conjugate-prior 0.5

Bayesian Statistics conjugate prior distributions

# Conjugate Prior Python implementation of the conjugate prior table for Bayesian Statistics

[](http://pepy.tech/count/conjugate-prior)

See wikipedia page:

https://en.wikipedia.org/wiki/Conjugate_prior#Table_of_conjugate_distributions

## Installation: pip install conjugate-prior

## Supported Models:

1. BetaBinomial - Useful for independent trials such as click-trough-rate (ctr), web visitor conversion. 1. BetaBernoulli - Same as above. 1. GammaExponential - Useful for churn-rate analysis, cost, dwell-time. 1. GammaPoisson - Useful for time passed until event, as above. 1. NormalNormalKnownVar - Useful for modeling a centralized distribution with constant noise. 1. NormalLogNormalKnownVar - Useful for modeling a Length of a support phone call. 1. InvGammaNormalKnownMean - Useful for modeling the effect of a noise. 1. InvGammaWeibullKnownShape - Useful for reasoning about particle sizes over time. 1. DirichletMultinomial - Extension of BetaBinomial to more than 2 types of events (Limited support).

## Basic API

1. model = GammaExponential(a, b) - A Bayesian model with an Exponential likelihood, and a Gamma prior. Where a and b are the prior parameters. 1. model.pdf(x) - Returns the probability-density-function of the prior function at x. 1. model.cdf(x) - Returns the cumulative-density-function of the prior function at x. 1. model.mean() - Returns the prior mean. 1. model.plot(l, u) - Plots the prior distribution between l and u. 1. model.posterior(l, u) - Returns the credible interval on (l,u) (equivalent to cdf(u)-cdf(l)). 1. model.update(data) - Returns a new model after observing data. 1. model.predict(x) - Predicts the likelihood of observing x (if a posterior predictive exists). 1. model.sample() - Draw a single sample from the posterior distribution.

## Coin flip example:

from conjugate_prior import BetaBinomial heads = 95 tails = 105 prior_model = BetaBinomial() # Uninformative prior updated_model = prior_model.update(heads, tails) credible_interval = updated_model.posterior(0.45, 0.55) print (“There’s {p:.2f}% chance that the coin is fair”.format(p=credible_interval*100)) predictive = updated_model.predict(50, 50) print (“The chance of flipping 50 Heads and 50 Tails in 100 trials is {p:.2f}%”.format(p=predictive*100))