backward and forward inferences

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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.