tpm_thinned

If the transition probability matrix of an inhomogeneous Markov chain varies only periodically (with period length $L$), it converges to a so-called periodically stationary distribution. 
This happens, because the thinned Markov chain, which has a full cycle as each time step, has homogeneous transition probability matrix
$$\Gamma_t = \Gamma^{(t)} \Gamma^{(t+1)} \dots \Gamma^{(t+L-1)}$$ for all $t = 1, \dots, L.$
This function calculates the matrix above efficiently as a preliminery step to calculating the periodically stationary distribution.

A variety of latent Markov models, including hidden Markov models, hidden semi-Markov models,
state-space models and continuous-time variants can be formulated and estimated within the same framework via directly maximising the likelihood function using the so-called forward algorithm.
Applied researchers often need custom models that standard software does not easily support.
Writing tailored 'R' code offers flexibility but suffers from slow estimation speeds.
We address these issues by providing easy-to-use functions (written in 'C++' for speed) for common tasks like the forward algorithm.
These functions can be combined into custom models in a Lego-type approach, offering up to 10-20 times faster estimation via standard numerical optimisers.
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_thinned function

<dl><dt>Gamma</dt>
<dd>array of transition probability matrices of dimension c(N,N,L).</dd>
<dt>t</dt>
<dd>integer index of the time point in the cycle, for which to calculate the thinned transition probility matrix</dd></dl>

Arguments

Compute the transition probability matrix of a thinned periodically inhomogeneous Markov chain. — tpm_thinned

<dl>

<dt>Gamma</dt>
<dd>array of transition probability matrices of dimension c(N,N,L).</dd>


<dt>t</dt>
<dd>integer index of the time point in the cycle, for which to calculate the thinned transition probility matrix</dd>

</dl>

tpm_thinned: Compute the transition probability matrix of a thinned periodically inhomogeneous Markov chain.

Description

Usage

Value

Arguments

Examples