incanter.bayes — incanter/incanter-core 1.9.3

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

sample-model-params clj

(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])

sample-multinomial-params clj

(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))))

sample-mvn-params clj

(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)))

sample-proportions clj

(sample-proportions size counts)

sample-proportions has been renamed sample-multinomial-params