mmpp: Markov Modulated Poisson Process Object
In HiddenMarkov: Hidden Markov Models

Description Usage Arguments Details Value References Examples

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

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

`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.

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).

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

Cited references are listed on the HiddenMarkov manual page.

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))

iter = 1 
LL = 361.0557716 
diff = Inf 

iter = 2 
LL = 362.5886854 
diff = 1.532914 

iter = 3 
LL = 362.8406330 
diff = 0.2519476 

iter = 4 
LL = 362.9252205 
diff = 0.08458748 

iter = 5 
LL = 362.9543815 
diff = 0.02916102 

iter = 6 
LL = 362.9645022 
diff = 0.01012071 

iter = 7 
LL = 362.9680245 
diff = 0.003522296 

iter = 8 
LL = 362.9692518 
diff = 0.001227252 

iter = 9 
LL = 362.9696795 
diff = 0.0004277787 

iter = 10 
LL = 362.9698287 
diff = 0.0001491253 

iter = 11 
LL = 362.9698806 
diff = 5.198553e-05 

iter = 12 
LL = 362.9698988 
diff = 1.812167e-05 

iter = 13 
LL = 362.9699051 
diff = 6.316798e-06 

$delta
[1] 0 1

$Q
            [,1]        [,2]
[1,] -0.17402168  0.17402168
[2,]  0.09433875 -0.09433875

$nonstat
[1] TRUE

$lambda
[1] 5.031719 1.054213

$n
[1] 5001

[1] 361.0558
[1] 362.9699