mmpp {HiddenMarkov}

Markov Modulated Poisson Process Object

Description

Creates a Markov modulated Poisson process model object with class "mmpp".

Usage

mmpp(tau, Q, delta, lambda, nonstat = TRUE)

Arguments

tau

vector containing the event times. Note that the first event is at time zero. Alternatively, tau could be specified as NULL, meaning that the data will be added later (e.g. simulated).

Q

the infinitesimal generator matrix of the Markov process.

delta

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

lambda

a vector containing the Poisson rates.

nonstat

is logical, TRUE if the homogeneous Markov process is assumed to be non-stationary, default.

Details

The Markov modulated Poisson process is based on a hidden Markov process in continuous time. The initial state probabilities (at time zero) are specified by delta and the transition rates by the Q matrix. The rate parameter of the Poisson process (lambda) is determined by the current state of the hidden Markov process. Within each state, the Poisson process is homogeneous (constant rate parameter). A Poisson event is assumed to occur at time zero and at the end of the observation period, however, state transitions of the Markov process do not necessarily coincide with Poisson events. For more details, see Ryden (1996).

Value

A list object with class "mmpp", containing the above arguments as named components.

References

Cited references are listed on the HiddenMarkov manual page.

Examples

Q <- matrix(c(-2,  2,
               1, -1),
            byrow=TRUE, nrow=2)/10

#    NULL indicates that we have no data at this point
x <- mmpp(NULL, Q, delta=c(0, 1), lambda=c(5, 1))

x <- simulate(x, nsim=5000, seed=5)

y <- BaumWelch(x)

print(summary(y))

#    log-likelihood using initial parameter values
print(logLik(x))

#    log-likelihood using estimated parameter values
print(logLik(y))