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.

`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.

*β = (β_{1},…,β_{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.

`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).

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