bilby.core.prior.conditional.DirichletElement

class bilby.core.prior.conditional.DirichletElement(order, n_dimensions, label)

Bases: ConditionalBeta

Single element in a dirichlet distribution. The probability defined as,

\[\begin{split}p(x_n\mid S_n) := \begin{cases} 1 & N = 1 \\ \displaystyle\frac{(N - n - 1)(1 - S_n - x_n)^{N - n - 2}}{(1-S_n)^{N-n-1}} & n < N - 1 \\ \displaystyle\delta(1-S_{N-1}-x_{N-1}) & n = N - 1 \end{cases}, \qquad 0 \leq x_n \leq 1 - S_n\end{split}\]

where, \(\delta\) is the Dirac delta function, \(N\) is the total number of dimensions and \(S_n\) is the sum of all previous dimensions,

\[S_n := \sum_{i=0}^{n-1}x_i \qquad n < N\]

Parameters:

order: int

Order of this element of the dirichlet distribution. Equivalent to \(n\).

n_dimensions: int

Total number of elements of the dirichlet distribution. Equivalent to \(N\).

label: str

Label for the dirichlet distribution. This should be the same for all elements.

Examples

n_dimensions = \(N = 1\):

\[p(x_0) = 1 ; 0 \leq x_0 \leq 1\]

n_dimensions = \(N = 2\):

\[p(x_0) = 1 ; \qquad 0 \leq x_0 \leq 1\]

\[p(x_1\mid x_0) = \delta(1-x_0-x_1); \qquad 0 \leq x_1 \leq 1 - x_0\]

__init__(order, n_dimensions, label)

__call__()

Overrides the __call__ special method. Calls the sample method.

Returns:

float: The return value of the sample method.

Methods

__init__(order, n_dimensions, label)
cdf(*args[, xp])
dirichlet_condition(reference_parms, **kwargs)
from_json(dct)
from_repr(string)	Generate the prior from its __repr__
get_instantiation_dict()
is_in_prior_range(val)	Returns True if val is in the prior boundaries, zero otherwise
ln_prob(*args[, xp])
prob(*args[, xp])	Return the prior probability of val, this should be overwritten
rescale(*args[, xp])	'Rescale' a sample from the unit line element to the prior.
reset_to_reference_parameters()	Reset the object attributes to match the original reference parameters
sample([size, random_state])	Draw a sample from the prior
to_json()
update_conditions(**required_variables)	This method updates the conditional parameters (depending on the parent class this could be e.g. minimum, maximum, mu, sigma, etc.) of this prior class depending on the required variables it depends on.

Attributes

boundary
condition_func
is_fixed	Returns True if the prior is fixed and should not be used in the sampler.
latex_label	Latex label that can be used for plots.
latex_label_with_unit	If a unit is specified, returns a string of the latex label and unit
maximum
minimum
reference_params	Initial values for attributes such as minimum, maximum.
required_variables	The required variables to pass into the condition function.
unit
width

classmethod from_repr(string)

Generate the prior from its __repr__

property is_fixed

Returns True if the prior is fixed and should not be used in the sampler. Does this by checking if this instance is an instance of DeltaFunction.

Returns:

bool: Whether it’s fixed or not!

is_in_prior_range(val)

Returns True if val is in the prior boundaries, zero otherwise

Parameters:

val: Union[float, int, array_like]

Returns:

np.nan

property latex_label

Latex label that can be used for plots.

Draws from a set of default labels if no label is given

Returns:

str: A latex representation for this prior

property latex_label_with_unit

If a unit is specified, returns a string of the latex label and unit

prob(*args, xp=None, **kwargs)

Return the prior probability of val, this should be overwritten

Parameters:

val: Union[float, int, array_like]

Returns:

np.nan

property reference_params

Initial values for attributes such as minimum, maximum. This depends on the prior_class, for example for the Gaussian prior this is mu and sigma. This is read-only.

property required_variables

The required variables to pass into the condition function.

rescale(*args, xp=None, **kwargs)

‘Rescale’ a sample from the unit line element to the prior.

This should be overwritten by each subclass.

Parameters:

val: Union[float, int, array_like]

A random number between 0 and 1

Returns:

None

reset_to_reference_parameters()

Reset the object attributes to match the original reference parameters

sample(size=None, *, random_state=None, **required_variables)

Draw a sample from the prior

Parameters:

size: int or tuple of ints, optional

See superclass

required_variables:

Any required variables that this prior depends on

Returns:

float: See superclass

update_conditions(**required_variables)

This method updates the conditional parameters (depending on the parent class this could be e.g. minimum, maximum, mu, sigma, etc.) of this prior class depending on the required variables it depends on.

If no variables are given, the most recently used conditional parameters are kept

Parameters:

required_variables:

Any required variables that this prior depends on. If none are given, self.reference_params will be used.