *= transitionMatrix[2][2]
                activityList.append("run")
        i+=1
        print(" after " + str(i) + " days: " + activitytoday)
        print("Possible states: " + str(activityList))
        print("Probability of the possible sequence of states: " + str(prob))
activity_forecast(2)

運行結(jié)果 ：

markov.png