Target distribution
A target distribution is the probability distribution that a sampling procedure is intended to reproduce.
Machine Learning Algorithms in Depth
A target distribution is the probability distribution from which a sampling method aims to generate samples.
- How it is used
- Defines what Metropolis–Hastings samples should follow and which distribution governs an importance-sampling expectation.
- How deep it goes
- Derives an MH correction through detailed balance and defines importance weights as p(x)/q(x), then implements both algorithms.
- Examples
- Uses a two-dimensional Gaussian mixture for MH and an unnormalized Chi-shaped target for an importance-sampling expectation.
- What you can do after
- Build it from scratch as an MH target density or use it with proposal-density weights to estimate an expectation.
Read how Machine Learning Algorithms in Depth explains target distribution →
Fabulous Adventures in Data Structures and Algorithms
A target distribution is the probability distribution that a sampling procedure is intended to reproduce.
- How it is used
- Guides sampling procedures toward reproducing a chosen probability distribution.
- How deep it goes
- Treats targets operationally through quantile inversion, rejection acceptance, and Metropolis chains.
- Examples
- Uses standard uniform, continuous uniform, normal, and posterior distributions as sampling contexts.
- What you can do after
- Apply it via quantile functions, rejection sampling, or the Metropolis algorithm to generate samples from a desired distribution.
Read how Fabulous Adventures in Data Structures and Algorithms explains target distribution →
Related concepts
- markov chain monte carloused by · Markov chain Monte Carlo is a family of sampling algorithms that generate samples using a Markov chain whose stationary or limiting distribution is a target probability distribution.
- posterior probabilityequivalent to · A posterior probability or distribution expresses the probability assigned to an event, hypothesis, or unknown quantity conditional on observed evidence and prior information.
- variational inferenceused by · Variational inference is an approximate inference technique that optimizes a tractable family of probability distributions to approximate a target distribution, often a posterior.
- metropolis-hastings samplingproduced by · Metropolis-Hastings sampling is a Markov chain Monte Carlo method that proposes state changes and accepts or rejects them probabilistically to generate samples from a target distribution.
- stationary distributionequivalent to · A stationary distribution is a probability distribution that remains unchanged under the transition dynamics of a stochastic process.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.