elisa.infer.likelihood#

Likelihood functions.

Optimized background for PG-statistics given estimate of source counts.

Note

The optimized background here is always non-negative, which differs from XSPEC [1].

Parameters:

s (Union[Array, ndarray, bool, number, bool, int, float, complex, TypedNdArray]) – Estimate of source counts.
n (Union[Array, ndarray, bool, number, bool, int, float, complex, TypedNdArray]) – Observed counts (source and background).
b_est (Union[Array, ndarray, bool, number, bool, int, float, complex, TypedNdArray]) – Estimate of background counts.
b_err (Union[Array, ndarray, bool, number, bool, int, float, complex, TypedNdArray]) – Uncertainty of background counts.
a (Union[Array, ndarray, bool, number, bool, int, float, complex, TypedNdArray]) – Exposure ratio between source and background observations.

Returns:

The profile background.

References

[1]

XSPEC Manual Appendix B: Statistics in XSPEC.

Optimized background for W-statistics [1] given the estimate of source.

Parameters:

s (Union[Array, ndarray, bool, number, bool, int, float, complex, TypedNdArray]) – Estimate of source counts.
n_on (Union[Array, ndarray, bool, number, bool, int, float, complex, TypedNdArray]) – Observed source and background counts in “on” observation.
n_off (Union[Array, ndarray, bool, number, bool, int, float, complex, TypedNdArray]) – Observed background counts in “off” observation.
a (Union[Array, ndarray, bool, number, bool, int, float, complex, TypedNdArray]) – Exposure ratio between “on” and “off” observations.

Returns:

The profile background.

References

[1]

Wachter, K., Leach, R., & Kellogg, E. (1979). Parameter estimation in X-ray astronomy using maximum likelihood. ApJ, 230, 274–287.

Bases: Normal

Attributes

`batch_shape`	Returns the shape over which the distribution parameters are batched.
`event_dim`
`event_shape`	Returns the shape of a single sample from the distribution without batching.
`mean`	Mean of the distribution.
`variance`	Variance of the distribution.

has_rsample
is_discrete

Methods

`__call__`(args, *kwargs)
`cdf`(value)	The cumulative distribution function of this distribution.
`entropy`()	Returns the entropy of the distribution.
`enumerate_support`([expand])	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.
`expand_by`(sample_shape)	Expands a distribution by adding `sample_shape` to the left side of its `batch_shape`.
`get_args`()	Get arguments of the distribution.
`icdf`(q)	The inverse cumulative distribution function of this distribution.
`infer_shapes`(args, *kwargs)	Infers `batch_shape` and `event_shape` given shapes of args to `__init__()`.
`log_prob`(value)	Evaluates the log probability density for a batch of samples given by value.
`mask`(mask)	Masks a distribution by a boolean or boolean-valued array that is broadcastable to the distributions `Distribution.batch_shape` .
`sample`(key[, sample_shape])	Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape.
`sample_with_intermediates`(key[, sample_shape])	Same as `sample` except that any intermediate computations are returned (useful for TransformedDistribution).
`shape`([sample_shape])	The tensor shape of samples from this distribution.
`to_event`([reinterpreted_batch_ndims])	Interpret the rightmost reinterpreted_batch_ndims batch dimensions as dependent event dimensions.
`validate_args`([strict])	Validate the arguments of the distribution.

gather_pytree_aux_fields
gather_pytree_data_fields
log_cdf
rsample
set_default_validate_args
support
tree_flatten
tree_unflatten

log_prob(value)[source]#

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:: ArrayLike

Bases: Poisson

Attributes

`batch_shape`	Returns the shape over which the distribution parameters are batched.
`event_dim`
`event_shape`	Returns the shape of a single sample from the distribution without batching.
`mean`	Mean of the distribution.
`variance`	Variance of the distribution.

has_rsample
is_discrete

Methods

`__call__`(args, *kwargs)
`cdf`(value)	The cumulative distribution function of this distribution.
`entropy`()	Returns the entropy of the distribution.
`enumerate_support`([expand])	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.
`expand_by`(sample_shape)	Expands a distribution by adding `sample_shape` to the left side of its `batch_shape`.
`get_args`()	Get arguments of the distribution.
`icdf`(q)	The inverse cumulative distribution function of this distribution.
`infer_shapes`(args, *kwargs)	Infers `batch_shape` and `event_shape` given shapes of args to `__init__()`.
`log_prob`(value)	Evaluates the log probability density for a batch of samples given by value.
`mask`(mask)	Masks a distribution by a boolean or boolean-valued array that is broadcastable to the distributions `Distribution.batch_shape` .
`sample`(key[, sample_shape])	Returns a sample from the distribution having shape given by sample_shape + batch_shape + event_shape.
`sample_with_intermediates`(key[, sample_shape])	Same as `sample` except that any intermediate computations are returned (useful for TransformedDistribution).
`shape`([sample_shape])	The tensor shape of samples from this distribution.
`to_event`([reinterpreted_batch_ndims])	Interpret the rightmost reinterpreted_batch_ndims batch dimensions as dependent event dimensions.
`validate_args`([strict])	Validate the arguments of the distribution.

gather_pytree_aux_fields
gather_pytree_data_fields
rsample
set_default_validate_args
support
tree_flatten
tree_unflatten

log_prob(value)[source]#

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:: ArrayLike

chi2(data: FixedData, model: Callable[[Array, dict[str, Array]], Array]) → Callable[[dict[str, Array], bool], None][source]#: S^2 statistic, Gaussian likelihood.

cstat(data: FixedData, model: Callable[[Array, dict[str, Array]], Array]) → Callable[[dict[str, Array], bool], None][source]#: C-statistic, Poisson likelihood.

pstat(data: FixedData, model: Callable[[Array, dict[str, Array]], Array]) → Callable[[dict[str, Array], bool], None][source]#: P-statistic, Poisson likelihood for data with a known background.

pgstat(data: FixedData, model: Callable[[Array, dict[str, Array]], Array]) → Callable[[dict[str, Array], bool], None][source]#: PG-statistic, Poisson likelihood for data and profile Gaussian likelihood for background.

wstat(data: FixedData, model: Callable[[Array, dict[str, Array]], Array]) → Callable[[dict[str, Array], bool], None][source]#: W-statistic, i.e. Poisson likelihood for data and profile Poisson likelihood for background.