Confidence intervals

Here we describe two methods for forming confidence intervals for empirical Bayes estimands.

F-Localization based intervals

`FLocalizationInterval`

FLocalizationInterval(flocalization::Empirikos.FLocalization,
                      convexclass::Empirikos.ConvexPriorClass,
                      solver,
                      n_bisection = 100,
                      optimization_method = nothing)

Method for computing frequentist confidence intervals for empirical Bayes estimands. Here flocalization is a Empirikos.FLocalization, convexclass is a Empirikos.ConvexPriorClass, solver is a JuMP.jl compatible solver.

n_bisection is relevant only for combinations of target, flocalization and convexclass for which the Charnes-Cooper transformation is not applicable/implemented. Instead, a quasi-convex optimization problem is solved by bisection and increasing n_bisection increases accuracy (at the cost of more computation).

optimization_method determines how the optimization problem is solved. If nothing, the default optimization method of the solver is used. If CharnesCooper, the Charnes-Cooper transformation is used. If QuasiConvexBisection, a quasi-convex optimization problem is solved by bisection.

References

Ignatiadis and Wager (2022)

AMARI intervals

`AMARI`

AMARI(convexclass::Empirikos.ConvexPriorClass,
      flocalization::Empirikos.FLocalization,
      solver,
      plugin_G = KolmogorovSmirnovMinimumDistance(convexclass, solver))

Affine Minimax Anderson-Rubin intervals for empirical Bayes estimands. Here flocalization is a pilot Empirikos.FLocalization, convexclass is a Empirikos.ConvexPriorClass, solver is a JuMP.jl compatible solver. plugin_G is a Empirikos.EBayesMethod used as an initial estimate of the marginal distribution of the i.i.d. samples \(Z\).

References

Ignatiadis and Wager (2022)

Interface

`confint`

confint(model::StatisticalModel; level::Real=0.95)

Compute confidence intervals for coefficients, with confidence level level (by default 95%).

StatsBase.confint(method::AMARI,
                  target::Empirikos.EBayesTarget,
                  Zs;
                  level=0.95)

Form a confidence interval for the Empirikos.EBayesTarget target with coverage level based on the samples Zs using the AMARI method.

Ignatiadis, Nikolaos, and Stefan Wager. 2022. “Confidence Intervals for Nonparametric Empirical Bayes Analysis (with Discussion and a Rejoinder by the Authors).” Journal of the American Statistical Association 117 (539): 1149–66. https://doi.org/10.1080/01621459.2021.2008403.