# Nonparametric Filters Non-parametric filters do not rely on a fixed functional form of the posterior, such as Gaussian. Instead, they approximate posteriors by a finite number of values, each roughly corresponding to a region in state space. There are two non-parametric approaches for approximating posteriors over continuous spaces with finitely many values. ### Histogram & Particle Filters Histogram filters decompose the state space into finitely many regions, and represent the posterior by a histogram. A histogram assigns each region a single cumulative probability; they are best thought of as piece wise constant approximations to a continuous density. Particle filters represent the posteriors by finitely many samples. Both techniques do not make strong parametric assumptions on the posterior density. They are well-suited to represent complex multi-modal beliefs. However, the representational power of these techniques comes at the price of added computational complexity. Fortunately, both techniques make it possible to adapt the number of parameters to the complexity of the posterior. Techniques that can adapt the number of parameters to represent the posterior online are called **adaptive**. They are called **resource-adaptive** if they can adapt based on the computational resources available for belief computation. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://calvinfeng.gitbook.io/probabilistic-robotics/basics/nonparametric-filters.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.