pypmc

pypmc is a python package focusing on adaptive importance sampling. It can be used for integration and sampling from a user-defined target density. A typical application is Bayesian inference, where one wants to sample from the posterior to marginalize over parameters and to compute the evidence. The key idea is to create a good proposal density by adapting a mixture of Gaussian or student’s t components to the target density. The package is able to efficiently integrate multimodal functions in up to about 30-40 dimensions at the level of 1% accuracy or less. For many problems, this is achieved without requiring any manual input from the user about details of the function. Importance sampling supports parallelization on multiple machines via mpi4py.

Useful tools that can be used stand-alone include:

• importance sampling (sampling & integration)

• adaptive Markov chain Monte Carlo (sampling)

• variational Bayes (clustering)

• population Monte Carlo (clustering)

How to use this documentation

If you don’t know yet whether pypmc is the right tool for your needs, you should first read through the overview. There, we introduce the basic algorithms implemented by pypmc. If you want to give pypmc a try, just follow the installation instructions. The user guide then explains adaptive importance sampling. In the examples section, we show how to use the algorithms on simple problems. Take them as a starting point to work on your problem. Finally, look through the reference guide if you need help on a specific function or class.

• 1. Overview
  • 1.1. Initial proposal density
  • 1.2. Proposal updates
  • 1.3. PMC
  • 1.4. Variational Bayes
  • 1.5. Performance
• 2. Installation
  • 2.1. Developer notes
    • 2.1.1. Debian or derivative
    • 2.1.2. Conda
• 3. User guide
  • 3.1. Densities
    • 3.1.1. Component density
    • 3.1.2. Mixture density
  • 3.2. Indicator function
  • 3.3. Markov chain
    • 3.3.1. Initialization
    • 3.3.2. Adaptation
  • 3.4. Importance sampling
    • 3.4.1. Standard
    • 3.4.2. Deterministic mixture
    • 3.4.3. Comparison
  • 3.5. PMC
    • 3.5.1. Basic approach
    • 3.5.2. Student’s t
    • 3.5.3. PMC with multiple EM steps
  • 3.6. Variational Bayes
    • 3.6.1. Classic version
  • 3.7. Mixture reduction
    • 3.7.1. Hierarchical clustering
    • 3.7.2. VBmerge
  • 3.8. Putting it all together
• 4. Examples
  • 4.1. MCMC
  • 4.2. PMC
    • 4.2.1. Serial
    • 4.2.2. Parallel
  • 4.3. Grouping by Gelman-Rubin R value
  • 4.4. Variational Bayes
  • 4.5. Mixture reduction
  • 4.6. MCMC + variational Bayes
• 5. References
• 6. Reference Guide
  • 6.1. Probability density
    • LocalDensity
    • ProbabilityDensity
    • 6.1.1. Gauss
    • 6.1.2. StudentT
    • 6.1.3. Mixture
  • 6.2. Sampler
    • 6.2.1. Markov Chain
    • 6.2.2. Importance Sampling
  • 6.3. Mixture adaptation
    • 6.3.1. Hierarchical clustering
    • 6.3.2. Variational Bayes
    • 6.3.3. PMC
    • 6.3.4. Gelman-Rubin R-value
  • 6.4. Tools
    • 6.4.1. Convergence diagnostics
    • 6.4.2. History
    • 6.4.3. Indicator
    • 6.4.4. Parallel sampler
    • 6.4.5. Partition
    • 6.4.6. Plot

Indices and tables

• Index

• Module Index

• Search Page