Description Usage Arguments Details Value Author(s) References See Also Examples
Computes the Aikaike's information criterion and the Bayesian information criterion for a discrete time hidden Markov model, given a time-series of observations.
1 2 |
size |
length of the time-series of observations x (also |
m |
number of states in the Markov chain of the model. |
k |
single numeric value representing the number of parameters of the underlying distribution of the observation process (e.g. k=2 for the normal distribution (mean and standard deviation)). |
logL |
logarithmized likelihood of the model. |
For a discrete-time hidden Markov model, AIC and BIC are as follows (MacDonald & Zucchini (2009, Paragraph 6.1 and A.2.3)):
AIC = -2 logL + 2p
BIC = -2 logL + p log(T),
where T
indicates the length/size of the observation time-series and p
denotes the number of independent parameters of the model. In case of a HMM as provided by this package, where k
and m
are defined as in the arguments above, p
can be calculated as follows:
p = m^2 + km - 1.
The AIC or BIC value of the fitted hidden Markov model.
Based on MacDonald & Zucchini (2009, Paragraph 6.1 and A.2.3). Implementation by Vitali Witowski (2013).
MacDonald, I. L., Zucchini, W. (2009) Hidden Markov Models for Time Series: An Introduction Using R, Boca Raton: Chapman & Hall.
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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ################################################################
### Fictitious observations ####################################
################################################################
x <- c(1,16,19,34,22,6,3,5,6,3,4,1,4,3,5,7,9,8,11,11,
14,16,13,11,11,10,12,19,23,25,24,23,20,21,22,22,18,7,
5,3,4,3,2,3,4,5,4,2,1,3,4,5,4,5,3,5,6,4,3,6,4,8,9,12,
9,14,17,15,25,23,25,35,29,36,34,36,29,41,42,39,40,43,
37,36,20,20,21,22,23,26,27,28,25,28,24,21,25,21,20,21,
11,18,19,20,21,13,19,18,20,7,18,8,15,17,16,13,10,4,9,
7,8,10,9,11,9,11,10,12,12,5,13,4,6,6,13,8,9,10,13,13,
11,10,5,3,3,4,9,6,8,3,5,3,2,2,1,3,5,11,2,3,5,6,9,8,5,
2,5,3,4,6,4,8,15,12,16,20,18,23,18,19,24,23,24,21,26,
36,38,37,39,45,42,41,37,38,38,35,37,35,31,32,30,20,39,
40,33,32,35,34,36,34,32,33,27,28,25,22,17,18,16,10,9,
5,12,7,8,8,9,19,21,24,20,23,19,17,18,17,22,11,12,3,9,
10,4,5,13,3,5,6,3,5,4,2,5,1,2,4,4,3,2,1)
### Assummptions (probability vector, transition matrix,
### and distribution parameters)
delta <- c(0.25,0.25,0.25,0.25)
gamma <- 0.7 * diag(length(delta)) + rep(0.3 / length(delta))
distribution_class <- "pois"
distribution_theta <- list(lambda = c(4,9,17,25))
### log-likelihood
logL <- forward_backward_algorithm (x = x,
delta = delta, gamma=gamma,
distribution_class= distribution_class,
distribution_theta=distribution_theta)$logL
### the Poisson distribution has one paramter, hence k=1
AIC_HMM(logL = logL, m = length(delta), k = 1)
BIC_HMM(size = length(x) , logL = logL, m = length(delta), k = 1)
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