# How does fHMM process model parameters?

#### 2021-06-16

In fHMM, four types of model parameters are estimated:

1. non-diagonal elements (column-wise) gammas of transition probability matrices Gamma,

2. expected values mus,

3. standard deviations sigmas,

4. degrees of freedom dfs.

All of these parameters have to fulfill constraints. Constrained parameters get the suffix Con, unconstrained parameters the suffix Uncon. Fine-scale parameters additionally get the suffix _star. Internally, collections of model parameters are processed using the following structures:

• thetaFull: A named list of all unconstrained model parameters.

• thetaUncon: A vector of all unconstrained model parameters to be estimated (in the above order).

• thetaCon: Constrained elements of thetaUncon.

• thetaUnconSplit: Splitted thetaUncon by fine-scale models.

• thetaListOrdered: thetaList in ordered form with respect to estimated expected values.

The package fHMM provides functions to transform these structures. Their names follow the logic x2y, where x and y are two structures.