bayesbay.prior.CustomPrior

class bayesbay.prior.CustomPrior(name, log_prior, sample, perturb_std, perturb_std_birth=None, position=None)

Class enabling the definition of an arbitrary prior for a free parameter

Parameters:

name (str) – name of the current parameter, for display and storing purposes
log_prior (Callable[[Number, Number], Number])
sample (Callable[[Number], Number]) – a function that samples a new value (optionally dependent on a position). The parameter initialization will also be done by calling this function
perturb_std (Union[Number, np.ndarray]) – standard deviation of the Gaussians used to randomly perturb the parameter. This can either be a scalar or an array if the defined probability distribution is a function of position in the discretization domain
position (np.ndarray, optional) – position in the discretization domain, used to define a position-dependent probability distribution. None by default

Reference Details

name

add_hyper_params(hyper_params)

Sets the attributes from the given dict and checks for errors

Parameters:: hyper_params (Dict[str, Union[Number, np.ndarray]]) – dictionary of attributes to be set

get_hyper_param(hyper_param, position=None)

Retrieves the value corresponding to the specified attribute, which may be a function of position

Parameters:

hyper_param (str) – the name of the attribute
position (Union[np.ndarray, Number], optional) – the position (in the discretization domain) associated with the value, None by default

Returns:

value corresponding to the specified attribute

Return type:

Union[Number, np.ndarray]

get_perturb_std(position=None)

get the standard deviation of the Gaussian used to perturb the parameter, which may be dependent on the position in the discretization domain

Parameters:: position (Union[Number, np.ndarray], optional) – the position in the discretization domain at which the standard deviation of the Gaussian used to perturb the parameter is returned. Default is None
Returns:: standard deviation of the Gaussian used to perturb the parameter, possibly at the specified position
Return type:: Number

get_perturb_std_birth(position=None)

get the standard deviation of the Gaussian used to perturb the parameter at birth, which may be dependent on the position in the discretization domain

Parameters:: position (Union[Number, np.ndarray], optional) – the position in the discretization domain at which the standard deviation of the Gaussian used to perturb the parameter at birth is returned. Default is None
Returns:: standard deviation of the Gaussian used to perturb the parameter at birth, possibly at the specified position
Return type:: Number

has_hyper_param(hyper_param)

Whether or not the Prior instance has the specified attribute

Parameters:: hyper_param (str) – the name of the attribute

initialize(positions=None)

initializes the values of this (possibly position-dependent) parameter

This is the vectorized version of the method sample().

Parameters:: positions (np.ndarray, optional) – the position (in the discretization domain) associated with the value, None by default
Returns:: an array of values or one value corresponding to the prior probability (at the given positions)
Return type:: np.ndarray

log_prior(value, position=None)

calculates the log of the prior probability density for the given value, which may be dependent on the position in the discretization domain

Parameters:

value (Number) – the value to calculate the probability density for
position (Union[Number, np.ndarray], optional) – the position in the discretization domain at which the prior probability of the parameter value is to be retrieved

Returns:

the log prior probability density

Return type:

Number

perturb_value(value, position=None, is_birth=False)

perturbs the given value, in a way that may depend on the position in the discretization domain, and calculates the log of the corresponding partial acceptance probability,

\[\begin{split}\underbrace{\alpha_{p}}_{\begin{array}{c} \text{Partial} \\ \text{acceptance} \\ \text{probability} \end{array}} = \underbrace{\frac{p\left({\bf m'}\right)}{p\left({\bf m}\right)}}_{\text{Prior ratio}} \underbrace{\frac{q\left({\bf m} \mid {\bf m'}\right)}{q\left({\bf m'} \mid {\bf m}\right)}}_{\text{Proposal ratio}} \underbrace{\lvert \mathbf{J} \rvert}_{\begin{array}{c} \text{Jacobian} \\ \text{determinant} \end{array}},\end{split}\]

where \(\bf m'\) denotes the perturbed model as obtained through a random deviate from a normal distribution \(\mathcal{N}(v, \theta)\), where \(v\) denotes the original value and \(\theta\) the standard deviation of the Gaussian used for the perturbation. \(\theta\) may be dependent on the specified position in the discretization domain (CustomPrior.perturb_std).

Parameters:

value (Number) – the current value to be perturbed from
position (Number, optional) – the position of the value to be perturbed
is_birth (bool, optional) – whether the perturbation is a birth or not, False by default

Returns:

the perturbed value and \(\alpha_{p} = \log( \frac{p({\bf m'})}{p({\bf m})} \frac{q\left({\bf m} \mid {\bf m'}\right)}{q\left({\bf m'} \mid {\bf m}\right)} \lvert \mathbf{J} \rvert)\)

Return type:

Tuple[Number, Number]

sample(position=None)

sample a new value from the prior

Paramters

positionUnion[np.ndarray, Number], optional: the position (in the discretization domain) associated with the value, None by default

returns:: a value corresponding to the prior probability (at the given position)
rtype:: Number

set_custom_initialize(initialize_func)

sets a custom initialization function

Parameters:: initialize_func (Callable[["Prior", np.ndarray], np.ndarray]) – The function to use for initialization. This function should take a Prior instance and optionally an array of positions as input arguments, and produce an array of values as output.

Examples

def my_init(
    param: bb.prior.Prior,
    position: np.ndarray
) -> np.ndarray:
    print("This is my custom init!")
    return np.ones(len(position))

my_param.set_custom_initialize(my_init)

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