StatRHLP-class function

A Reference Class which contains statistics of a RHLP model.

StatRHLP contains all the statistics associated to a RHLP model. It mainly includes the E-Step of the EM algorithm calculating the posterior distribution of the hidden variables, as well as the calculation of the log-likelhood at each step of the algorithm and the obtained values of model selection criteria.. class

Fields

• pi_ik: Matrix of size $(m, K)$ representing the prior/logistic probabilities $\pi_{k}(x_{i}; \Psi) = P(z_{i} = k | x; \Psi)$ of the latent variable $z_{i}, i = 1,\dots,m$.

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

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

• klas: Column matrix of the labels issued from z_ik. Its elements are $klas(i) = k$, $k = 1,\dots,K$.

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

• polynomials: Matrix of size $(m, K)$ giving the values of the estimated polynomial regression components.

• Ex: Column matrix of dimension m. Ex is the curve expectation (estimated signal): sum of the polynomial components weighted by the logistic probabilities pi_ik.

• loglik: Numeric. Observed-data log-likelihood of the RHLP model.

• com_loglik: Numeric. Complete-data log-likelihood of the RHLP model.

• stored_loglik: Numeric vector. Stored values of the log-likelihood at each EM iteration.

• stored_com_loglik: Numeric vector. Stored values of the Complete log-likelihood at each EM iteration.

• BIC: Numeric. Value of BIC (Bayesian Information Criterion).

• ICL: Numeric. Value of ICL (Integrated Completed Likelihood).

• AIC: Numeric. Value of AIC (Akaike Information Criterion).

• log_piik_fik: Matrix of size $(m, K)$ giving the values of the logarithm of the joint probability $P(y_{i}, z_{i} = k | x, \Psi)$, c("$i\n$", "$= 1,\\dots,m$").

• log_sum_piik_fik: Column matrix of size m giving the values of $log \sum_{k = 1}^{K} P(y_{i}, z_{i} = k | x, \Psi)$, $i = 1,\dots,m$.

Methods

• computeLikelihood(reg_irls): Method to compute the log-likelihood. reg_irls is the value of the regularization part in the IRLS algorithm.

• computeStats(paramRHLP): Method used in the EM algorithm to compute statistics based on parameters provided by the object paramRHLP of class ParamRHLP .

• EStep(paramRHLP): Method used in the EM algorithm to update statistics based on parameters provided by the object paramRHLP of class ParamRHLP

   (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("$\n$", "$      z_{ik} = 1 if z_ik = arg max_{s} \\pi_{k}(x_{i}; \\Psi); 0 otherwise$")
  

See Also

ParamRHLP