think-bayes

think-bayes

An algorithm collection of probability and statistics for browser and Node.js environment.

In progress...

适用于 浏览器 和 Node.js 环境的概率统计算法集（非正式版本，功能亟待完善，努力 coding 中...）

Install

yarn add think-bayes # OR npm i --save think-bayes

Quickstart

Let us resolve the cookie problem by using the class Suite:

import { Suite } from 'think-bayes';

class Cookie extends Suite {
  mixes = {
    Bowl1: {
      vanilla: 0.75,
      chocolate: 0.25,
    },
    Bowl2: {
      vanilla: 0.5,
      chocolate: 0.5,
    },
  };

  likelihood(data, hypo) {
    const mix = this.mixes[hypo];
    const like = mix[data];
    return like;
  }
}

const hypos = ['Bowl1', 'Bowl2'];
const pmf = new Cookie(hypos);
pmf.update('vanilla');

const result = pmf.render();
console.log(result); // [ [ 'Bowl1', 0.6 ], [ 'Bowl2', 0.4 ] ]

// You can also print the result as a table
pmf.print();
// | Value | Prob |
// |-------|------|
// | Bowl1 | 0.6  |
// | Bowl2 | 0.4  |

In addition, here are some simple demos you can refer directly to resolve some classic problems of probability and statistics.

Algorithm Classes

This library provides some ES Classes following for calculations related to probability and statistics.

These classes can be imported by the same way following:

import { Pmf, Cdf, Pdf, Suite } from 'think-bayes';

DictWrapper

Pmf inherits DictWrapper

Cdf inherits DictWrapper

Pdf

Suite inherits Pmf

Hist inherits DictWrapper

Interpolater

Joint inherits Pmf

GaussianPdf inherits Pdf

GaussianKde

EstimatedPdf inherits Pdf

Utility Functions

This library provides some Utility Functions following for calculations related to probability and statistics.

These functions can be imported by the same way following:

import { Util } from 'think-bayes';
const { odds, probability, percentile } = Util;

odds(p)

Computes odds for a given probability.

Example: p=0.75 means 75 for and 25 against, or 3:1 odds in favor.

Note: when p=1, the formula for odds divides by zero, which is

normally undefined. But I think it is reasonable to define Odds(1)

to be infinity, so that's what this function does.

@Params:

param	type	description
p	number	float 0~1

@Returns: float odds

probability(o)

Computes the probability corresponding to given odds.

Example: o=2 means 2:1 odds in favor, or 2/3 probability

@Params:

param	type	description
o	number	float odds, strictly positive

@Returns: float probability

probability2(yes, no)

Computes the probability corresponding to given odds.

Example: yes=2, no=1 means 2:1 odds in favor, or 2/3 probability.

@Params:

param	type	description
yes	number	int or float odds in favor
no	number	int or float odds in favor

percentile(pmf, percentage)

Computes a percentile of a given Pmf.

@Params:

param	type	description
pmf	pmf
percentage	number	float 0-100

credibleInterval(pmf, percentage = 90)

Computes a credible interval for a given distribution.

If percentage=90, computes the 90% CI.

@Params:

param	type	description
pmf	pmf	Pmf object representing a posterior distribution
percentage	number	float between 0 and 100

@Returns: sequence of two floats, low and high

pmfProbLess(pmf1, pmf2)

Probability that a value from pmf1 is less than a value from pmf2.

@Params:

param	type	description
pmf1	pmf	Pmf object
pmf2	pmf	Pmf object

@Returns: float probability

pmfProbGreater(pmf1, pmf2)

Probability that a value from pmf1 is greater than a value from pmf2.

@Params:

param	type	description
pmf1	pmf	Pmf object
pmf2	pmf	Pmf object

@Returns: float probability

pmfProbEqual(pmf1, pmf2)

Probability that a value from pmf1 equals a value from pmf2.

@Params:

param	type	description
pmf1	pmf	Pmf object
pmf2	pmf	Pmf object

@Returns: float probability

randomSum(dists)

Chooses a random value from each dist and returns the sum.

@Params:

param	type	description
dists	array	sequence of Pmf or Cdf objects

@Returns: numerical sum

sampleSum(dists, n)

Draws a sample of sums from a list of distributions.

@Params:

param	type	description
dists	array	sequence of Pmf or Cdf objects
n	number	sample size

@Returns: new Pmf of sums

evalGaussianPdf(x, mu, sigma)

Computes the unnormalized PDF of the normal distribution.

@Params:

param	type	description
x	number	value
mu	number	mean
sigma	number	standard deviation

@Returns: float probability density

makeGaussianPdf(mu, sigma, numSigmas, n = 201)

Makes a PMF discrete approx to a Gaussian distribution.

@Params:

param	type	description
mu	number	float mean
sigma	number	float standard deviation
numSigmas	number	how many sigmas to extend in each direction
n	number	number of values in the Pmf

@Returns: normalized Pmf

evalBinomialPmf(k, n, p)

Evaluates the binomial pmf.

@Returns: the probabily of k successes in n trials with probability p.

evalPoissonPmf(k, lam)

Computes the Poisson PMF.

@Params:

param	type	description
k	number	number of events
lam	number	parameter lambda in events per unit time

@Returns: float probability

makeJoint(pmf1, pmf2)

Joint distribution of values from pmf1 and pmf2.

@Params:

param	type	description
pmf1	pmf	Pmf object
pmf2	pmf	Pmf object

@Returns: Joint pmf of value pairs

makeHistFromList(t, name)

Makes a histogram from an unsorted sequence of values.

@Params:

param	type	description
t	array	sequence of numbers
name	string	string name for this histogram

@Returns: Hist object

makeHistFromDict(d, name)

Makes a histogram from a map from values to frequencies.

@Params:

param	type	description
d	object	map
name	string	string name for this histogram

@Returns: Hist object

makePmfFromList(t, name)

Makes a PMF from an unsorted sequence of values.

@Params:

param	type	description
t	array	sequence of numbers
name	string	string name for this PMF

@Returns: Pmf object

makePmfFromDict(d, name)

Makes a PMF from a map from values to probabilities.

@Params:

param	type	description
d	object	map
name	string	string name for this PMF * @returns Pmf object

makePmfFromItems(t, name)

Makes a PMF from a sequence of value-probability pairs

@Params:

param	type	description
t	array	sequence of value-probability pairs
name	string	string name for this PMF * @returns Pmf object

makePmfFromHist(hist, name)

Makes a normalized PMF from a Hist object.

@Params:

param	type	description
hist	hist	Hist object
name	string	string name

@Returns: Pmf object

makePmfFromCdf(cdf, name)

Makes a normalized Pmf from a Cdf object.

@Params:

param	type	description
cdf	cdf	Cdf object
name	string	string name for the new Pmf

@Returns: Pmf object

makeMixture(metapmf, name = 'mix')

Make a mixture distribution.

@Params:

param	type	description
metapmf	pmf	Pmf that maps from Pmfs to probs.
name	string	string name for the new Pmf

@Returns: Pmf object

makeUniformPmf(low, high, n)

Make a uniform Pmf.

@Params:

param	type	description
low	number	lowest value (inclusive)
high	number	highest value (inclusize)
n	number	number of values

makeCdfFromItems(items, name = '')

Makes a cdf from an unsorted sequence of (value, frequency) pairs.

@Params:

param	type	description
items	array	unsorted sequence of (value, frequency) pairs
name	string	string name for this CDF

@Returns: cdf: list of (value, fraction) pairs

makeCdfFromDict(d, name)

Makes a CDF from a dictionary that maps values to frequencies.

@Params:

param	type	description
d	object	map
name	string	string name for the data.

@Returns: Cdf object

makeCdfFromHist(hist, name)

Makes a CDF from a Hist object.

@Params:

param	type	description
hist	hist	Hist object
name	string	string name for the data.

@Returns: Cdf object

makeCdfFromList(seq, name)

Creates a CDF from an unsorted sequence.

@Params:

param	type	description
seq	array	unsorted sequence of sortable values
name	string	string name for the cdf

@Returns: Cdf object

makeCdfFromPmf(pmf, name)

Makes a CDF from a Pmf object.

@Params:

param	type	description
pmf	pmf	Pmf object
name	string	string name for the data.

@Returns: Cdf object

makeSuiteFromDict(d, name)

Makes a suite from a map from values to probabilities.

@Params:

param	type	description
d	object	map
name	string	string name for this suite

@Returns: Suite object

makeSuiteFromList(t, name)

Makes a suite from an unsorted sequence of values.

@Params:

param	type	description
t	array	sequence of numbers
name	string	string name for this suite

makeSuiteFromHist(hist, name)

Makes a normalized suite from a Hist object.

@Params:

param	type	description
hist	hist	Hist object
name	string	string name

makeSuiteFromCdf(cdf, name)

Makes a normalized Suite from a Cdf object.

@Params:

param	type	description
cdf	cdf	Cdf object
name	string	string name for the new Suite

@Returns: Suite object

Q&A

How to reduce the precision loss caused by the calculation of float point number in javascript?

This library use decimal.js to handle the problem what calculation of float point number, in the same way, you can use it in this library:

import { Decimal } from 'think-bayes';

Decimal.add(0.1, 0.2).toNumber() === 0.3; // true