API for bayes - Incanter 2.0 (in development)

Overview

This is library provides functions for performing
basic Bayesian modeling and inference.

Usage: (sample-model-params size {:keys [x y coefs residuals]})

Returns a sample of the given size of the parameters (coefficients and
error variance) of the given linear-model. The sample is generated using
Gibbs sampling.

See also:
  incanter.stats/linear-model

Examples:
  (use '(incanter core datasets stats charts bayes))

  (def ols-data (to-matrix (get-dataset :survey)))
  (def x (sel ols-data (range 0 2313) (range 1 10)))
  (def y (sel ols-data (range 0 2313) 10))
  (def lm (linear-model y x :intercept false))
  (def param-samp (sample-model-params 5000 lm))

  ;; view trace plots
  (view (trace-plot (:var param-samp )))
  (view (trace-plot (sel (:coefs param-samp) :cols 0)))

  ;; view histograms
  (view (histogram (:var param-samp)))
  (view (histogram (sel (:coefs param-samp) :cols 0)))

  ;; calculate statistics
  (map mean (trans (:coefs param-samp)))
  (map median (trans (:coefs param-samp)))
  (map sd (trans (:coefs param-samp)))

  ;; show the 95% bayesian confidence interval for the first coefficient
  (quantile (sel (:coefs param-samp) :cols 0) :probs [0.025 0.975])

Usage: (sample-multinomial-params size counts)

Returns a sample of multinomial proportion parameters.
The counts are assumed to have a multinomial distribution.
A uniform prior distribution is assigned to the multinomial vector
theta, then the posterior distribution of theta is
proportional to a dirichlet distribution with parameters
(plus counts 1).


Examples:
  (use '(incanter core stats bayes charts))

  (def  samp-props (sample-multinomial-params 1000 [727 583 137]))

  ;; view means, 95% CI, and histograms of the proportion parameters
  (mean (sel samp-props :cols 0))
  (quantile (sel samp-props :cols 0) :probs [0.0275 0.975])
  (view (histogram (sel samp-props :cols 0)))
  (mean (sel samp-props :cols 1))
  (quantile (sel samp-props :cols 1) :probs [0.0275 0.975])
  (view (histogram (sel samp-props :cols 1)))
  (mean (sel samp-props :cols 2))
  (quantile (sel samp-props :cols 2) :probs [0.0275 0.975])
  (view (histogram (sel samp-props :cols 2)))

  ;; view  a histogram of the difference in proportions between the first
  ;; two candidates
  (view (histogram (minus (sel samp-props :cols 0) (sel samp-props :cols 1))))

Usage: (sample-mvn-params size y & options)

Returns samples of means (sampled from an mvn distribution) and vectorized covariance
matrices (sampled from an inverse-wishart distribution) for the given mvn data.

Arguments:
  size -- the number of samples to return
  y -- the data used to estimate the parameters


Returns map with following fields:
  :means
  :sigmas


Examples:

  (use '(incanter core stats bayes charts))
  (def y (sample-mvn 500 :mean [0 0] :sigma (identity-matrix 2)))
  (def samp (sample-mvn-params 1000 y))

  (map mean (trans (:means samp)))
  (symmetric-matrix (map mean (trans (:sigmas samp))) :lower false)

  (view (histogram (sel (:means samp) :cols 0) :x-label "mean 1"))
  (view (histogram (sel (:means samp) :cols 1) :x-label "mean 2"))
  (view (histogram (sel (:sigmas samp) :cols 1) :x-label "covariance"))
  (view (histogram (sel (:sigmas samp) :cols 0) :x-label "variance 1"))
  (view (histogram (sel (:sigmas samp) :cols 2) :x-label "variance 2"))

  (map #(quantile % :probs [0.025 0.0975]) (trans (:means samp)))
  (map #(quantile % :probs [0.025 0.0975]) (trans (:sigmas samp)))




  (use '(incanter core stats bayes charts))
  (def y (sample-mvn 500 :sigma (symmetric-matrix [10 5 10]) :mean [5 2]))
  (def samp (sample-mvn-params 1000 y))
  (symmetric-matrix (map mean (trans (:sigmas samp))) :lower false)
  (map mean (trans (:means samp)))

Usage: (sample-proportions size counts)

sample-proportions has been renamed sample-multinomial-params