Base Distribution

Distribution

class Distribution(batch_shape=(), event_shape=(), validate_args=None)

Bases: object

Base class for probability distributions in NumPyro. The design largely follows from torch.distributions.

Parameters:

• batch_shape – The batch shape for the distribution. This designates independent (possibly non-identical) dimensions of a sample from the distribution. This is fixed for a distribution instance and is inferred from the shape of the distribution parameters.
• event_shape – The event shape for the distribution. This designates the dependent dimensions of a sample from the distribution. These are collapsed when we evaluate the log probability density of a batch of samples using .log_prob.
• validate_args – Whether to enable validation of distribution parameters and arguments to .log_prob method.

As an example:

>>> import jax.numpy as jnp
>>> import numpyro.distributions as dist
>>> d = dist.Dirichlet(jnp.ones((2, 3, 4)))
>>> d.batch_shape
(2, 3)
>>> d.event_shape
(4,)

arg_constraints = {}

support = None

has_enumerate_support = False

is_discrete = False

reparametrized_params = []

tree_flatten()

classmethod tree_unflatten(aux_data, params)

static set_default_validate_args(value)

batch_shape

Returns the shape over which the distribution parameters are batched.

Returns:batch shape of the distribution. Return type:tuple

event_shape

Returns the shape of a single sample from the distribution without batching.

Returns:event shape of the distribution. Return type:tuple

event_dim

Returns:Number of dimensions of individual events. Return type:int

shape(sample_shape=())

The tensor shape of samples from this distribution.

Samples are of shape:

d.shape(sample_shape) == sample_shape + d.batch_shape + d.event_shape

Parameters:sample_shape (tuple) – the size of the iid batch to be drawn from the distribution. Returns:shape of samples. Return type:tuple

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

sample_with_intermediates(key, sample_shape=())

Same as sample except that any intermediate computations are returned (useful for TransformedDistribution).

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(value)

Evaluates the log probability density for a batch of samples given by value.

Parameters:value – A batch of samples from the distribution. Returns:an array with shape value.shape[:-self.event_shape] Return type:numpy.ndarray

mean

Mean of the distribution.

variance

Variance of the distribution.

to_event(reinterpreted_batch_ndims=None)

Interpret the rightmost reinterpreted_batch_ndims batch dimensions as dependent event dimensions.

Parameters:reinterpreted_batch_ndims – Number of rightmost batch dims to interpret as event dims. Returns:An instance of Independent distribution. Return type:Independent

enumerate_support(expand=True)

Returns an array with shape len(support) x batch_shape containing all values in the support.

expand(batch_shape)

Returns a new ExpandedDistribution instance with batch dimensions expanded to batch_shape.

Parameters:batch_shape (tuple) – batch shape to expand to. Returns:an instance of ExpandedDistribution. Return type:ExpandedDistribution

expand_by(sample_shape)

Expands a distribution by adding sample_shape to the left side of its batch_shape. To expand internal dims of self.batch_shape from 1 to something larger, use expand() instead.

Parameters:sample_shape (tuple) – The size of the iid batch to be drawn from the distribution. Returns:An expanded version of this distribution. Return type:ExpandedDistribution

mask(mask)

Masks a distribution by a boolean or boolean-valued array that is broadcastable to the distributions Distribution.batch_shape .

Parameters:mask (bool or jnp.ndarray) – A boolean or boolean valued array (True includes a site, False excludes a site). Returns:A masked copy of this distribution. Return type:MaskedDistribution

ExpandedDistribution

class ExpandedDistribution(base_dist, batch_shape=())

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {}

expand(batch_shape)

Returns a new ExpandedDistribution instance with batch dimensions expanded to batch_shape.

Parameters:batch_shape (tuple) – batch shape to expand to. Returns:an instance of ExpandedDistribution. Return type:ExpandedDistribution

has_enumerate_support

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

is_discrete

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

support

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(value)

Evaluates the log probability density for a batch of samples given by value.

Parameters:value – A batch of samples from the distribution. Returns:an array with shape value.shape[:-self.event_shape] Return type:numpy.ndarray

enumerate_support(expand=True)

Returns an array with shape len(support) x batch_shape containing all values in the support.

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

classmethod tree_unflatten(aux_data, params)

ImproperUniform

class ImproperUniform(support, batch_shape, event_shape, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

A helper distribution with zero log_prob() over the support domain.

Note

sample method is not implemented for this distribution. In autoguide and mcmc, initial parameters for improper sites are derived from init_to_uniform or init_to_value strategies.

Usage:

>>> from numpyro import sample
>>> from numpyro.distributions import ImproperUniform, Normal, constraints
>>>
>>> def model():
...     # ordered vector with length 10
...     x = sample('x', ImproperUniform(constraints.ordered_vector, (), event_shape=(10,)))
...
...     # real matrix with shape (3, 4)
...     y = sample('y', ImproperUniform(constraints.real, (), event_shape=(3, 4)))
...
...     # a shape-(6, 8) batch of length-5 vectors greater than 3
...     z = sample('z', ImproperUniform(constraints.greater_than(3), (6, 8), event_shape=(5,)))

If you want to set improper prior over all values greater than a, where a is another random variable, you might use

>>> def model():
...     a = sample('a', Normal(0, 1))
...     x = sample('x', ImproperUniform(constraints.greater_than(a), (), event_shape=()))

or if you want to reparameterize it

>>> from numpyro.distributions import TransformedDistribution, transforms
>>> from numpyro.handlers import reparam
>>> from numpyro.infer.reparam import TransformReparam
>>>
>>> def model():
...     a = sample('a', Normal(0, 1))
...     with reparam(config={'x': TransformReparam()}):
...         x = sample('x',
...                    TransformedDistribution(ImproperUniform(constraints.positive, (), ()),
...                                            transforms.AffineTransform(a, 1)))

Parameters:

• support (Constraint) – the support of this distribution.
• batch_shape (tuple) – batch shape of this distribution. It is usually safe to set batch_shape=().
• event_shape (tuple) – event shape of this distribution.

arg_constraints = {}

log_prob(*args, **kwargs)

tree_flatten()

Independent

class Independent(base_dist, reinterpreted_batch_ndims, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

Reinterprets batch dimensions of a distribution as event dims by shifting the batch-event dim boundary further to the left.

From a practical standpoint, this is useful when changing the result of log_prob(). For example, a univariate Normal distribution can be interpreted as a multivariate Normal with diagonal covariance:

>>> import numpyro.distributions as dist
>>> normal = dist.Normal(jnp.zeros(3), jnp.ones(3))
>>> [normal.batch_shape, normal.event_shape]
[(3,), ()]
>>> diag_normal = dist.Independent(normal, 1)
>>> [diag_normal.batch_shape, diag_normal.event_shape]
[(), (3,)]

Parameters:

• base_distribution (numpyro.distribution.Distribution) – a distribution instance.
• reinterpreted_batch_ndims (int) – the number of batch dims to reinterpret as event dims.

arg_constraints = {}

support

has_enumerate_support

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

is_discrete

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

reparameterized_params

mean

Mean of the distribution.

variance

Variance of the distribution.

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(value)

Evaluates the log probability density for a batch of samples given by value.

Parameters:value – A batch of samples from the distribution. Returns:an array with shape value.shape[:-self.event_shape] Return type:numpy.ndarray

expand(batch_shape)

Returns a new ExpandedDistribution instance with batch dimensions expanded to batch_shape.

Parameters:batch_shape (tuple) – batch shape to expand to. Returns:an instance of ExpandedDistribution. Return type:ExpandedDistribution

tree_flatten()

classmethod tree_unflatten(aux_data, params)

MaskedDistribution

class MaskedDistribution(base_dist, mask)

Bases: numpyro.distributions.distribution.Distribution

Masks a distribution by a boolean array that is broadcastable to the distribution’s Distribution.batch_shape. In the special case mask is False, computation of log_prob() , is skipped, and constant zero values are returned instead.

Parameters:mask (jnp.ndarray or bool) – A boolean or boolean-valued array.

arg_constraints = {}

has_enumerate_support

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

is_discrete

bool(x) -> bool

Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed.

support

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(value)

Evaluates the log probability density for a batch of samples given by value.

Parameters:value – A batch of samples from the distribution. Returns:an array with shape value.shape[:-self.event_shape] Return type:numpy.ndarray

enumerate_support(expand=True)

Returns an array with shape len(support) x batch_shape containing all values in the support.

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

classmethod tree_unflatten(aux_data, params)

TransformedDistribution

class TransformedDistribution(base_distribution, transforms, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

Returns a distribution instance obtained as a result of applying a sequence of transforms to a base distribution. For an example, see LogNormal and HalfNormal.

Parameters:

• base_distribution – the base distribution over which to apply transforms.
• transforms – a single transform or a list of transforms.
• validate_args – Whether to enable validation of distribution parameters and arguments to .log_prob method.

arg_constraints = {}

support

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

sample_with_intermediates(key, sample_shape=())

Same as sample except that any intermediate computations are returned (useful for TransformedDistribution).

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

Unit

class Unit(log_factor, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

Trivial nonnormalized distribution representing the unit type.

The unit type has a single value with no data, i.e. value.size == 0.

This is used for numpyro.factor() statements.

arg_constraints = {'log_factor': <numpyro.distributions.constraints._Real object>}

support = <numpyro.distributions.constraints._Real object>

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(value)

Evaluates the log probability density for a batch of samples given by value.

Parameters:value – A batch of samples from the distribution. Returns:an array with shape value.shape[:-self.event_shape] Return type:numpy.ndarray

Continuous Distributions

Beta

class Beta(concentration1, concentration0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'concentration0': <numpyro.distributions.constraints._GreaterThan object>, 'concentration1': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._Interval object>

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

Cauchy

class Cauchy(loc=0.0, scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._Real object>

reparametrized_params = ['loc', 'scale']

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

Chi2

class Chi2(df, validate_args=None)

Bases: numpyro.distributions.continuous.Gamma

arg_constraints = {'df': <numpyro.distributions.constraints._GreaterThan object>}

Dirichlet

class Dirichlet(concentration, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'concentration': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._Simplex object>

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

Exponential

class Exponential(rate=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

reparametrized_params = ['rate']

arg_constraints = {'rate': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._GreaterThan object>

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

Gamma

class Gamma(concentration, rate=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'concentration': <numpyro.distributions.constraints._GreaterThan object>, 'rate': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._GreaterThan object>

reparametrized_params = ['rate']

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

Gumbel

class Gumbel(loc=0.0, scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._Real object>

reparametrized_params = ['loc', 'scale']

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

GaussianRandomWalk

class GaussianRandomWalk(scale=1.0, num_steps=1, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'num_steps': <numpyro.distributions.constraints._IntegerGreaterThan object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._RealVector object>

reparametrized_params = ['scale']

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

classmethod tree_unflatten(aux_data, params)

HalfCauchy

class HalfCauchy(scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

reparametrized_params = ['scale']

support = <numpyro.distributions.constraints._GreaterThan object>

arg_constraints = {'scale': <numpyro.distributions.constraints._GreaterThan object>}

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

HalfNormal

class HalfNormal(scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

reparametrized_params = ['scale']

support = <numpyro.distributions.constraints._GreaterThan object>

arg_constraints = {'scale': <numpyro.distributions.constraints._GreaterThan object>}

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

InverseGamma

class InverseGamma(concentration, rate=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.TransformedDistribution

arg_constraints = {'concentration': <numpyro.distributions.constraints._GreaterThan object>, 'rate': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._GreaterThan object>

reparametrized_params = ['rate']

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

Laplace

class Laplace(loc=0.0, scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._Real object>

reparametrized_params = ['loc', 'scale']

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

LKJ

class LKJ(dimension, concentration=1.0, sample_method='onion', validate_args=None)

Bases: numpyro.distributions.distribution.TransformedDistribution

LKJ distribution for correlation matrices. The distribution is controlled by concentration parameter \(\eta\) to make the probability of the correlation matrix \(M\) propotional to \(\det(M)^{\eta - 1}\). Because of that, when concentration == 1, we have a uniform distribution over correlation matrices.

When concentration > 1, the distribution favors samples with large large determinent. This is useful when we know a priori that the underlying variables are not correlated.

When concentration < 1, the distribution favors samples with small determinent. This is useful when we know a priori that some underlying variables are correlated.

Parameters:

• dimension (int) – dimension of the matrices
• concentration (ndarray) – concentration/shape parameter of the distribution (often referred to as eta)
• sample_method (str) – Either “cvine” or “onion”. Both methods are proposed in [1] and offer the same distribution over correlation matrices. But they are different in how to generate samples. Defaults to “onion”.

References

[1] Generating random correlation matrices based on vines and extended onion method, Daniel Lewandowski, Dorota Kurowicka, Harry Joe

arg_constraints = {'concentration': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._CorrMatrix object>

mean

Mean of the distribution.

tree_flatten()

classmethod tree_unflatten(aux_data, params)

LKJCholesky

class LKJCholesky(dimension, concentration=1.0, sample_method='onion', validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

LKJ distribution for lower Cholesky factors of correlation matrices. The distribution is controlled by concentration parameter \(\eta\) to make the probability of the correlation matrix \(M\) generated from a Cholesky factor propotional to \(\det(M)^{\eta - 1}\). Because of that, when concentration == 1, we have a uniform distribution over Cholesky factors of correlation matrices.

When concentration > 1, the distribution favors samples with large diagonal entries (hence large determinent). This is useful when we know a priori that the underlying variables are not correlated.

When concentration < 1, the distribution favors samples with small diagonal entries (hence small determinent). This is useful when we know a priori that some underlying variables are correlated.

Parameters:

• dimension (int) – dimension of the matrices
• concentration (ndarray) – concentration/shape parameter of the distribution (often referred to as eta)
• sample_method (str) – Either “cvine” or “onion”. Both methods are proposed in [1] and offer the same distribution over correlation matrices. But they are different in how to generate samples. Defaults to “onion”.

References

[1] Generating random correlation matrices based on vines and extended onion method, Daniel Lewandowski, Dorota Kurowicka, Harry Joe

arg_constraints = {'concentration': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._CorrCholesky object>

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

tree_flatten()

classmethod tree_unflatten(aux_data, params)

LogNormal

class LogNormal(loc=0.0, scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.TransformedDistribution

arg_constraints = {'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

reparametrized_params = ['loc', 'scale']

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

Logistic

class Logistic(loc=0.0, scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._Real object>

reparametrized_params = ['loc', 'real']

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

MultivariateNormal

class MultivariateNormal(loc=0.0, covariance_matrix=None, precision_matrix=None, scale_tril=None, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'covariance_matrix': <numpyro.distributions.constraints._PositiveDefinite object>, 'loc': <numpyro.distributions.constraints._RealVector object>, 'precision_matrix': <numpyro.distributions.constraints._PositiveDefinite object>, 'scale_tril': <numpyro.distributions.constraints._LowerCholesky object>}

support = <numpyro.distributions.constraints._RealVector object>

reparametrized_params = ['loc', 'covariance_matrix', 'precision_matrix', 'scale_tril']

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

covariance_matrix

precision_matrix

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

classmethod tree_unflatten(aux_data, params)

LowRankMultivariateNormal

class LowRankMultivariateNormal(loc, cov_factor, cov_diag, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'cov_diag': <numpyro.distributions.constraints._GreaterThan object>, 'cov_factor': <numpyro.distributions.constraints._Real object>, 'loc': <numpyro.distributions.constraints._RealVector object>}

support = <numpyro.distributions.constraints._RealVector object>

mean

Mean of the distribution.

variance

scale_tril

covariance_matrix

precision_matrix

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

entropy()

Normal

class Normal(loc=0.0, scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._Real object>

reparametrized_params = ['loc', 'scale']

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

icdf(q)

mean

Mean of the distribution.

variance

Variance of the distribution.

Pareto

class Pareto(scale, alpha, validate_args=None)

Bases: numpyro.distributions.distribution.TransformedDistribution

arg_constraints = {'alpha': <numpyro.distributions.constraints._GreaterThan object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

mean

Mean of the distribution.

variance

Variance of the distribution.

support

tree_flatten()

StudentT

class StudentT(df, loc=0.0, scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'df': <numpyro.distributions.constraints._GreaterThan object>, 'loc': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._Real object>

reparametrized_params = ['loc', 'scale']

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

TruncatedCauchy

class TruncatedCauchy(low=0.0, loc=0.0, scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.TransformedDistribution

arg_constraints = {'loc': <numpyro.distributions.constraints._Real object>, 'low': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

reparametrized_params = ['low', 'loc', 'scale']

support

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

classmethod tree_unflatten(aux_data, params)

TruncatedNormal

class TruncatedNormal(low=0.0, loc=0.0, scale=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.TransformedDistribution

arg_constraints = {'loc': <numpyro.distributions.constraints._Real object>, 'low': <numpyro.distributions.constraints._Real object>, 'scale': <numpyro.distributions.constraints._GreaterThan object>}

reparametrized_params = ['low', 'loc', 'scale']

support

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

classmethod tree_unflatten(aux_data, params)

TruncatedPolyaGamma

class TruncatedPolyaGamma(batch_shape=(), validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

truncation_point = 2.5

num_log_prob_terms = 7

num_gamma_variates = 8

arg_constraints = {}

support = <numpyro.distributions.constraints._Interval object>

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

tree_flatten()

classmethod tree_unflatten(aux_data, params)

Uniform

class Uniform(low=0.0, high=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.TransformedDistribution

arg_constraints = {'high': <numpyro.distributions.constraints._Dependent object>, 'low': <numpyro.distributions.constraints._Dependent object>}

reparametrized_params = ['low', 'high']

support

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

classmethod tree_unflatten(aux_data, params)

Discrete Distributions

Bernoulli

Bernoulli(probs=None, logits=None, validate_args=None)

BernoulliLogits

class BernoulliLogits(logits=None, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'logits': <numpyro.distributions.constraints._Real object>}

support = <numpyro.distributions.constraints._Boolean object>

has_enumerate_support = True

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

probs

mean

Mean of the distribution.

variance

Variance of the distribution.

enumerate_support(expand=True)

Returns an array with shape len(support) x batch_shape containing all values in the support.

BernoulliProbs

class BernoulliProbs(probs, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'probs': <numpyro.distributions.constraints._Interval object>}

support = <numpyro.distributions.constraints._Boolean object>

has_enumerate_support = True

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

enumerate_support(expand=True)

Returns an array with shape len(support) x batch_shape containing all values in the support.

BetaBinomial

class BetaBinomial(concentration1, concentration0, total_count=1, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

Compound distribution comprising of a beta-binomial pair. The probability of success (probs for the Binomial distribution) is unknown and randomly drawn from a Beta distribution prior to a certain number of Bernoulli trials given by total_count.

Parameters:

• concentration1 (numpy.ndarray) – 1st concentration parameter (alpha) for the Beta distribution.
• concentration0 (numpy.ndarray) – 2nd concentration parameter (beta) for the Beta distribution.
• total_count (numpy.ndarray) – number of Bernoulli trials.

arg_constraints = {'concentration0': <numpyro.distributions.constraints._GreaterThan object>, 'concentration1': <numpyro.distributions.constraints._GreaterThan object>, 'total_count': <numpyro.distributions.constraints._IntegerGreaterThan object>}

has_enumerate_support = True

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

support

enumerate_support(expand=True)

Returns an array with shape len(support) x batch_shape containing all values in the support.

Binomial

Binomial(total_count=1, probs=None, logits=None, validate_args=None)

BinomialLogits

class BinomialLogits(logits, total_count=1, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'logits': <numpyro.distributions.constraints._Real object>, 'total_count': <numpyro.distributions.constraints._IntegerGreaterThan object>}

has_enumerate_support = True

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

probs

mean

Mean of the distribution.

variance

Variance of the distribution.

support

enumerate_support(expand=True)

Returns an array with shape len(support) x batch_shape containing all values in the support.

BinomialProbs

class BinomialProbs(probs, total_count=1, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'probs': <numpyro.distributions.constraints._Interval object>, 'total_count': <numpyro.distributions.constraints._IntegerGreaterThan object>}

has_enumerate_support = True

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

support

enumerate_support(expand=True)

Returns an array with shape len(support) x batch_shape containing all values in the support.

Categorical

Categorical(probs=None, logits=None, validate_args=None)

CategoricalLogits

class CategoricalLogits(logits, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'logits': <numpyro.distributions.constraints._RealVector object>}

has_enumerate_support = True

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

probs

mean

Mean of the distribution.

variance

Variance of the distribution.

support

enumerate_support(expand=True)

Returns an array with shape len(support) x batch_shape containing all values in the support.

CategoricalProbs

class CategoricalProbs(probs, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'probs': <numpyro.distributions.constraints._Simplex object>}

has_enumerate_support = True

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

support

enumerate_support(expand=True)

Returns an array with shape len(support) x batch_shape containing all values in the support.

Delta

class Delta(value=0.0, log_density=0.0, event_dim=0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'log_density': <numpyro.distributions.constraints._Real object>, 'value': <numpyro.distributions.constraints._Real object>}

support = <numpyro.distributions.constraints._Real object>

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

tree_flatten()

classmethod tree_unflatten(aux_data, params)

GammaPoisson

class GammaPoisson(concentration, rate=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

Compound distribution comprising of a gamma-poisson pair, also referred to as a gamma-poisson mixture. The rate parameter for the Poisson distribution is unknown and randomly drawn from a Gamma distribution.

Parameters:

• concentration (numpy.ndarray) – shape parameter (alpha) of the Gamma distribution.
• rate (numpy.ndarray) – rate parameter (beta) for the Gamma distribution.

arg_constraints = {'concentration': <numpyro.distributions.constraints._GreaterThan object>, 'rate': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._IntegerGreaterThan object>

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

Multinomial

Multinomial(total_count=1, probs=None, logits=None, validate_args=None)

MultinomialLogits

class MultinomialLogits(logits, total_count=1, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'logits': <numpyro.distributions.constraints._RealVector object>, 'total_count': <numpyro.distributions.constraints._IntegerGreaterThan object>}

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

probs

mean

Mean of the distribution.

variance

Variance of the distribution.

support

MultinomialProbs

class MultinomialProbs(probs, total_count=1, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'probs': <numpyro.distributions.constraints._Simplex object>, 'total_count': <numpyro.distributions.constraints._IntegerGreaterThan object>}

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

support

OrderedLogistic

class OrderedLogistic(predictor, cutpoints, validate_args=None)

Bases: numpyro.distributions.discrete.CategoricalProbs

A categorical distribution with ordered outcomes.

References:

1. Stan Functions Reference, v2.20 section 12.6, Stan Development Team

Parameters:

• predictor (numpy.ndarray) – prediction in real domain; typically this is output of a linear model.
• cutpoints (numpy.ndarray) – positions in real domain to separate categories.

arg_constraints = {'cutpoints': <numpyro.distributions.constraints._OrderedVector object>, 'predictor': <numpyro.distributions.constraints._Real object>}

Poisson

class Poisson(rate, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'rate': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._IntegerGreaterThan object>

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

Mean of the distribution.

variance

Variance of the distribution.

PRNGIdentity

class PRNGIdentity

Bases: numpyro.distributions.distribution.Distribution

Distribution over PRNGKey(). This can be used to draw a batch of PRNGKey() using the seed handler. Only sample method is supported.

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

ZeroInflatedPoisson

class ZeroInflatedPoisson(gate, rate=1.0, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

A Zero Inflated Poisson distribution.

Parameters:

• gate (numpy.ndarray) – probability of extra zeros.
• rate (numpy.ndarray) – rate of Poisson distribution.

arg_constraints = {'gate': <numpyro.distributions.constraints._Interval object>, 'rate': <numpyro.distributions.constraints._GreaterThan object>}

support = <numpyro.distributions.constraints._IntegerGreaterThan object>

is_discrete = True

sample(key, sample_shape=())

Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape. Note that when sample_shape is non-empty, leading dimensions (of size sample_shape) of the returned sample will be filled with iid draws from the distribution instance.

Parameters:

• key (jax.random.PRNGKey) – the rng_key key to be used for the distribution.
• sample_shape (tuple) – the sample shape for the distribution.

Returns:

an array of shape sample_shape + batch_shape + event_shape

Return type:

numpy.ndarray

log_prob(*args, **kwargs)

mean

variance

Directional Distributions

VonMises

class VonMises(loc, concentration, validate_args=None)

Bases: numpyro.distributions.distribution.Distribution

arg_constraints = {'concentration': <numpyro.distributions.constraints._GreaterThan object>, 'loc': <numpyro.distributions.constraints._Real object>}

support = <numpyro.distributions.constraints._Interval object>

sample(key, sample_shape=())

Generate sample from von Mises distribution

Parameters:

• sample_shape – shape of samples
• key – random number generator key

Returns:

samples from von Mises

log_prob(*args, **kwargs)

mean

Computes circular mean of distribution. NOTE: same as location when mapped to support [-pi, pi]

variance

Computes circular variance of distribution

Constraints

Constraint

class Constraint

Bases: object

Abstract base class for constraints.

A constraint object represents a region over which a variable is valid, e.g. within which a variable can be optimized.

check(value)

Returns a byte tensor of sample_shape + batch_shape indicating whether each event in value satisfies this constraint.

boolean

boolean = <numpyro.distributions.constraints._Boolean object>

corr_cholesky

corr_cholesky = <numpyro.distributions.constraints._CorrCholesky object>

corr_matrix

corr_matrix = <numpyro.distributions.constraints._CorrMatrix object>

dependent

dependent = <numpyro.distributions.constraints._Dependent object>

greater_than

greater_than(lower_bound)

Abstract base class for constraints.

A constraint object represents a region over which a variable is valid, e.g. within which a variable can be optimized.

integer_interval

integer_interval(lower_bound, upper_bound)

Abstract base class for constraints.

A constraint object represents a region over which a variable is valid, e.g. within which a variable can be optimized.

integer_greater_than

integer_greater_than(lower_bound)

Abstract base class for constraints.

A constraint object represents a region over which a variable is valid, e.g. within which a variable can be optimized.

interval

interval(lower_bound, upper_bound)

Abstract base class for constraints.

A constraint object represents a region over which a variable is valid, e.g. within which a variable can be optimized.

less_than

less_than(upper_bound)

Abstract base class for constraints.

A constraint object represents a region over which a variable is valid, e.g. within which a variable can be optimized.

lower_cholesky

lower_cholesky = <numpyro.distributions.constraints._LowerCholesky object>

multinomial

multinomial(upper_bound)

Abstract base class for constraints.

A constraint object represents a region over which a variable is valid, e.g. within which a variable can be optimized.

nonnegative_integer

nonnegative_integer = <numpyro.distributions.constraints._IntegerGreaterThan object>

ordered_vector

ordered_vector = <numpyro.distributions.constraints._OrderedVector object>

positive

positive = <numpyro.distributions.constraints._GreaterThan object>

positive_definite

positive_definite = <numpyro.distributions.constraints._PositiveDefinite object>

positive_integer

positive_integer = <numpyro.distributions.constraints._IntegerGreaterThan object>

real

real = <numpyro.distributions.constraints._Real object>

real_vector

real_vector = <numpyro.distributions.constraints._RealVector object>

simplex

simplex = <numpyro.distributions.constraints._Simplex object>

unit_interval

unit_interval = <numpyro.distributions.constraints._Interval object>

Transforms

biject_to

biject_to(constraint)

Transform

class Transform

Bases: object

domain = <numpyro.distributions.constraints._Real object>

codomain = <numpyro.distributions.constraints._Real object>

event_dim = 0

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

call_with_intermediates(x)

AbsTransform

class AbsTransform

Bases: numpyro.distributions.transforms.Transform

domain = <numpyro.distributions.constraints._Real object>

codomain = <numpyro.distributions.constraints._GreaterThan object>

inv(y)

AffineTransform

class AffineTransform(loc, scale, domain=<numpyro.distributions.constraints._Real object>)

Bases: numpyro.distributions.transforms.Transform

Note

When scale is a JAX tracer, we always assume that scale > 0 when calculating codomain.

codomain

event_dim

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.__int__(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by ‘+’ or ‘-‘ and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal. >>> int(‘0b100’, base=0) 4

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

ComposeTransform

class ComposeTransform(parts)

Bases: numpyro.distributions.transforms.Transform

domain

codomain

event_dim

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.__int__(). For floating point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by ‘+’ or ‘-‘ and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer literal. >>> int(‘0b100’, base=0) 4

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

call_with_intermediates(x)

CorrCholeskyTransform

class CorrCholeskyTransform

Bases: numpyro.distributions.transforms.Transform

Transforms a uncontrained real vector \(x\) with length \(D*(D-1)/2\) into the Cholesky factor of a D-dimension correlation matrix. This Cholesky factor is a lower triangular matrix with positive diagonals and unit Euclidean norm for each row. The transform is processed as follows:

1. First we convert \(x\) into a lower triangular matrix with the following order:

\[\begin{split}\begin{bmatrix} 1 & 0 & 0 & 0 \\ x_0 & 1 & 0 & 0 \\ x_1 & x_2 & 1 & 0 \\ x_3 & x_4 & x_5 & 1 \end{bmatrix}\end{split}\]

2. For each row \(X_i\) of the lower triangular part, we apply a signed version of class StickBreakingTransform to transform \(X_i\) into a unit Euclidean length vector using the following steps:

1. Scales into the interval \((-1, 1)\) domain: \(r_i = \tanh(X_i)\).
2. Transforms into an unsigned domain: \(z_i = r_i^2\).
3. Applies \(s_i = StickBreakingTransform(z_i)\).
4. Transforms back into signed domain: \(y_i = (sign(r_i), 1) * \sqrt{s_i}\).

domain = <numpyro.distributions.constraints._RealVector object>

codomain = <numpyro.distributions.constraints._CorrCholesky object>

event_dim = 2

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

ExpTransform

class ExpTransform(domain=<numpyro.distributions.constraints._Real object>)

Bases: numpyro.distributions.transforms.Transform

codomain

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

IdentityTransform

class IdentityTransform(event_dim=0)

Bases: numpyro.distributions.transforms.Transform

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

InvCholeskyTransform

class InvCholeskyTransform(domain=<numpyro.distributions.constraints._LowerCholesky object>)

Bases: numpyro.distributions.transforms.Transform

Transform via the mapping \(y = x @ x.T\), where x is a lower triangular matrix with positive diagonal.

event_dim = 2

codomain

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

LowerCholeskyAffine

class LowerCholeskyAffine(loc, scale_tril)

Bases: numpyro.distributions.transforms.Transform

Transform via the mapping \(y = loc + scale\_tril\ @\ x\).

Parameters:

• loc – a real vector.
• scale_tril – a lower triangular matrix with positive diagonal.

domain = <numpyro.distributions.constraints._RealVector object>

codomain = <numpyro.distributions.constraints._RealVector object>

event_dim = 1

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

LowerCholeskyTransform

class LowerCholeskyTransform

Bases: numpyro.distributions.transforms.Transform

domain = <numpyro.distributions.constraints._RealVector object>

codomain = <numpyro.distributions.constraints._LowerCholesky object>

event_dim = 2

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

OrderedTransform

class OrderedTransform

Bases: numpyro.distributions.transforms.Transform

Transform a real vector to an ordered vector.

References:

1. Stan Reference Manual v2.20, section 10.6, Stan Development Team

domain = <numpyro.distributions.constraints._RealVector object>

codomain = <numpyro.distributions.constraints._OrderedVector object>

event_dim = 1

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

PermuteTransform

class PermuteTransform(permutation)

Bases: numpyro.distributions.transforms.Transform

domain = <numpyro.distributions.constraints._RealVector object>

codomain = <numpyro.distributions.constraints._RealVector object>

event_dim = 1

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

PowerTransform

class PowerTransform(exponent)

Bases: numpyro.distributions.transforms.Transform

domain = <numpyro.distributions.constraints._GreaterThan object>

codomain = <numpyro.distributions.constraints._GreaterThan object>

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

SigmoidTransform

class SigmoidTransform

Bases: numpyro.distributions.transforms.Transform

codomain = <numpyro.distributions.constraints._Interval object>

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

StickBreakingTransform

class StickBreakingTransform

Bases: numpyro.distributions.transforms.Transform

domain = <numpyro.distributions.constraints._RealVector object>

codomain = <numpyro.distributions.constraints._Simplex object>

event_dim = 1

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

Flows

InverseAutoregressiveTransform

class InverseAutoregressiveTransform(autoregressive_nn, log_scale_min_clip=-5.0, log_scale_max_clip=3.0)

Bases: numpyro.distributions.transforms.Transform

An implementation of Inverse Autoregressive Flow, using Eq (10) from Kingma et al., 2016,

\(\mathbf{y} = \mu_t + \sigma_t\odot\mathbf{x}\)

where \(\mathbf{x}\) are the inputs, \(\mathbf{y}\) are the outputs, \(\mu_t,\sigma_t\) are calculated from an autoregressive network on \(\mathbf{x}\), and \(\sigma_t>0\).

References

1. Improving Variational Inference with Inverse Autoregressive Flow [arXiv:1606.04934], Diederik P. Kingma, Tim Salimans, Rafal Jozefowicz, Xi Chen, Ilya Sutskever, Max Welling

domain = <numpyro.distributions.constraints._RealVector object>

codomain = <numpyro.distributions.constraints._RealVector object>

event_dim = 1

call_with_intermediates(x)

inv(y)

Parameters:y (numpy.ndarray) – the output of the transform to be inverted

log_abs_det_jacobian(x, y, intermediates=None)

Calculates the elementwise determinant of the log jacobian.

Parameters:

• x (numpy.ndarray) – the input to the transform
• y (numpy.ndarray) – the output of the transform

BlockNeuralAutoregressiveTransform

class BlockNeuralAutoregressiveTransform(bn_arn)

Bases: numpyro.distributions.transforms.Transform

An implementation of Block Neural Autoregressive flow.

References

1. Block Neural Autoregressive Flow, Nicola De Cao, Ivan Titov, Wilker Aziz

event_dim = 1

call_with_intermediates(x)

inv(y)

log_abs_det_jacobian(x, y, intermediates=None)

Calculates the elementwise determinant of the log jacobian.

Parameters:

• x (numpy.ndarray) – the input to the transform
• y (numpy.ndarray) – the output of the transform