ParamMHMMR-class function

A Reference Class which contains parameters of a MHMMR model.

ParamMHMMR contains all the parameters of a MHMMR model. The parameters are calculated by the initialization Method and then updated by the Method implementing the M-Step of the EM algorithm. class

Fields

• mData: MData object representing the sample (covariates/inputs X and observed multivariate responses/outputs Y).
• K: The number of regimes (MHMMR components).
• p: The order of the polynomial regression.
• variance_type: Character indicating if the model is homoskedastic (variance_type = "homoskedastic") or heteroskedastic (variance_type = "heteroskedastic"). By default the model is heteroskedastic.
• prior: The prior probabilities of the Markov chain. prior is a row matrix of dimension $(1, K)$.
• trans_mat: The transition matrix of the Markov chain. trans_mat is a matrix of dimension $(K, K)$.
• mask: Mask applied to the transition matrices trans_mat. By default, a mask of order one is applied.
• beta: Parameters of the polynomial regressions. c("$\\beta =\n$", "$(\\beta_{1},\\dots,\\beta_{K})$") is an array of dimension $(p + 1, d, K)$, with p the order of the polynomial regression. p is fixed to 3 by default.
• sigma2: The variances for the K regimes. If MRHLP model is heteroskedastic (variance_type = "heteroskedastic") then sigma2 is an array of size $(d, d, K)$ (otherwise MRHLP model is homoskedastic (variance_type = "homoskedastic") and sigma2 is a matrix of size $(d, d)$).
• nu: The degree of freedom of the MHMMR model representing the complexity of the model.
• phi: A list giving the regression design matrices for the polynomial and the logistic regressions.

Methods

• initParam(try_algo = 1): Method to initialize parameters prior, trans_mat, beta and sigma2.

   If `try_algo = 1` then `beta` and `sigma2` are initialized by segmenting the time series `Y` uniformly into `K` contiguous segments. Otherwise, `beta` and `sigma2` are initialized by segmenting randomly the time series `Y` into `K` segments.
  

• MStep(statMHMMR): Method which implements the M-step of the EM algorithm to learn the parameters of the MHMMR model based on statistics provided by the object statMHMMR of class StatMHMMR (which contains the E-step).