---
title: "belief"
type: concept
related: [Filters, Gaussian Distribution, Probability Distributions, Belief]
source: https://www.jemoka.com/posts/kbhbelief/
confidence: high
status: active
---

belief is a probability distribution over your states.
&ldquo;an informational state decoupled from motivational states&rdquo;
\begin{equation} b \leftarrow update(b,a,o) \end{equation}
There are two main flavours of how to represent beliefs
parametric: belief distribution is fully represented over all states by a set of parameters (categorical, gaussian, etc.) non-parametric: belief is represented by a non-weighted list of possible locations of where you are; such as a Particle Filter To update parametric beliefs, we can use a discrete state filter (for categorical belief distributions) or a Kalman Filter (for linear Gaussian). To update non-parametric beliefs, we can use a Particle Filter.
If we have an parametric belief that&rsquo;s not categorical nor linear Gaussian, we can use Extended Kalman Filter or Unscented Kalman Filter to approximate a belief update.
belief update To update belief, we need to initialize it somehow. If you have no knowledge of the situation, you want to diffuse your initial distributions because you don&rsquo;t want to be overconfident For non-parametric situations, this may cause logistical problems; so, you may need to make many observations before you can be confident enough to seed a belief observation model \(O(o|a,s&rsquo;)\) is a model for what observations we may get if we are in a particular state/action.
error model there is some model which is a probability distribution over the state given observation:
let orange \(d\) be state, the green would be the error model
filters filters are how beliefs are updated from observation. &ldquo;we want to perform localization&rdquo;
