distributions.intervals

Module: distributions.intervals

Inheritance diagram for selectinf.distributions.intervals:

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This module contains a class for forming confindence intervals and testing 1-dimensional linear hypotheses about the underlying mean vector of a Gaussian subjected to selection.

intervals_from_sample

class selectinf.distributions.intervals.intervals_from_sample(reference, sample, observed, covariance)

Bases: object

Construct confidence intervals for real-valued parameters by tilting a multiparameter exponential family with reference measure a Monte Carlo sample.

The exponential family is assumed to be derived from a Gaussian with some selective weight and the parameters are linear functionals of the mean parameter of the Gaussian.

__init__(reference, sample, observed, covariance)

Parameters

reference : np.float(k)

Reference value of mean parameter. Often taken to be an unpenalized MLE or perhaps (approximate) selective MLE / MAP.

sample : np.float(s, k)

A Monte Carlo sample drawn from selective distribution.

observed : np.float(k)

Observed value of Gaussian estimator. Often an unpenalized MLE.

covariance : np.float(k, k)

Covariance of original Gaussian. Used only to compute unselective variance of linear functionals of the (approximately) Gaussian estimator.

pivots_all(parameter=None)

Compute pivotal quantities, i.e. the selective distribution function under \(H_{0,k}: heta_k= heta_{0,k}\) where :math:` heta_0` is parameter.

Parameters

parameter : np.float(k) (optional)

Value of mean parameter under coordinate null hypotheses. Defaults to np.zeros(k)

Returns

pivots : np.float(k)

Pivotal quantites. Each is (asymptotically) uniformly distributed on [0,1] under corresponding \(H_{0,k}\).

confidence_interval(linear_func, level=0.9)

Construct a `level*100`% confidence interval for a linear functional of the mean parameter of the underlying Gaussian.

Parameters

linear_func : np.float(k)

Linear functional determining parameter.

level : float (optional)

Specify the confidence level.

Returns

L, U : float

Lower and upper limits of confidence interval.

confidence_intervals_all(level=0.9)

Construct a level*100`% confidence interval for each :math: heta_j` of the mean parameter of the underlying Gaussian.

Parameters

level : float (optional)

Specify the confidence level.

Returns

LU : np.float(k,2)

Array with lower and upper confidence limits.