Hidden semi Markov models; stochastic control.

隐半马尔可夫模型；

基本信息

批准号：
RGPIN-2014-04416
负责人：
Elliott, Robert
金额：
$ 2.7万
依托单位：
University of Calgary
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2014
资助国家：
加拿大
起止时间：
2014-01-01 至 2015-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=566508
关键词：
Hidden semi Markov models stochastic

项目摘要

In addition to signal processing, speech processing and other areas, one of the most successful applications of hidden Markov models has been to genome and protein sequencing. My book with L Aggoun and J Moore on "Hidden Markov Models: Estimation and Control" was published in 1995 by Springer Verlag and reprinted in 1997. A revised and expanded edition was printed in 2008. I have published several other contributions to hidden Markov models. However, when modelling discrete sequences, for example in discrete time or in biological applications, if the hidden process is a Markov chain its (random) occupation time in any state is a geometrically distributed random variable. For biological applications it appears that more general occupation times should be considered. This leads us to consider semi-Markov models where the probability of jumping to a new state depends not only on the present state but how long the chain has been in that state. We shall consider 'hidden' semi-Markov models, that is situations where the semi-Markov chain is not observed directly but modulates a second, observed, process. We believe these will better model behaviour exhibited in protein and other 'gnome' sequencing. We shall develop for these models the results found in our book and previous works. A second line of research will use our recent results on backward stochastic differential equations to investigate partially observed stochastic control problems. The adjoint process is described by a backward stochastic differential equation; for partially observed problems this is a backward stochastic partial differential equation. Initial work will consider this problem for the control of a partially observed Markov chain

除了信号处理、语音处理和其他领域外，隐马尔可夫模型最成功的应用之一是基因组和蛋白质测序。我与 L Aggoun 和 J Moore 合着的《隐马尔可夫模型：估计与控制》一书于 1995 年由 Springer Verlag 出版，并于 1997 年重印。修订和扩展版于 2008 年印刷。我还发表了其他几篇关于隐马尔可夫模型的文章。然而，当对离散序列进行建模时，例如在离散时间或生物应用中，如果隐藏过程是马尔可夫链，则其在任何状态下的（随机）占用时间都是几何分布的随机变量。对于生物应用来说，似乎应该考虑更一般的占用时间。这导致我们考虑半马尔可夫模型，其中跳转到新状态的概率不仅取决于当前状态，还取决于链处于该状态的时间长度。我们将考虑“隐藏”半马尔可夫模型，即不直接观察半马尔可夫链而是调制第二个观察到的过程的情况。我们相信这些将更好地模拟蛋白质和其他“侏儒”测序中表现出的行为。我们将为这些模型开发我们的书和以前的作品中发现的结果。第二个研究方向将利用我们最近关于向后随机微分方程的结果来研究部分观察到的随机控制问题。伴随过程由向后随机微分方程描述；对于部分观察到的问题，这是一个向后随机偏微分方程。初步工作将考虑这个问题来控制部分观察的马尔可夫链