tpm_cont

A continuous-time Markov chain is described by an infinitesimal generator matrix \(Q\). 
When observing data at time points \(t_1, \dots, t_n\) the transition probabilites between \(t_i\) and \(t_{i+1}\) are caluclated as 
\(\Gamma(\Delta t_i) = \exp(Q \Delta t_i)\), 
where \(\exp()\) is the matrix exponential. The mapping \(\Gamma(\Delta t)\) is also called the Markov semigroup.
This function calculates all transition matrices based on a given generator and time differences.

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_cont function

<dl><dt>Q</dt>
<dd>Infinitesimal generator matrix of the continuous-time Markov chain of dimension c(N,N)</dd>
<dt>timediff</dt>
<dd>Time differences between observations of length n-1 when based on n observations</dd></dl>

Arguments

A continuous-time Markov chain is described by an infinitesimal generator matrix \(Q\). 
When observing data at time points \(t_1, \dots, t_n\) the transition probabilites between \(t_i\) and \(t_{i+1}\) are caluclated as 
\(\Gamma(\Delta t_i) = \exp(Q \Delta t_i)\), 
where \(\exp()\) is the matrix exponential. The mapping \(\Gamma(\Delta t)\) is also called the Markov semigroup.
This function calculates all transition matrices based on a given generator and time differences.

Calculation of continuous time transition probabilities — tpm_cont

<dl>

<dt>Q</dt>
<dd>Infinitesimal generator matrix of the continuous-time Markov chain of dimension c(N,N)</dd>


<dt>timediff</dt>
<dd>Time differences between observations of length n-1 when based on n observations</dd>

</dl>

tpm_cont: Calculation of continuous time transition probabilities

Description

Usage

Value

Arguments

Examples