def partially_pooled(at_bats: jnp.ndarray, hits: Optional[jnp.ndarray] = None) -> None:
m = numpyro.sample("m", dist.Uniform(0, 1))
kappa = numpyro.sample("kappa", dist.Pareto(1, 1.5))
num_players = at_bats.shape[0]
with numpyro.plate("num_players", num_players):
phi = numpyro.sample("phi", dist.Beta(m * kappa, (1 - m) * kappa))
numpyro.sample("obs", dist.Binomial(at_bats, probs=phi), obs=hits)
def partially_pooled(at_bats, hits=None):
r"""
Number of hits has a Binomial distribution with independent
probability of success, $\phi_i$. Each $\phi_i$ follows a Beta
distribution with concentration parameters $c_1$ and $c_2$, where
$c_1 = m * kappa$, $c_2 = (1 - m) * kappa$, $m ~ Uniform(0, 1)$,
and $kappa ~ Pareto(1, 1.5)$.
:param (jnp.DeviceArray) at_bats: Number of at bats for each player.
:param (jnp.DeviceArray) hits: Number of hits for the given at bats.
:return: Number of hits predicted by the model.
"""
m = numpyro.sample("m", dist.Uniform(0, 1))
kappa = numpyro.sample("kappa", dist.Pareto(1, 1.5))
num_players = at_bats.shape[0]
with numpyro.plate("num_players", num_players):
phi_prior = dist.Beta(m * kappa, (1 - m) * kappa)
phi = numpyro.sample("phi", phi_prior)
return numpyro.sample("obs", dist.Binomial(at_bats, probs=phi), obs=hits)
def partially_pooled(at_bats, hits=None):
r"""
Number of hits has a Binomial distribution with independent
probability of success, $\phi_i$. Each $\phi_i$ follows a Beta
distribution with concentration parameters $c_1$ and $c_2$, where
$c_1 = m * kappa$, $c_2 = (1 - m) * kappa$, $m ~ Uniform(0, 1)$,
and $kappa ~ Pareto(1, 1.5)$.
:param (np.DeviceArray) at_bats: Number of at bats for each player.
:param (np.DeviceArray) hits: Number of hits for the given at bats.
:return: Number of hits predicted by the model.
"""
num_players = at_bats.shape[0]
m = sample("m", dist.Uniform(np.array([0.]), np.array([1.])))
kappa = sample("kappa", dist.Pareto(np.array([1.5])))
shape = np.shape(kappa)[:np.ndim(kappa) - 1] + (num_players,)
phi_prior = dist.Beta(np.broadcast_to(m * kappa, shape),
np.broadcast_to((1 - m) * kappa, shape))
phi = sample("phi", phi_prior)
return sample("obs", dist.Binomial(at_bats, probs=phi), obs=hits)