# Beta CDF in NumPyro

I am developing a model that requires calculating a posterior Beta CDF. I spent some time looking for guidance on implementing CDFs in NumPyro, but wasn’t able to find much. I did see that the suggested approach for Pyro is to import from Torch distributions. Is there a similar approach for NumPyro?

EDIT: I was just looking at Torch distributions and noticed that no cdf method is implemented for Beta.

I’ve included a model below with the line:

``````cdf_50 = numpyro.deterministic("cdf_50", dist.Beta(a,b).cdf(.5))
``````

Obviously, this doesn’t work, but I thought it might be useful to provide an example of the estimate I’m trying to obtain.

Thanks!

``````# Generate Data

# specify number of observations for each group
n1 = 2000
n2 = 1000

# Sample observations from different beta distributions for each group, given specified sample size
np.random.seed(seed=123)
y1 = beta.rvs(.5, .5, size=n1)
np.random.seed(seed=321)
y2 = beta.rvs(3, 1, size=n2)

# Combine samples
y = np.array([y1, y2], order='K').T

sample_sizes =  np.array([n1, n2])

def model(sample_sizes, y = None):

# Define the number of groups from which we've attained samples
n_groups =  sample_sizes.shape[0]

# Initialize a plate for each group
with numpyro.plate("n_groups", n_groups):

# Set priors on a and b within each group
a = numpyro.sample('a', dist.Gamma(.5, .5))
b =  numpyro.sample('b', dist.Gamma(3, 3))

# Calculate maximum group size
I = sample_sizes.max().item()
# Create a range of 0:I
i = torch.arange(I).unsqueeze(-1).numpy()

# Initialize a plate for each observation
with numpyro.plate('data', I):
# Mask observations that exceed sample size in the respective plate
# Estimate y_hat
y_hat = numpyro.sample('y_hat', dist.Beta(a, b), obs=y)

# Example code, doesn't work
cdf_50 = numpyro.deterministic("cdf_50", dist.Beta(a,b).cdf(.5))

rng_key = random.PRNGKey(0)
rng_key, rng_key_ = random.split(rng_key)

num_warmup, num_samples = 500, 2000

# Run NUTS.
kernel = NUTS(model)
mcmc = MCMC(kernel, num_warmup, num_samples, num_chains = 3)

start = time.time()
mcmc.run(rng_key_, sample_sizes=sample_sizes, y = y)
end = time.time()
mcmc.print_summary()
``````

Could you make a github issue or contribute? This method can be computed using betainc function.

Yep, I’d be happy to open an issue and make a contribution; I just wanted to make sure I wasn’t missing an implementation. Thanks!

1 Like

For reference,

``````dist.Beta(a,b).cdf(.5)
``````

can be computed as

``````jax.scipy.special.betainc(.5, a, b)
``````