forward_probabilities: Forward and backward (log-)probabilities

In AdvancedR-2021/hmm: Hidden Markov Models

Description

Calculate matrices of forward and backward (log-)probabilities for a given data set and parameters in a hidden Markov model. Essentially just a wrapper for the true function written in C++. Useful for avoiding underflow (by using the log-exp-sum-trick) when the HMM is large. Not expected to be called by the user, instead only being used during the EM-algorithm.

Usage

backward_logprobabilities(x, Gamma, p)

backward_probabilities(x, Gamma, p)

forward_logprobabilities(x, Gamma, p, delta)

forward_probabilities(x, Gamma, p, delta)

Arguments

x	Vector of observed emissions
Gamma	Matrix (m x m) of transition probabilities of the underlying Markov chain
p	A function where p(i, x)=P(X_t=x | Y_t=i)

Details

Let (X, Y)_i, i=1,...,n constitute a HMM, that is, Y_1,...,Y_n is a Markov chain with states 1,...,m and the X_i's are dependent only through the Y_i's with common conditional distributions X_i | Y_i=j = P_j for all i=1,...,n. This function then generates a matrix where the i,j'th entry is log P(X_j+1=x_j+1, ..., X_n=x_n | Y_j=i), where x_1,...,x_n are the observed values (emissions) of X.

Functions

• backward_logprobabilities: Matrix of backwards log-probabilities

• backward_probabilities: Matrix of backward probabilities

• forward_logprobabilities: Matrix of forward log-probabilities

• forward_probabilities: Matrix of forward probabilities

AdvancedR-2021/hmm documentation built on Dec. 17, 2021, 7:41 a.m.