Proposal distribution
A proposal distribution is a probability distribution from which a sampling or inference algorithm generates candidate states or samples.
Machine Learning Algorithms in Depth
A proposal distribution is a conditional or unconditional probability distribution used to generate candidate states for a sampling method.
- How it is used
- Supplies candidate states for Metropolis–Hastings and sample locations for importance-sampling estimates.
- How deep it goes
- Derives the Metropolis–Hastings correction from detailed balance and implements proposal-density evaluation and importance weights.
- Examples
- Uses a Gaussian proposal for a two-dimensional Gaussian mixture and a positive-domain Gaussian proposal for an expectation under a chi-shaped target.
- What you can do after
- Build it from scratch to generate Metropolis–Hastings candidates or weight samples in an importance-sampling estimate.
Read how Machine Learning Algorithms in Depth explains proposal distribution →
Fabulous Adventures in Data Structures and Algorithms
A proposal distribution is a probability distribution that generates a candidate next state conditional on a Markov chain's current state.
- How it is used
- Deploys candidate generation inside Metropolis sampling for distributions whose normalized density is difficult to obtain.
- How deep it goes
- Defines conditional generation, explains acceptance behavior, and demonstrates C# construction, but defers systematic proposal tuning.
- Examples
- Uses current-centered normal proposals for target sampling and posterior estimation of coin fairness after observed flips.
- What you can do after
- Apply it via Metropolis to sample target or posterior distributions from non-normalized weight functions.
Read how Fabulous Adventures in Data Structures and Algorithms explains proposal distribution →
Related concepts
- metropolis-hastings samplingused 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.
- 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.
- importance samplingused by · Importance sampling is a statistical technique that estimates expectations under a target distribution by reweighting samples drawn from another distribution.
- normal distributionconfigured by · A normal distribution is a continuous probability distribution with a symmetric, bell-shaped density determined by its mean and variance.
- guide functionimplemented by · A guide function is a Pyro stochastic function that defines the variational approximating process used for inference.
- simulated annealingused by · Simulated annealing is a stochastic optimization method that gradually reduces the probability of accepting worse solutions to escape local optima.
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