Unnormalized distribution
An unnormalized distribution is a nonnegative function assigning relative weights to outcomes whose total mass or integral has not been scaled to one.
Fabulous Adventures in Data Structures and Algorithms
A non-normalized probability density function is a nonnegative function proportional to a continuous distribution's density but not necessarily integrating to one.
- How it is used
- Enables sampling from continuous posterior densities when their evidence-dependent normalizing constant is unavailable.
- How deep it goes
- Works through constant cancellation, consistent likelihood scaling, and Metropolis weight ratios; leaves initial and proposal selection for further consideration.
- Examples
- Uses a C# posteriorPDF expression, a continuous uniform weight function, and a Metropolis transition that compares target weights.
- What you can do after
- Build it from scratch as a continuous posterior weight function and apply it via Metropolis without computing the evidence probability.
Read how Fabulous Adventures in Data Structures and Algorithms explains unnormalized distribution →
Machine Learning Algorithms in Depth
An unnormalized distribution assigns probability weights proportional to a distribution density but lacks the factor required for its total mass to equal one.
- How it is used
- Supports importance sampling when target or proposal normalization constants are unknown.
- How deep it goes
- Derives unnormalized weights and partition-function ratios, then analyzes estimator variance and consistency.
- Examples
- Uses a power-exponential target, a scaled truncated Gaussian proposal, and a from-scratch importance-sampling implementation.
- What you can do after
- Apply it via importance sampling to estimate expectations without explicitly evaluating normalization constants.
Read how Machine Learning Algorithms in Depth explains unnormalized distribution →
Related concepts
- inverse distance interpolationused by · Inverse distance interpolation is a spatial interpolation method that estimates an unknown value by weighting nearby known values according to the inverse of their distances.
- distanceuses · Distance is a measure of separation between points or entities in a defined space or context.
- interpolantconfigures · An interpolant is a function or mathematical expression that matches specified data values at selected inputs.
- metropolis-hastings samplingaddressed 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.
- probability densitycontrasts with · A probability density function is a nonnegative function describing the distribution of a continuous random variable, whose integral over a region gives the probability of values in that region.
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