Title:  Hidden Markov Modelling in greta 

Description:  Extends greta by providing functionality for fitting Hidden Markov Models (HMMs). 
Authors:  Nick Golding [aut, cre] 
Maintainer:  Nick Golding <[email protected]> 
License:  Apache License 2.0 
Version:  0.0.0.9000 
Built:  20240623 05:34:58 UTC 
Source:  https://github.com/gretadev/greta.hmm 
hmm()
create a variable greta array following a Hidden Markov
Model (HMM) 'distribution'. That is a probability distribution whose
density is given by the probability of observing a sequence of observed
states (the variable greta array), given a transition and an emission
matrix as its parameters. This can be viewed as a compound distribution
consisting of a categorical distribution over observed states, conditional
on hidden states which (sequentially) follow another categorical
distribution of states. The log density is calculated by analytically
integrating out the hidden states using the forward algorithm.
This is a discrete, multivariate distribution, and is most likely to be
used with distribution()
to define a complete HMM, as in the
example.
The transition and emission matrices should represent simplices; having
rows summing to 1. These can be create with e.g.
imultilogit()
.
hmm(initial, transition, emission, n_timesteps)
hmm(initial, transition, emission, n_timesteps)
initial 
a length K row vector (ie. 1 x K matrix) of probabilities of initial hidden states 
transition 
a K x K matrix of transition probabilities between hidden states 
emission 
a K x N matrix of emission probabilities between hidden and observed states 
n_timesteps 
the number of timesteps (length of the observed state matrix)  must be a positive scalar integer 
## Not run: # simulate data n_hidden < 2 n_observable < 2 timesteps < 20 initial < random_simplex_matrix(1, n_hidden) transition < random_simplex_matrix(n_hidden, n_hidden) emission < random_simplex_matrix(n_hidden, n_observable) hmm_data < simulate_hmm(initial, transition, emission, timesteps) obs < hmm_data$observed # create simplex variables for the parameters initial < dirichlet(ones(1, n_hidden)) transition < dirichlet(ones(n_hidden, n_hidden)) emission < dirichlet(ones(n_hidden, n_observable)) # define the HMM over the observed states distribution(obs) < hmm(initial, transition, emission, timesteps) # build the model m < model(transition, emission, initial) ## End(Not run)
## Not run: # simulate data n_hidden < 2 n_observable < 2 timesteps < 20 initial < random_simplex_matrix(1, n_hidden) transition < random_simplex_matrix(n_hidden, n_hidden) emission < random_simplex_matrix(n_hidden, n_observable) hmm_data < simulate_hmm(initial, transition, emission, timesteps) obs < hmm_data$observed # create simplex variables for the parameters initial < dirichlet(ones(1, n_hidden)) transition < dirichlet(ones(n_hidden, n_hidden)) emission < dirichlet(ones(n_hidden, n_observable)) # define the HMM over the observed states distribution(obs) < hmm(initial, transition, emission, timesteps) # build the model m < model(transition, emission, initial) ## End(Not run)
Generate corresponding sequences of hidden and observed states from a Hidden Markov Model (HMM) with specified transition and emission matrices. The simulation is carried out directly in R and is provided only to generate datasets for demonstrating or testing HMMs.
simulate_hmm(initial = random_simplex_matrix(1, 3), transition = random_simplex_matrix(3, 3), emission = random_simplex_matrix(3, 5), n_timesteps = 10) random_simplex_matrix(nrow, ncol)
simulate_hmm(initial = random_simplex_matrix(1, 3), transition = random_simplex_matrix(3, 3), emission = random_simplex_matrix(3, 5), n_timesteps = 10) random_simplex_matrix(nrow, ncol)
initial 
a length K row vector (ie. 1 x K matrix) of probabilities of initial hidden states 
transition 
a K x K matrix of transition probabilities between hidden states 
emission 
a K x N matrix of emission probabilities between hidden and observed states 
n_timesteps 
the number of timesteps (length of the observed state matrix)  must be a positive scalar integer 
nrow , ncol

the number of rows and columns in the matrix 
# numbers of hidden and observable states n_hidden < 3 n_observable < 5 # generate a square matrix of transition probabilities in the hidden states transition < simulate_simplex_matrix(n_hidden, n_hidden) # and a rectangular matrix of probabilities of each observable state, # given each hidden state emission < simulate_simplex_matrix(n_hidden, n_observable) # simulate an HMM for 10 timesteps hmm_data < simulate_hmm(transition, emission, 10) # pull out the observed states hmm_data$observed
# numbers of hidden and observable states n_hidden < 3 n_observable < 5 # generate a square matrix of transition probabilities in the hidden states transition < simulate_simplex_matrix(n_hidden, n_hidden) # and a rectangular matrix of probabilities of each observable state, # given each hidden state emission < simulate_simplex_matrix(n_hidden, n_observable) # simulate an HMM for 10 timesteps hmm_data < simulate_hmm(transition, emission, 10) # pull out the observed states hmm_data$observed