Yet another Bayesian inference library for Clojure

• Easy to use MCMC based framework
• Common PPL pattern: generative model -> inference...
• ...but pure CLJ, no continuations
• Explicit priors and log-likelihood in the model
• Easy to extend
• Available visualizations

Influenced by LaplacesDemonR and BayesianTools. Also Anglican and WebPPL.

To create a model you have to use defmodel or make-model macros. Here is the structure of the model:

(defmodel NAME
  [PRIORS]
  (MODEL-BODY
    (MODEL-RESULT-FN LOG-LIKELIHOOD-SEQUENCE TRACE-VALUE-OR-MAP)

For example:

(defmodel observer-model
 [p (distr :uniform-real)]
 (let [coin-spinner (distr :binomial {:trials 20 :p p})
       bernoulli (distr :bernoulli {:p p})
       binomial (distr :binomial {:trials 10 :p p})]
   (model-result [(observe1 coin-spinner 15)]
                 {:next-outcome (r/sample bernoulli)
                  :next-ten-outcomes (r/sample binomial)})))

Where:

• NAME is a name of your model, model is regular function
• PRIORS has form of let with symbols and distribution creators. Values of priors (created randomly or using MCMC steps) are passed to the model function as parameters. PRIORS can be empty.
• MODEL-BODY any Clojure code necessary to calculate model
• MODEL-RESULT-FN is one of model-result or trace-result macros. Macro creates internal structure used by inference algorithms.
  • model-result accepts two parameters: list of log likelihood values and parameters you want to trace
  • trace-result can be used when you want to do only trace parameters from the model
• LOG-LIKELIHOOD-SEQUENCE - list of log of likelihoods, log probabilities against your data, conditions etc. It should be just sequence of numbers where ##-Inf means probability=0 and 0 means probability=1. Log of probabilities can be calculated with condition, observe1 or observe helpers.
• TRACE-VALUE-OR-MAP is a any value you want to trace. It can be map or any value. One note: you don't have to trace priors, they will be added for you by inference algorithm.

Currently 3 inference algorithms are implemented:

• :forward-sampling - every result with positive probability is traced, input parameters are randomly sampled from priors (if available). This method is good to generate samples from generative model.
• :rejection-sampling - every result with probability proportional to returned likelihood is traced, input parameters are randomly sampled from priors (if available)
• :metropolis-hastings - MCMC
• :metropolis-within-gibbs - MCMC, gibbs steps
• :elliptical-slice-sampling - "This algorithm is applicable only to models in which the prior mean of all parameters is zero.". See more HERE and HERE

To gather samples just call (infer METHOD MODEL OPTIONAL-PARAMETERS). For example (infer :metropolis-hastings observer-model).

Optional parameters is a map with following keys:

• :samples - maximum number of samples to gather
• :max-iters - maximum number of iterations
• :max-time - maximum time

Inference algorithm stops when on of the limits is passed.

Also for specific algorithm there are additional tuning parameters:

• :log-bound - log of bound value for rejection-sampling

For MCMC:

• :burn - number of dropped samples
• :thin - record every thin sample
• :initial-point - starting point for algorithm
• :steps - explicit MCMC step standard deviations
• :step-scale - scale for inferred steps
• kernel - jump kernel (default Gaussian)

Inference algorithm returns map where under the key :accepted you can find sequence of maps of returned values. To access specific trace you can use helper macro (trace RESULT KEYWORD) like (trace observer-result :next-outcome)

[TODO]

Distributions are backed by fastmath library. [TODO - list of parameters]

• regular, bactrian

[TODO]

[TODO]

Check notebooks folder for rework of ProMods book and some Agnlican examples