Representations for Probability distributions:
Table of values
- Discretization effects
Particles
Use sampling with replacement to re-normalize
Use motion model to separate duplicates from sampling with replacement
Closed form
Conjugate priors - http://www.cis.hut.fi/ahonkela/dippa/node23.html
- Basically the initial distribution is of the same class as the transition model (eg both gaussian)
Normal (Gaussian) Distribution:
In multi-dimensions, mean becomes a vector and co-variance (measure of spread) becomes a matrix
Known as a Kalman filter when implemented with Matrix math
Assumes linear-gaussian transition and sensor models (linear function + gaussian noise)
Works well with "any system characterised by continuous state variables and noisy measurements" (R&N p557)
Use tagent as approximation to linear form (linearization) if a distribution is non-gaussian
Also: Beta, Dirichet distributions (the conjugate prior for multinomial distributions)
Also covered decomposition of P(x,y) into P(x).P(y|x)
e.g. P(x, y, theta) split into P(x, y) and P(theta | x, y)
Much smaller tables, cannot represent correlations