Description Fields Methods See Also

StatMRHLP contains all the statistics associated to a MRHLP 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..

`pi_ik`

Matrix of size

*(m, K)*representing the prior/logistic probabilities*π_{k}(x_{i}; Ψ) = P(z_{i} = k | x; Ψ)*of the latent variable*z_{i}, i = 1,…,m*.`z_ik`

Hard segmentation logical matrix of dimension

*(m, K)*obtained by the Maximum a posteriori (MAP) rule:*z_ik = 1 if z_ik = arg max_s π_{s}(x_{i}; Ψ); 0 otherwise*,*k = 1,…,K*.`klas`

Column matrix of the labels issued from

`z_ik`

. Its elements are*klas(i) = k*,*k = 1,…,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`

Array of size

*(m, d, K)*giving the values of the estimated polynomial regression components.`weighted_polynomials`

Array of size

*(m, d, K)*giving the values of the estimated polynomial regression components weighted by the prior probabilities`pi_ik`

.`Ex`

Matrix of size

*(m, d)*.`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 MRHLP model.

`com_loglik`

Numeric. Complete-data log-likelihood of the MRHLP 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, Ψ)*,*i = 1,…,m*.`log_sum_piik_fik`

Column matrix of size

*m*giving the values of*log ∑_{k = 1}^{K} P(y_{i}, z_{i} = k | x, Ψ)*,*i = 1,…,m*.

`computeLikelihood(reg_irls)`

Method to compute the log-likelihood.

`reg_irls`

is the value of the regularization part in the IRLS algorithm.`computeStats(paramMRHLP)`

Method used in the EM algorithm to compute statistics based on parameters provided by the object

`paramMRHLP`

of class ParamMRHLP.`EStep(paramMRHLP)`

Method used in the EM algorithm to update statistics based on parameters provided by the object

`paramMRHLP`

of class ParamMRHLP (prior and posterior probabilities).`MAP()`

MAP calculates values of the fields

`z_ik`

and`klas`

by applying the Maximum A Posteriori Bayes allocation rule.*z_{ik} = 1 if z_ik = arg max_{s} π_{k}(x_{i}; Ψ); 0 otherwise*

ParamMRHLP

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