StatMHMMR-class {samurais} | R Documentation |
A Reference Class which contains statistics of a MHMMR model.
Description
StatMHMMR contains all the statistics associated to a MHMMR model. It mainly includes the E-Step of the EM algorithm calculating the posterior distribution of the hidden variables (ie the smoothing probabilities), as well as the calculation of the prediction and filtering probabilities, the log-likelhood at each step of the algorithm and the obtained values of model selection criteria..
Fields
tau_tk
Matrix of size
giving the posterior probability that the observation
originates from the
-th regression model.
alpha_tk
Matrix of size
giving the forwards probabilities:
.
beta_tk
Matrix of size
, giving the backwards probabilities:
.
xi_tkl
Array of size
giving the joint post probabilities:
for
.
f_tk
Matrix of size
giving the cumulative distribution function
.
log_f_tk
Matrix of size
giving the logarithm of the cumulative distribution
f_tk
.loglik
Numeric. Log-likelihood of the MHMMR model.
stored_loglik
Numeric vector. Stored values of the log-likelihood at each iteration of the EM algorithm.
klas
Column matrix of the labels issued from
z_ik
. Its elements are,
.
z_ik
Hard segmentation logical matrix of dimension
obtained by the Maximum a posteriori (MAP) rule:
,
.
state_probs
Matrix of size
giving the distribution of the Markov chain.
with
the prior probabilities (field
prior
of the class ParamMHMMR) andthe transition matrix (field
trans_mat
of the class ParamMHMMR) of the Markov chain.BIC
Numeric. Value of BIC (Bayesian Information Criterion).
AIC
Numeric. Value of AIC (Akaike Information Criterion).
regressors
Matrix of size
giving the values of the estimated polynomial regression components.
predict_prob
Matrix of size
giving the prediction probabilities:
.
predicted
Row matrix of size
giving the sum of the polynomial components weighted by the prediction probabilities
predict_prob
.filter_prob
Matrix of size
giving the filtering probabilities
.
filtered
Row matrix of size
giving the sum of the polynomial components weighted by the filtering probabilities.
smoothed_regressors
Matrix of size
giving the polynomial components weighted by the posterior probability
tau_tk
.smoothed
Row matrix of size
giving the sum of the polynomial components weighted by the posterior probability
tau_tk
.
Methods
computeLikelihood(paramMHMMR)
Method to compute the log-likelihood based on some parameters given by the object
paramMHMMR
of class ParamMHMMR.computeStats(paramMHMMR)
Method used in the EM algorithm to compute statistics based on parameters provided by the object
paramMHMMR
of class ParamMHMMR.EStep(paramMHMMR)
Method used in the EM algorithm to update statistics based on parameters provided by the object
paramMHMMR
of class ParamMHMMR (prior and posterior probabilities).MAP()
MAP calculates values of the fields
z_ik
andklas
by applying the Maximum A Posteriori Bayes allocation rule.