Description Fields Methods See Also

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..

`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:*P(Y_{1},…,Y_{t}, z_{t} = k)*.`beta_tk`

Matrix of size

*(m, K)*, giving the backwards probabilities:*P(Y_{t+1},…,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*t = 2,…,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,…,K*.`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 P(z_{i} = s | Y) = tau_tk; 0 otherwise*,*k = 1,…,K*.`state_probs`

Matrix of size

*(m, K)*giving the distribution of the Markov chain.*P(z_{1},…,z_{m};π,A)*with*π*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:*P(z_{t} = k | y_{1},…,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*Pr(z_{t} = k | y_{1},…,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`

.

`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.*z_ik = 1 if z_ik = arg max_s P(z_{i} = s | Y) = tau_tk; 0 otherwise*

ParamMHMMR

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