# BIC_Mk: BIC (Markov model) In SMM: Simulation and Estimation of Multi-State Discrete-Time Semi-Markov and Markov Models

BIC

## Usage

 `1` ```BIC_Mk(seq, E, mu, Ptrans, k) ```

## Arguments

 `seq` List of sequence(s) `E` Vector of state space `mu` Vector of initial distribution `Ptrans` Matrix of transition probabilities `k` Order of the Markov chain

## Details

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

## Value

 `BIC` List: value of BIC for each sequence

## Author(s)

Vlad Stefan Barbu, barbu@univ-rouen.fr
Caroline Berard, caroline.berard@univ-rouen.fr
Dominique Cellier, dominique.cellier@laposte.net
Mathilde Sautreuil, mathilde.sautreuil@etu.univ-rouen.fr
Nicolas Vergne, nicolas.vergne@univ-rouen.fr

## See Also

simulSM, estimMk, simulMk, estimSM, LoglikelihoodSM, LoglikelihoodMk, AIC_Mk

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ```alphabet = c("a","c","g","t") S = length(alphabet) # 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 ## Simulation of two sequences of length 20 and 50 respectively seq2 = simulMk(E = alphabet, nbSeq = 2, lengthSeq = c(20,50), Ptrans = Pij, init = rep(1/4,4), k = 1) ################################# ## Computation of BIC ################################# BIC_Mk(seq = seq2, E = alphabet, mu = rep(1/4,4), Ptrans = Pij, k = 1) #[[1]] #[1] 78.39401 # #[[2]] #[1] 133.7015 ```

### Example output

```Loading required package: seqinr
Loading required package: DiscreteWeibull
Loading required package: Rsolnp
[[1]]
[1] 80.14494

[[2]]
[1] 136.5464
```

SMM documentation built on Jan. 31, 2020, 5:07 p.m.