NHMSAR (version 1.0)

forwards_backwards: Forward Backward for homogeneous MSAR models

Description

Computes the posterior (or smoothing) probabilities in an homogenenous HMM or MSAR model using the forwards backwards algo. 'filter_only' is an optional argument (default: 0). If 1, we do filtering, if 0, smoothing.

Usage

forwards_backwards(prior, transmat, obslik, filter_only = FALSE)

Arguments

prior

prior probabilities PRIOR(I) = Pr(X(1) = I)

transmat

transition matrice TRANSMAT(I,J) = Pr(X(T+1)=J | X(T)=I)

obslik

emission probabilities OBSLIK(I,t) = Pr(Y(t) | X(t)=I)

filter_only

optional argument (default: 0). If TRUE, we do filtering, if FALSE, smoothing (default).

Value

• List including
• ..$gamma
  smoothing probabilities P(X(t)|Y(0),...,Y(T))
• ..$xi
  two steps smoothing probabilities P(X(t),X(t+1)|Y(0),...,Y(T))
• ..$loglik
  log likelihood
• ..$M
  Number of regimes
• ..$alpha
  intermediate component in the FB algorithm (forward)
• ..$beta
  intermediate component in the FB algorithm (backward)

See Also

fit.MSAR, Estep.MSAR