One prediction of a HiddenMarkovFilter as a smoother needs it: the distribution the step started from, the prediction, and the matrix that moved one to the other. More...

#include <EmrysFilter/Filters/HiddenMarkovFilter.h>

Public Types
using	MatrixType = typename MarkovChain<Space, Scalar>::MatrixType
	the transitions' type

Public Attributes
CategoricalParams< Space, Scalar >	filtered
	\( p(x_k \mid z_{1:k}) \), the state before the step
CategoricalParams< Space, Scalar >	predicted
	the state after it, before the next update
MatrixType	transitions
	\( K \), with predicted \( = K^T \) filtered

Detailed Description

template<DiscreteSpace Space, RealScalar Scalar>
struct Emrys::CategoricalPredictedJoint< Space, Scalar >

One prediction of a HiddenMarkovFilter as a smoother needs it: the distribution the step started from, the prediction, and the matrix that moved one to the other.

The discrete counterpart of PredictedJoint (decisions.md [smoothing]): with \( K \) the transitions, \( \mathrm{predicted} = K^T \mathrm{filtered} \) exactly, so the joint of the values before and after the step is \( \mathrm{filtered}_i K_{ij} \). For a MarkovChain \( K \) is \( \Pi \); for a ContinuousTimeMarkovChain over \( \Delta t \) it is \( e^{Q \Delta t} \); and for an ArrivalInterval it is the step \( e^{(Q - \Lambda) \Delta t} [\Lambda] \) divided by its total, which is no longer stochastic, since the step observed something. CategoricalHistory records them.

Template Parameters

Space	the discrete space
Scalar	scalar type of the probabilities

The documentation for this struct was generated from the following file:

EmrysFilter/Filters/HiddenMarkovFilter.h

Public Types

Public Attributes

Detailed Description