def model(design_matrix: jnp.ndarray, outcome: jnp.ndarray = None) -> None:
"""
Model definition: Log odds of making a purchase is a linear combination
of covariates. Specify a Normal prior over regression coefficients.
:param design_matrix: Covariates. All categorical variables have been one-hot
encoded.
:param outcome: Binary response variable. In this case, whether or not the
customer made a purchase.
"""
beta = numpyro.sample('coefficients', dist.MultivariateNormal(loc=0.,
covariance_matrix=jnp.eye(design_matrix.shape[1])))
logits = design_matrix.dot(beta)
with numpyro.plate('data', design_matrix.shape[0]):
numpyro.sample('obs', dist.Bernoulli(logits=logits), obs=outcome)
def logpdf(x: jnp.ndarray, kappa: float, mu: jnp.ndarray) -> jnp.ndarray:
"""Log-density function of the power spherical distribution.
Args:
x: The set of points at which to evaluate the power spherical density.
kappa: Concentration parameter.
mu: Mean direction on the sphere. The dimensionality of the sphere is
determined from this paramter.
Returns:
out: The log-density of the power spherical distribution with the
specified concentration and mean parameter at the desired points.
"""
d = mu.size
alpha = (d - 1.) / 2. + kappa
beta = (d - 1.) / 2.
lognormalizer = ((alpha + beta) * jnp.log(2.) + beta * jnp.log(jnp.pi) +
jspsp.gammaln(alpha) - jspsp.gammaln(alpha + beta))
unlogprob = kappa * jnp.log(1. + x.dot(mu))
return unlogprob - lognormalizer
