Hidden semi Markov models; stochastic control.

隐半马尔可夫模型；

• 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

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，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摩尔合著的《隐马尔可夫模型：估计与控制》一书于1995年由施普林格出版社出版，1997年再版。2008年出版了修订和扩充版。我已经发表了其他几个贡献隐马尔可夫模型。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，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。我们将考虑“隐藏”半马尔可夫模型，即半马尔可夫链不能直接观察到，但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型在蛋白质和其他'侏儒'测序中表现出的行为。我们将为这些模型发展在我们的书和以前的工作中找到的结果。 第二条研究线将使用我们最近的结果倒向随机微分方程，调查部分观察随机控制问题。伴随过程由一个倒向随机微分方程描述;对于部分观测问题，这是一个倒向随机偏微分方程。最初的工作将考虑这个问题的控制部分观测马尔可夫链