for_back: Perform the forward backward algorithm (see Rabiner 89)

In Marie-PerrotDockes/sanssouci.hmm: Confindence bound on the FDP after post-selection under an HMM

Perform the forward backward algorithm (see Rabiner 89)

Description

Perform the forward backward algorithm (see Rabiner 89)

Usage

for_back(m, A, f0x, f1x, Pi)

Arguments

m	the number of positions (hypothesis)
A	a matrix 2 * 2 the transition probabilities
f0x	a vector of the values of the density under the null hypothesis on the observations
f1x	a vector of the values of the density under the alternative hypothesis on the observations
Pi	a vector of the initial state probabilities

Value

alpha the forward variables, the lines corespond to the position, the first column is for state 0 and the second for state one

beta the backward variables (same as alpha)

gamma matrix such that gamma\[i , 0\] = P(\theta_i = 0 | X), gamma\[i,1\] = P(\theta_i = 1 | X)

ksi matrix such that ksi\[i , 0\] = P(\theta_i = 0 | X), ksi\[i,1\] = P(\theta_i = 1 | X)

Examples

 m <-  10
 A <- matrix(c(0.95, 0.05, 0.2, 0.80), 2, 2, byrow = T)
 f0 <- c(0, 1)
 f1 <- c(2, 1)
 Pi <- c( 0.9, 0.1)
 rdata <- sim_hmm_2states(m, Pi, A, f0, f1)
 x <- rdata$x
 theta <- rdata$theta
 mod <- for_back(m, A, f0x = dnorm(x), f1x = dnorm(x, 1,2), Pi)

Marie-PerrotDockes/sanssouci.hmm documentation built on Oct. 26, 2023, 10:36 a.m.