bwfw.hmm: backward and forward inferences

In PLIS: Multiplicity Control using Pooled LIS Statistic

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

bwfw.hmm(x, pii, A, pc, 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
pc	(c[1], ..., c[L])–the probability weights in the mixture for each component
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.

PLIS documentation built on Oct. 2, 2022, 5:06 p.m.