Basics

Common Options

Arguments

Name	Type	Default	Description
a	`AbstractVector`	-	Initial probabilities vector
A	`AbstractMatrix`	-	Transition matrix
L	`AbstractMatrix`	-	(Log-)likelihoods
rng	`AbstractRNG`	`GLOBAL_RNG`	Random number generator to use
hmm	`AbstractHMM`	-	HMM model
observations	`AbstractVector` or `AbstractMatrix`	-	`T` or `T x dim(obs)`

Keyword Arguments

Name	Type	Default	Description
logl	`Bool`	`false`	Use log-likelihoods instead of likelihoods, if set to true
robust	`Bool`	`false`	Truncate `-Inf` to `eps()` and `+Inf` to `prevfloat(Inf)` (`log(prevfloat(Inf))` in the log. case)

Notations

Symbol	Size	Description	Definition
K	-	Number of states in an HMM	_
T	-	Number of observations	_
a	K	Initial state distribution	$\sum_i a_i = 1$
A	(K, K)	Transition matrix	$\sum_j A_{i,j} = 1, \forall i$
B	K	Vector of observation distributions	_
z	T	Hidden states vector	$z_1 \sim a$, $z_t \sim A_{z_{t-1}\bullet}$
y	(T, .)	Observations vector	$y_t \sim B_{z_t}$
L	(T, K)	Observations (log-)likelihoods	$L(t,i) = p_{B_i}(y_t)$
α	(T, K)	Forward (filter) probabilities	$\alpha(i) = \mathbb{P}(y_{1:t}, z_t = i)$
β	(T, K)	Backward (smoothed) probabilities	$\beta(i) = \mathbb{P}(y_{t+1:T} \,\|\, z_t = i)$
γ	(T, K)	Posterior probabilities (α * β)	$\gamma(i) = \mathbb{P}(z_t = i \,\|\, y_{1:T})$

Before version 1.0:

Symbol	Shape	Description
π0	K	Initial state distribution
π	KxK	Transition matrix
D	K	Vector of observation distributions