multi_LH: Likelihood of the Hidden Markov Model

In pneff93/HMM: Fitting a Hidden Markov Model

Description

This function calculates the log-likelihood of the HMM mode. For this, the scaled forward probabilities are computed. In respect of the LH function, the multi_LH function incorporates the multi Thetas for the indivudal likelihoods.

Usage

multi_LH(factor, x, m, L1, L2, L3 = NULL, L4 = NULL, L5 = NULL,
  start_index)

Arguments

factor	Input of variables that are unrestricted
x	a sample of a Hidden Markov Model
m	the number of states
L1	likelihood of the first hidden state
L2	likelihood of the second hidden state
L3	optional. likelihood of the third hidden state
L4	optional. likelihood of the 4th hidden state
L5	optional. likelihood of the 5th hidden state
start_index	index parameter to assign the Thetas to their corresponding individual hidden state likelihood.

Details

This function computes the log-likelihood of the forward probabilities of the HMM. Given the fact that the inputed factor vector is not restricted, we need to apply a transformation to transform the factor variables to our suitable canditates Delta, Gamma and Theta. For this we apply the function trans().

The likelihood is constructed using the scaling/normalizing of the forward probabilities such that for each time point the sum of the foward probability is equal to one. The scaling is neccesary to tackle the underflow problem, that arrises with an increasing sample size.

The multi_LH function only differes in the computation of the likelihood probability vector p, because we imput multiple Thetas in the corresponding individual likelihoods.

Value

negative Likelihood

pneff93/HMM documentation built on Oct. 26, 2019, 8:16 a.m.