马尔可夫链如何工作?什么是无记忆? [英] How do Markov Chains work and what is memorylessness?

问题描述

马尔可夫链如何工作?我已经阅读了 Markov Chain 的维基百科，但是我没有得到的就是记忆力不足.无记忆说明:

How do Markov Chains work? I have read wikipedia for Markov Chain, But the thing I don't get is memorylessness. Memorylessness states that:

下一个状态仅取决于当前状态，而不取决于当前状态. 之前发生的事件的顺序.

The next state depends only on the current state and not on the sequence of events that preceded it.

如果马尔可夫链具有这种性质，那么马尔可夫模型中链的用途是什么?
解释此属性.

If Markov Chain has this kind of property, then what is the use of chain in markov model?
Explain this property.

推荐答案

您可以可视化马尔可夫链，就像一只青蛙从池塘的睡莲到睡莲跳来跳去.青蛙不记得它以前去过哪个睡莲.对于i和j的所有可能组合，它也具有从睡莲叶Ai跃迁到睡莲叶Aj的给定概率.马尔可夫链允许您计算在任何给定时刻青蛙在特定睡莲上的概率.

You can visualize Markov chains like a frog hopping from lily pad to lily pad on a pond. The frog does not remember which lily pad(s) it has previously visited. It also has a given probability for leaping from lily pad Ai to lily pad Aj, for all possible combinations of i and j. The Markov chain allows you to calculate the probability of the frog being on a certain lily pad at any given moment.

如果青蛙是素食者，并且每次落在睡垫上时都会在睡垫上ni，那么它从睡垫Aj降落在睡垫Ai上的可能性也将取决于先前拜访过Ai的次数.然后，您将无法使用马尔可夫链对行为进行建模，从而无法预测青蛙的位置.

If the frog was a vegetarian and nibbled on the lily pad each time it landed on it, then the probability of it landing on lily pad Ai from lily pad Aj would also depend on how many times Ai was visited previously. Then, you would not be able to use a Markov chain to model the behavior and thus predict the location of the frog.

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