multi_theta_estimation: Multi Theta Estimation function

In pneff93/HMM: Fitting a Hidden Markov Model

Description

This function calculates part of the global log-likelihood that is only dependent on the Theta value. Due to its proportionality, it is therefore optimal for the maximisation of the Theta values and will be used by the EM-algorithm. For the multi_HMM_EM(), small changes where made to calculate the index of the Theta alues right.

Usage

multi_theta_estimation(m, N, u, x, theta, L1, L2, L3 = NULL, L4 = NULL,
  L5 = NULL, start_index)

Arguments

m	number of likelihoods
N	length of the supplied dataset
u	output matrix of the u_function
x	a sample of a Hidden Markov Model
theta	Theta vector
L1	likelihood of the first hidden state
L2	likelihood of the second hidden state
L3	optional. likelihoods of the third hidden state
L4	optional. likelihoods of the 4th hidden state
L5	optional. likelihoods of the 5th hidden state
start_index	index paramter to assign the right amount of thetas to the likelihoods

Details

For more detailed explanation we recommend the source Hidden Markov Models for Times Series by Walter Zucchini, Iain MacDonald & Roland Langrock, especially page 72.

Value

returns the corresponding likelihood

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