tpm_phsmm

Hidden semi-Markov models (HSMMs) are a flexible extension of HMMs. For direct numerical maximum likelhood estimation, HSMMs can be represented as HMMs on an enlarged state space (of size \(M\)) and with structured transition probabilities.
This function computes the transition matrices of a periodically inhomogeneos HSMMs.

The class of latent Markov models, including hidden Markov models,
hidden semi-Markov models, state space models, and point processes, is a very popular and powerful framework for inference of time series driven by latent processes.
Furthermore, all these models can be fitted using direct numerical maximum likelihood estimation using the so-called forward algorithm as discussed in
Zucchini et al. (2016) <doi:10.1201/b20790>.
However, due to their great flexibility, researchers using these models in applied work often need to build highly customized models for which standard software implementation is lacking,
or the construction of such models in said software is as complicated as writing fully tailored 'R' code.
While providing greater flexibility and control, the latter suffers from slow estimation speeds that make custom solutions inconvenient.
We address the above issues in two ways. First, standard blocks of code, common to all these model classes, are implemented as simple-to-use functions that can be added like Lego blocks to an otherwise fully custom likelihood function, making writing custom code much easier.
Second, under the hood, these functions are written in 'C++', allowing for 10-20 times faster evaluation time, and thus drastically speeding up model estimation.
To aid in building fully custom likelihood functions, several vignettes are included that show how to simulate data from and estimate all the above model classes.

Jan-Ole Koslik

LaMa

Fast Numerical Maximum Likelihood Estimation for Latent Markov
Models

tpm_phsmm function

<dl><dt>omega</dt>
<dd>Embedded transition probability matrix.
Either a matrix of dimension c(N,N) for homogeneous conditional transition probabilities, or an array of dimension c(N,N,L) for inhomogeneous conditional transition probabilities.</dd>
<dt>dm</dt>
<dd>State dwell-time distributions arranged in a list of length(N).
Each list element needs to be a matrix of dimension c(L, N_i), where each row t is the (approximate) probability mass function of state i at time t.</dd>
<dt>eps</dt>
<dd>Rounding value: If an entry of the transition probabily matrix is smaller, than it is rounded to zero.</dd></dl>

Arguments

Build all transition probability matrices of an periodic-HSMM-approximating HMM — tpm_phsmm

<dl>

<dt>omega</dt>
<dd>Embedded transition probability matrix.
Either a matrix of dimension c(N,N) for homogeneous conditional transition probabilities, or an array of dimension c(N,N,L) for inhomogeneous conditional transition probabilities.</dd>


<dt>dm</dt>
<dd>State dwell-time distributions arranged in a list of length(N).
Each list element needs to be a matrix of dimension c(L, N_i), where each row t is the (approximate) probability mass function of state i at time t.</dd>


<dt>eps</dt>
<dd>Rounding value: If an entry of the transition probabily matrix is smaller, than it is rounded to zero.</dd>

</dl>

tpm_phsmm: Build all transition probability matrices of an periodic-HSMM-approximating HMM

Description

Usage

Value

Arguments

Examples