Confidence intervals

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

F-Localization based intervals

`FLocalizationInterval`

:::{.callout appearance="minimal"}

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 {.unnumbered}

@ignatiadis2022confidence

:::

AMARI intervals

`AMARI`

:::{.callout appearance="minimal"}

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 {.unnumbered}

@ignatiadis2022confidence

:::

Interface

`confint`

:::{.callout appearance="minimal"}

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.

:::