Approximating the Variance of the Conditional Probability of the State of a Hidden Markov Model
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David O Siegmund
In a hidden Markov model, one "estimates" the state of the hidden Markov chain at t by computing via the forwards-backwards algorithm the conditional distribution of the state vector given the observed data. The covariance matrix of this conditional distribution measures the information lost by failure to observe directly the state of the hidden process. In the case where changes of state occur slowly relative to the speed at which information about the underlying state accumulates in the observed data, we compute approximately these covariances in terms of functionals of Brownian motion that arise in change-point analysis. Applications in gene mapping, where these covariances play a role in standardizing the score statistic and in evaluating the loss of noncentrality due to incomplete information, are discussed. Numerical examples illustrate the range of validity and limitations of our results.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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Articles in the same Issue
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- Accounting for Dependence in Similarity Data from DNA Fingerprinting
- Normalization of Dye Bias in Microarray Data Using the Mixture of Splines Model
- A Generalized Sidak-Holm Procedure and Control of Generalized Error Rates under Independence
- Using Duplicate Genotyped Data in Genetic Analyses: Testing Association and Estimating Error Rates
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- Sparse Logistic Regression with Lp Penalty for Biomarker Identification
- Super Learning: An Application to the Prediction of HIV-1 Drug Resistance
- Supervised Detection of Conserved Motifs in DNA Sequences with Cosmo
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- A Bayesian Model of AFLP Marker Evolution and Phylogenetic Inference
- Sequential Quantitative Trait Locus Mapping in Experimental Crosses
- Case-Control Inference of Interaction between Genetic and Nongenetic Risk Factors under Assumptions on Their Distribution
- Inference on the Limiting False Discovery Rate and the P-value Threshold Parameter Assuming Weak Dependence between Gene Expression Levels within Subject
- Reconstructing Gene Regulatory Networks with Bayesian Networks by Combining Expression Data with Multiple Sources of Prior Knowledge
- Cox Survival Analysis of Microarray Gene Expression Data Using Correlation Principal Component Regression
- A Method for Meta-Analysis of Case-Control Genetic Association Studies Using Logistic Regression
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- Using Linear Mixed Models for Normalization of cDNA Microarrays
- Experimental Design for Two-Color Microarrays Applied in a Pre-Existing Split-Plot Experiment
- The Cyclohedron Test for Finding Periodic Genes in Time Course Expression Studies
- H-Tuple Approach to Evaluate Statistical Significance of Biological Sequence Comparison with Gaps
- Multiple Testing Issues in Discriminating Compound-Related Peaks and Chromatograms from High Frequency Noise, Spikes and Solvent-Based Noise in LC - MS Data Sets
- A Bayesian Approach to Estimation and Testing in Time-course Microarray Experiments
- Super Learner
- Testing for Trends in Dose-Response Microarray Experiments: A Comparison of Several Testing Procedures, Multiplicity and Resampling-Based Inference
- On the Operational Characteristics of the Benjamini and Hochberg False Discovery Rate Procedure
- A Comparison of Methods to Control Type I Errors in Microarray Studies
- Selection of Biologically Relevant Genes with a Wrapper Stochastic Algorithm
- T-BAPS: A Bayesian Statistical Tool for Comparison of Microbial Communities Using Terminal-restriction Fragment Length Polymorphism (T-RFLP) Data
- Population Structure and Covariate Analysis Based on Pairwise Microsatellite Allele Matching Frequencies
- Estimating the Arm-Wise False Discovery Rate in Array Comparative Genomic Hybridization Experiments
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