probhmm {HiddenMarkov}

Conditional Distribution Function of DTHMM

Description

Calculates the distribution function at each point for a dthmm process given the complete observed process except the given point.

Usage

probhmm(logalpha, logbeta, Pi, delta, cumprob)

Arguments

logalpha

an n \times m matrix containing the logarithm of the forward probabilities.

logbeta

an n \times m matrix containing the logarithm of the backward probabilities.

Pi

is the m \times m transition probability matrix of the hidden Markov chain.

delta

is the marginal probability distribution of the m hidden states at the first time point.

cumprob

an n \times m matrix where the (i,k)th element is \Pr\{ X_i \le x_i \,|\, C_k = c_k\}.

Details

Let X^{(-i)} denote the entire process, except with the point X_i removed. The distribution function at the point X_i is

\Pr\{ X_i \le x_i \,|\, X^{(-i)} = x^{(-i)} \}\,.

This R function calculates the distribution function for each point X_i for i=1, \cdots, n. This is done by using the forward and backward probabilities before and after the ith point, respectively.

In the programming code, note the subtraction of the mean. This is to stop underflow when the exponential is taken. Removal of the mean is automatically compensated for by the fact that the same factor is removed in both the numerator and denominator.

Value

A vector containing the probability.

See Also

residuals