src/probability/probability.lisp

   1 ;;; -*- mode: lisp -*-
   2
   3 ;;; Time-stamp: <2010-11-30 08:55:58 tony>
   4 ;;; Creation:   <2010-11-06 01:51:20 tony>
   5 ;;; File:       probability.lisp
   6 ;;; Author:     AJ Rossini <blindglobe@gmail.com>
   7 ;;; Copyright:  (c)2010--, AJ Rossini.  Currently licensed under MIT
   8 ;;;             license.  See file LICENSE.mit in top-level directory
   9 ;;;             for information.
  10 ;;; Purpose:    Probability functions
  11
  12 ;;; What is this talk of 'release'? Klingons do not make software
  13 ;;; 'releases'.  Our software 'escapes', leaving a bloody trail of
  14 ;;; designers and quality assurance people in its wake.
  15
  16 ;;; This organization and structure is new to the 21st Century
  17 ;;; version..   Think, "21st Century Schizoid Man".
  18
  19
  20 ;;; Current computations are handled by leveraging the cl-variates and
  21 ;;; gsll packages, as they have flexibility and the capability to be
  22 ;;; reproducible.  This is just a stub for the interface/API that we
  23 ;;; would like to be able to use.
  24
  25 ;;; A bit of theory behind this:
  26 ;;; We would like to think about where probability fits into
  27 ;;; statistics.  For example, consider the simple case of the "mean".
  28 ;;; If we treat both empirical distributions and theoretical
  29 ;;; distributions as equivalent first-class objects, it leads to some
  30 ;;; computationally interesting ways of doing things.  This means that
  31 ;;; observed data implies a first-class (discrete) empirical
  32 ;;; distribution in its first right, and also implies that we need to
  33 ;;; include a means of computing both functionals of 1 distribution as
  34 ;;; well as functionals of multiple distributions (think of the
  35 ;;; kullback-leibler distance).
  36 ;;;
  37 ;;; This file should describe the primary generic functions and data
  38 ;;; structures that imply what is feasible in this case.
  39 ;;;
  40 ;;; We will map empirical and theoretical distributions into this
  41 ;;; structure in different files, as well as common (and uncommon)
  42 ;;; functionals.
  43
  44
  45 (in-package :cls-probability)
  46
  47 (defgeneric density (probability-law-instance value))
  48
  49 (defmethod density ((pli probability-law) (value real)))
  50 (defmethod density ((pli probability-law) (value list)))
  51 (defmethod density ((pli probability-law) (value vector-like)))
  52
  53
  54 (defgeneric distribution (probability-law-instance value))
  55
  56 (defgeneric quantile (probability-law-instance value))
  57
  58 (defgeneric interquartile-range (probability-law))
  59
  60 (defgeneric draw-variates (probability-law-instance n))
  61
  62 (defclass probability-parameters ()
  63   ()
  64   :documentation "Virtual class to denote prob parameters")
  65
  66 ;; TODO: need to understand how to manage multiple parameterizations
  67 ;; for the same family of probability laws.
  68
  69 (defclass probability-law ()
  70   ((density-function
  71     :type prob-function
  72     :documention "density function, if exists")
  73    (mass-function
  74     :type prob-function
  75     :documention "function")
  76    (support-function
  77     :documentation "List of values for discrete mass functions, list of pairs denoting for ranges")
  78    (support-class
  79     :type symbol
  80     :documentation "'REAL, 'DISCRETE'")
  81    (parameters
  82     :type list)
  83    (prng-stream
  84     :type unif-stream
  85     :documentation "current underlying prng stream object, typically
  86     Uniform[0,1], but could be Uniform{0,...,n} for some discrete pRNGs."))
  87   (:documentation "Sufficient data to compute probabilistic quantities
  88   and draw from the particularly specified probability law.  Given the
  89   support of the probability law, and a function mapping the law to
  90   the prob result, we can compute, in an expensive manner, most
  91   quantities.  When feasible, we can accelerate this quite a bit.")
  92   ())
  93
  94
  95 #|
  96
  97 ;; We basically want to support the following style of construct:
  98
  99  (let ((my-abstract-law (make 'probability-law
 100                              :density/mass (gaussian-law
 101                                             :parameters '(:mean 5 :variance 3))
 102                              :seed 1324
 103                              :name "Gaussian(5,3)"
 104                              :documentation "model-distribution, used
 105                              for likelihoods, probabilities of
 106                              asympts, and other somethings."))
 107       (my-empirical-law (make 'probability-law
 108                               :density/mass (empirical-law data-vector-or-data-list)
 109                               :seed 415
 110                               :name "Empirical Law from observations"
 111                               :documentation "based on observations,
 112                                bootstrap/resampling style
 113                                probability.")))
 114   (mean my-law)
 115   (variance my-law)
 116   (standard-deviation my-law)
 117   (draw-variates my-law 10)
 118   ;; one of the following would return a number, the other would return a 'nil
 119   (probability-density-function my-law x)
 120   (probability-mass-function my-law x)
 121   (cumulative-distribution-function my-law x)
 122   (survivorship-function my-law x)
 123   (hazard-function my-law x)
 124   (cumulative-hazard-function my-law x)
 125
 126
 127   (mean my-empirical-law) ; empirical mean
 128   (draw-variates my-empirical-law 10) ; bootstrap (unweighted)
 129   ;; the rest would consist of empirical
 130
 131   ())
 132
 133 |#
 134