Conjugate Prior

Python implementation of the conjugate prior table for Bayesian Statistics

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.
2. BetaBernoulli - Same as above.
3. GammaExponential - Useful for churn-rate analysis, cost, dwell-time.
4. GammaPoisson - Useful for time passed until event, as above.
5. NormalNormalKnownVar - Useful for modeling a centralized distribution with constant noise.
6. NormalLogNormalKnownVar - Useful for modeling a Length of a support phone call.
7. InvGammaNormalKnownMean - Useful for modeling the effect of a noise.
8. InvGammaWeibullKnownShape - Useful for reasoning about particle sizes over time.
9. 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.
2. model.pdf(x) - Returns the probability-density-function of the prior function at x.
3. model.cdf(x) - Returns the cumulative-density-function of the prior function at x.
4. model.mean() - Returns the prior mean.
5. model.plot(l, u) - Plots the prior distribution between l and u.
6. model.posterior(l, u) - Returns the credible interval on (l,u) (equivalent to cdf(u)-cdf(l)).
7. model.update(data) - Returns a new model after observing data.
8. model.predict(x) - Predicts the likelihood of observing x (if a posterior predictive exists).

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))