English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study properties of confidence intervals (CIs) for the difference of twoBernoulli distributions' success parameters, $p_x - p_y$, in the case where thegoal is to obtain a CI of a given half-width while minimizing sampling costswhen the observation costs may be different between the two distributions.Assuming that we are provided with preliminary estimates of the successparameters, we propose three different methods for constructing fixed-widthCIs: (i) a two-stage sampling procedure, (ii) a sequential method that carriesout sampling in batches, and (iii) an $\ell$-stage "look-ahead" procedure. Weuse Monte Carlo simulation to show that, under diverse success probability andobservation cost scenarios, our proposed algorithms obtain significant costsavings versus their baseline counterparts (up to 50\% for the two-stageprocedure, up to 15\% for the sequential methods). Furthermore, for the batteryof scenarios under study, our sequential-batches and $\ell$-stage "look-ahead"procedures approximately obtain the nominal coverage while also meeting thedesired width requirement. Our sequential-batching method turned out to be moreefficient than the "look-ahead" method from a computational standpoint, withaverage running times at least an order-of-magnitude faster over all thescenarios tested.

Cost-Efficient Fixed-Width Confidence Intervals for the Difference of Two Bernoulli Proportions