Difference between BetaBinomial and "Beta and Binomial"

pymc3

Solution

You need a separate `p` for each sample (the `shape` parameter is new):

with pm.Model() as model1:
    alpha1 = pm.Uniform('alpha', 1, 100)
    beta1 = pm.Uniform('beta', 1, 100)
    p1 = pm.Beta('prob', alpha=alpha1, beta=beta1, shape=1000)
    X1 = pm.Binomial('X1', n=n_data, p=p1, observed=x_data)
    trace1 = pm.sample(2000, tune=1000)

I switched to NUTS, too. You can't really fit high dimensional models using the Metropolis sampler.

Problem

I created two models in `pymc3`. One is with `pm.BetaBinomial` and another is with `pm.Beta` and `pm.Binomial`. If we use `pymc3.BetaBinomial`, $\alpha$ and $\beta$ converge. ``` import numpy as np from scipy.stats import binom, beta import pymc3 as pm %matplotlib inline np.random.seed(42) ''' we have values of X and n ''' n_data = np.random.randint(10, 30, size=1000) x_data = binom.rvs(n_data, beta.rvs(10, 20, size=1000)) with pm.Model() as model0: alpha0 = pm.Uniform('alpha', 1, 100) beta0 = pm.Uniform('beta', 1, 100) X0 = pm.BetaBinomial('X', alpha=alpha0, beta=beta0, n=n_data, observed=x_data) trace0 = pm.sample(25000, step=pm.Metropolis(vars=[alpha0, beta0, X0])) ``` But if we combine `pymc3.Beta` and `pymc3.Binomial`, then $\beta$ does not seem to converge and the trace looks very different. (Note that $\alpha=10$ and $\beta=20$.) ``` with pm.Model() as model1: alpha1 = pm.Uniform('alpha', 1, 100) beta1 = pm.Uniform('beta', 1, 100) p1 = pm.Beta('prob', alpha=alpha1, beta=beta1) X1 = pm.Binomial('X1', n=n_data, p=p1, observed=x_data) trace1 = pm.sample(25000, step=pm.Metropolis(vars=[alpha1, beta1, p1, X1])) ``` Why does the above difference happen? The above two models are theoretically equivalent. So I think that my usage of `pymc3` is problematic.

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