StatMHMMR-class function

A Reference Class which contains statistics of a MHMMR model.

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.. class

Fields

• tau_tk: Matrix of size $(m, K)$ giving the posterior probability that the observation $Y_{i}$ originates from the $k$-th regression model.

• alpha_tk: Matrix of size $(m, K)$ giving the forwards probabilities: c("$P(Y_{1},\\dots,Y_{t},\n$", "$z_{t} = k)$").

• beta_tk: Matrix of size $(m, K)$, giving the backwards probabilities: $P(Y_{t+1},\dots,Y_{m} | z_{t} = k)$.

• xi_tkl: Array of size $(m - 1, K, K)$ giving the joint post probabilities: $xi_tk[t, k, l] = P(z_{t} = k, z_{t-1} = l | Y)$ for c("$t\n$", "$= 2,\\dots,m$").

• f_tk: Matrix of size $(m, K)$ giving the cumulative distribution function $f(y_{t} | z_{t} = k)$.

• log_f_tk: Matrix of size $(m, K)$ 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 $klas(i) = k$, $k = 1,\dots,K$.

• z_ik: Hard segmentation logical matrix of dimension $(m, K)$

   obtained by the Maximum a posteriori (MAP) rule: c("$z_ik = 1 if z_ik = arg\n$", "$  max_s P(z_{i} = s | Y)  = tau_tk; 0 otherwise$"), $k = 1,\dots,K$.
  

• state_probs: Matrix of size $(m, K)$ giving the distribution of the Markov chain. $P(z_{1},\dots,z_{m};\pi,A)$

   with $\pi$ the prior probabilities (field `prior` of the class ParamMHMMR ) and $A$ the 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 $(m, K)$ giving the values of the estimated polynomial regression components.

• predict_prob: Matrix of size $(m, K)$ giving the prediction probabilities: c("$P(z_{t} = k |\n$", "$y_{1},\\dots,y_{t-1})$").

• predicted: Row matrix of size $(m, 1)$ giving the sum of the polynomial components weighted by the prediction probabilities predict_prob.

• filter_prob: Matrix of size $(m, K)$ giving the filtering probabilities c("$Pr(z_{t} = k |\n$", "$y_{1},\\dots,y_{t})$").

• filtered: Row matrix of size $(m, 1)$ giving the sum of the polynomial components weighted by the filtering probabilities.

• smoothed_regressors: Matrix of size $(m, K)$ giving the polynomial components weighted by the posterior probability tau_tk.

• smoothed: Row matrix of size $(m, 1)$ 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 and klas

   by applying the Maximum A Posteriori Bayes allocation rule.
   
    c("$z_ik = 1 if z_ik = arg max_s P(z_{i} = s | Y)  =\n$", "$      tau_tk; 0 otherwise$")
  

See Also

ParamMHMMR