bwfw1.hmm: backward and forward inferences

Description

When L=1, calculate values for backward, forward variables, probabilities of hidden states. A supporting function called by em.hmm.

Usage

 1 bwfw1.hmm(x, pii, A, f0, f1) 

Arguments

 x the observed Z values pii (prob. of being 0, prob. of being 1), the initial state distribution A A=(a00 a01\\a10 a11), transition matrix f0 (mu, sigma), the parameters for null distribution f1 (mu[1], sigma[1]\\...\\mu[L], sigma[L])–an L by 2 matrix, the parameter set for the non-null distribution

Details

calculates values for backward, forward variables, probabilities of hidden states,
–the lfdr variables and etc.
–using the forward-backward procedure (Rabiner 89)
–based on a sequence of observations for a given hidden markov model M=(pii, A, f)
–see Sun and Cai (2009) for a detailed instruction on the coding of this algorithm

Value

 alpha rescaled backward variables beta rescaled forward variables lfdr lfdr variables gamma probabilities of hidden states dgamma rescaled transition variables omega rescaled weight variables

Author(s)

Wei Z, Sun W, Wang K and Hakonarson H

References

Multiple Testing in Genome-Wide Association Studies via Hidden Markov Models, Bioinformatics, 2009
Large-scale multiple testing under dependence, Sun W and Cai T (2009), JRSSB, 71, 393-424
A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition, Rabiner L (1989), Procedings of the IEEE, 77, 257-286.

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

All documentation is copyright its authors; we didn't write any of that.