BIC_SM {SMM}

BIC (semi-Markov model)

Description

BIC

Usage

BIC_SM(seq, E, mu, Ptrans, distr = "NP", param = NULL, laws = NULL, TypeSojournTime)

Arguments

seq

List of sequence(s)

E

Vector of state space

mu

Vector of initial distribution

Ptrans

Matrix of transition probabilities of the embedded Markov chain J=(J_m)_{m}

distr

- "NP" for nonparametric case, laws have to be used, param is useless

- Matrix of distributions of size SxS if TypeSojournTime is equal to "fij";

- Vector of distributions of size S if TypeSojournTime is equal to "fi" or "fj";

- A distribution if TypeSojournTime is equal to "f".

The distributions to be used in distr must be one of "uniform", "geom", "pois", "dweibull", "nbinom".

param

- Useless if distr = "NP"

- Array of distribution parameters of size SxSx2 (2 corresponds to the maximal number of distribution parameters) if TypeSojournTime is equal to "fij";

- Matrix of distribution parameters of size Sx2 if TypeSojournTime is equal to "fi" or "fj";

- Vector of distribution parameters of length 2 if TypeSojournTime is equal to "f".

laws

- Useless if distr \neq "NP"

- Array of size SxSxKmax if TypeSojournTime is equal to "fij";

- Matrix of size SxKmax if TypeSojournTime is equal to "fi" or "fj";

- Vector of length Kmax if the TypeSojournTime is equal to "f".

Kmax is the maximum length of the sojourn times.

TypeSojournTime

Character: "fij", "fi", "fj", "f"

Details

BIC(M) = -2*log{L} + log(n)*M, where L is the log-likelihood, M is the number of parameters of the model.

Value

BIC

List: value of BIC for each sequence

Author(s)

Vlad Stefan Barbu, [e-mail]
Caroline Berard, [e-mail]
Dominique Cellier, [e-mail]
Mathilde Sautreuil, [e-mail]
Nicolas Vergne, [e-mail]

See Also

simulSM, estimMk, simulMk, estimSM, LoglikelihoodSM, LoglikelihoodMk, BIC_Mk, AIC_SM

Examples

alphabet = c("a","c","g","t")
S = length(alphabet)
## creation of the initial distribution
vect.init = c(1/4,1/4,1/4,1/4)
# creation of the transition matrix
Pij = matrix(c(0,0.2,0.3,0.5,0.4,0,0.2,0.4,0.1,0.2,0,0.7,0.8,0.1,0.1,0), 
nrow = S, ncol = S, byrow = TRUE)

#Pij
#     [,1] [,2] [,3] [,4]
#[1,]  0.0  0.2  0.3  0.5
#[2,]  0.4  0.0  0.2  0.4
#[3,]  0.1  0.2  0.0  0.7
#[4,]  0.8  0.1  0.1  0.0


################################
## Parametric simulation of several trajectories (3 trajectories of length 1000, 10 000
## and 2000 respectively)
## where the sojourn time depend on the present state and the next state
## the sojourn time is modelled by different distributions
################################
lengthSeq3 = c(1000, 10000, 2000)
## creation of the distribution matrix
distr.matrix = matrix(c("dweibull", "pois", "geom", "nbinom", "geom", "nbinom", 
"pois", "dweibull", "pois", "pois", "dweibull", "geom", "pois","geom", "geom",
 "nbinom"), nrow = S, ncol = S, byrow = TRUE)
## creation of an array containing the parameters
param1.matrix = matrix(c(0.6,2,0.4,4,0.7,2,5,0.6,2,3,0.6,0.6,4,0.3,0.4,4),
 nrow = S, ncol = S, byrow = TRUE)
param2.matrix = matrix(c(0.8,0,0,2,0,5,0,0.8,0,0,0.8,0,4,0,0,4),
 nrow = S, ncol = S, byrow = TRUE)
param.array = array(c(param1.matrix, param2.matrix), c(S,S,2))
## Simulation of 3 sequences
seq3 = simulSM(E = alphabet, NbSeq = 3, lengthSeq = lengthSeq3,
 TypeSojournTime = "fij", init = vect.init, Ptrans = Pij, distr = distr.matrix,
 param = param.array, File.out = NULL)
                
#################################
## Computation of BIC
#################################
BIC_SM(seq = seq3, E = alphabet, mu = rep(1/4,4), Ptrans = Pij, distr = distr.matrix, 
      param = param.array, TypeSojournTime = "fij")

#[[1]]
#[1] 1607.322
#
#[[2]]
#[1] 15846.36
#
#[[3]]
#[1] 3121.074