StatHMMR-class {samurais}

A Reference Class which contains statistics of a HMMR model.

Description

StatHMMR contains all the statistics associated to a HMMR 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 (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},\dots,Y_{t}, 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 | \boldsymbol{Y}) for t = 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 HMMR 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: z\_ik = 1 \ \textrm{if} \ z\_ik = \textrm{arg} \ \textrm{max}_{s} \ P(z_{i} = s | \boldsymbol{Y}) = tau\_tk;\ 0 \ \textrm{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,\boldsymbol{A}) with \pi the prior probabilities (field prior of the class ParamHMMR) and \boldsymbol{A} the transition matrix (field trans_mat of the class ParamHMMR) 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},\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 Pr(z_{t} = k | 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(paramHMMR)

Method to compute the log-likelihood based on some parameters given by the object paramHMMR of class ParamHMMR.

computeStats(paramHMMR)

Method used in the EM algorithm to compute statistics based on parameters provided by the object paramHMMR of class ParamHMMR.

EStep(paramHMMR)

Method used in the EM algorithm to update statistics based on parameters provided by the object paramHMMR of class ParamHMMR (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 \ \textrm{if} \ z\_ik = \textrm{arg} \ \textrm{max}_{s} \ P(z_{i} = s | \boldsymbol{Y}) = tau\_tk;\ 0 \ \textrm{otherwise}

See Also

ParamHMMR