有使用马尔可夫链的商业示例吗？
使用马尔可夫链有哪些业务案例？ 我见过将马尔可夫链的游戏区域应用于某人的博客来写假帖子。 我想要一些实际的例子吗？ 例如，在商业或股票市场预测等方面有用...
编辑：感谢所有提供示例的人，我对每个示例都投了赞成票，因为它们都很有用。
编辑2：我选择了最详细的答案作为接受的答案。 所有答案我都赞成。
What business cases are there for using Markov chains? I've seen the sort of play area of a markov chain applied to someone's blog to write a fake post. I'd like some practical examples though? E.g. useful in business or prediction of stock market, or the like...
Edit: Thanks to all who gave examples, I upvoted each one as they were all useful.
Edit2: I selected the answer with the most detail as the accepted answer. All answers I upvoted.
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最明显的一个是：Google 的 PageRank。
The obvious one: Google's PageRank.
隐马尔可夫模型基于马尔可夫链，广泛应用于语音识别，尤其是生物信息学。
Hidden Markov models are based on a Markov chain and extensively used in speech recognition and especially bioinformatics.
我见过明显是使用马尔可夫链生成的垃圾邮件——当然这符合“商业用途”的条件。 :)
I've seen spam email that was clearly generated using a Markov chain -- certainly that qualifies as a "business use". :)
一类基于马尔可夫链蒙特卡罗 (MCMC) 方法的优化方法。 这些已应用于各种实际问题，例如信号和信号处理。 图像处理在数据分割和分类中的应用。 演讲与演讲 图像识别、时间序列分析，计算机视觉和模式识别中有很多类似的例子。
There is a class of optimization methods based on Markov Chain Monte Carlo (MCMC) methods. These have been applied to a wide variety of practical problems, for example signal & image processing applications to data segmentation and classification. Speech & image recognition, time series analysis, lots of similar examples come out of computer vision and pattern recognition.
我们使用日志文件链分析来派生并提升到帮助系统（1000 万个文档的集合）中其他不相关文档的二级和三级链接。
这对于桥接其他单独的分类法特别有帮助。 例如，SQL 文档与 IIS 文档。
We use log-file chain-analysis to derive and promote secondary and tertiary links to otherwise-unrelated documents in our help-system (a collection of 10m docs).
This is especially helpful in bridging otherwise separate taxonomies. e.g. SQL docs vs. IIS docs.
我知道 AccessData 在其取证密码破解工具中使用它们。 它可以让您首先探索更有可能的密码短语，从而加快密码恢复速度（平均而言）。
I know AccessData uses them in their forensic password-cracking tools. It lets you explore the more likely password phrases first, resulting in faster password recovery (on average).
必应等搜索公司使用马尔可夫链根据用户在结果页面上的点击顺序来推断文档的相关性。 典型查询会话中的底层用户行为被建模为马尔可夫链，其中特定行为为状态转换......
例如，如果文档是相关的，用户仍然可以检查更多文档（但概率较小），否则他可以检查更多文档（概率较大）。
Markov chains are used by search companies like bing to infer the relevance of documents from the sequence of clicks made by users on the results page. The underlying user behaviour in a typical query session is modeled as a markov chain , with particular behaviours as state transitions...
for example if the document is relevant, a user may still examine more documents (but with a smaller probability) or else he may examine more documents (with a much larger probability).
有一些商业光线追踪系统实现了Metropolis Light Transport（由 Eric Veach 发明，基本上他将 Metropolis Hastings 应用于光线追踪），还有双向和<重要性采样- 路径追踪器使用马尔可夫链。
粗体文本可以在谷歌上搜索，为了这个线程，我省略了进一步的解释。
There are some commercial Ray Tracing systems that implement Metropolis Light Transport (invented by Eric Veach, basically he applied metropolis hastings to ray tracing), and also Bi-Directional- and Importance-Sampling- Path Tracers use Markov-Chains.
The bold texts are googlable, I omitted further explanation for the sake of this thread.
我们计划将其用于手持设备上的预测文本输入，以便在工业环境中输入数据。 在词汇量合理的情况下，可以根据频率建议过渡到下一个单词。 我们的初步测试表明这可以很好地满足我们的需求。
We plan to use it for predictive text entry on a handheld device for data entry in an industrial environment. In a situation with a reasonable vocabulary size, transitions to the next word can be suggested based on frequency. Our initial testing suggests that this will work well for our needs.
我最近偶然发现了一个使用马尔可夫链创建测试数据的博客示例...
http://github.com/emelski/code.melski.net/blob/master/markov/main.cpp
I recently stumbled on a blog example of using markov chains for creating test data...
http://github.com/emelski/code.melski.net/blob/master/markov/main.cpp
马尔可夫模型是一种描述经历一系列状态的过程的方法。
HMM 可以应用于许多领域，其目标是恢复不能立即观察的数据序列（但取决于该序列上的一些其他数据）。
常见应用包括：
密码分析、语音识别、词性标记、机器翻译、股票预测、基因预测、生物序列比对、手势识别、活动识别、检测用户在浏览器上的浏览模式网站。
Markov model is a way of describing a process that goes through a series of states.
HMMs can be applied in many fields where the goal is to recover a data sequence that is not immediately observable (but depends on some other data on that sequence).
Common applications include:
Crypt-analysis, Speech recognition, Part-of-speech tagging, Machine translation, Stock Prediction, Gene prediction, Alignment of bio-sequences, Gesture Recognition, Activity recognition, Detecting browsing pattern of a user on a website.
IBM 有 CELM。 请在此处了解更多相关信息。
IBM has CELM. Read more about it here.
马尔可夫链可以用来模拟用户交互，fg浏览服务时。
我的朋友正在使用马尔可夫链编写文凭工作抄袭识别（他说输入数据必须是整本书才能成功）。
这可能不是很“商业”，但马尔可夫链可以用来生成虚构的地理和人名，尤其是在角色扮演游戏中。
Markov Chains can be used to simulate user interaction, f.g. when browsing service.
My friend was writing as diplom work plagiat recognision using Markov Chains (he said the input data must be whole books to succeed).
It may not be very 'business' but Markov Chains can be used to generate fictitious geographical and person names, especially in RPG games.
马尔可夫链用于人寿保险，特别是永久残疾模型。 有 3 种状态
在永久性残疾模型中，如果被保险人残疾，保险公司可能会支付某种保险金，并且/或在被保险人死亡时支付人寿保险保险金。 然后，保险公司可能会基于该马尔可夫链运行蒙特卡洛模拟，以确定提供此类保险的可能成本。
Markov Chains are used in life insurance, particularly in the permanent disability model. There are 3 states
In a permanent disability model the insurer may pay some sort of benefit if the insured becomes disabled and/or the life insurance benefit when the insured dies. The insurance company would then likely run a monte carlo simulation based on this Markov Chain to determine the likely cost of providing such an insurance.