Glossary

This chapter is a very short summary of the book where the central concepts are recalled as an extended glossary.

Bayesian filters are a particular case of Bayesian programs (see Section 17.4) defined as follows:

Pr

 

Ds

 

Sp(π)

 

V a :

S0, · · · , ST , O0, · · · , OT Dc : 

P ( S0 ∧ · · · ∧ ST ∧O0 ∧ · · · ∧OT |π)

= P ( S0 ∧O0)× T∏

[ P ( St|St−1)× P (Ot|St)]

Fo :  P ( S0 ∧O0)

P ( St|St−1)

P ( Ot|St)

Id

Qu : 

P ( St+k|O0 ∧ · · · ∧Ot)

(k = 0) ≡ Filtering (k > 0) ≡ Prediction (k < 0) ≡ Smoothing

(17.1)

See Section 13.1.2 for details and special cases like hidden Markov models (HMMs), Kalman filters, and particle filters.