scholarly journals Asymptotic normality of M-estimators in nonhomogeneous hidden Markov models

2011 ◽  
Vol 48 (A) ◽  
pp. 295-306 ◽  
Author(s):  
Jens Ledet Jensen
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Hidden Markov Models ◽  
Maximum Likelihood Estimate ◽  
Markov Models ◽  
Hidden Markov ◽  
Likelihood Estimate ◽  
Mixing Properties ◽  
Dependent Variables ◽  
Hidden Markov Process

Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore, a class of estimating equations is considered instead of the maximum likelihood estimate. The basic ingredients are mixing properties of the process and a general central limit theorem for weakly dependent variables.

scholarly journals Asymptotic normality of M-estimators in nonhomogeneous hidden Markov models

2011 ◽  
Vol 48 (A) ◽  
pp. 295-306
Author(s):  
Jens Ledet Jensen
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Hidden Markov Models ◽  
Maximum Likelihood Estimate ◽  
Markov Models ◽  
Hidden Markov ◽  
Likelihood Estimate ◽  
Mixing Properties ◽  
Dependent Variables ◽  
Hidden Markov Process

Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore, a class of estimating equations is considered instead of the maximum likelihood estimate. The basic ingredients are mixing properties of the process and a general central limit theorem for weakly dependent variables.

scholarly journals Variational Inference for Coupled Hidden Markov Models Applied to the Joint Detection of Copy Number Variations

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Xiaoqiang Wang ◽  
Emilie Lebarbier ◽  
Julie Aubert ◽  
Stéphane Robin
Keyword(s):  
Hidden Markov Models ◽  
Copy Number ◽  
Markov Models ◽  
Hidden Markov ◽  
R Package ◽  
Copy Number Variations ◽  
Structural Variations ◽  
Statistical Framework ◽  
Coupled Hidden Markov Models ◽  
Hidden Markov Process

Abstract Hidden Markov models provide a natural statistical framework for the detection of the copy number variations (CNV) in genomics. In this context, we define a hidden Markov process that underlies all individuals jointly in order to detect and to classify genomics regions in different states (typically, deletion, normal or amplification). Structural variations from different individuals may be dependent. It is the case in agronomy where varietal selection program exists and species share a common phylogenetic past. We propose to take into account these dependencies inthe HMM model. When dealing with a large number of series, maximum likelihood inference (performed classically using the EM algorithm) becomes intractable. We thus propose an approximate inference algorithm based on a variational approach (VEM), implemented in the CHMM R package. A simulation study is performed to assess the performance of the proposed method and an application to the detection of structural variations in plant genomes is presented.

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