50 Date 20140503 Imports boot gam 109 Author Thomas Lotze and Markus Loecher Maintainer Thomas Lotze Description A set of functions for doing analysis of AB split test data and web metrics in general License GPL3 NeedsCompilation no Repository CRAN ID: 52013
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2best_binomial_bandit bandit-packageFunctionsforsimpleA/Bsplittestandmulti-armedbanditanalysis DescriptionAsetoffunctionsfordoinganalysisofA/Bsplittestdataandwebmetricsingeneral.DetailsPackage:banditType:PackageTitle:FunctionsforsimpleA/Bsplittestandmulti-armedbanditanalysisVersion:0.5.0Date:2014-05-03Imports:boot,gam�(=1.09)Author:ThomasLotzeandMarkusLoecherMaintainer:ThomasLotze&#xthom; slo;&#xtze@;&#xthom; slo;&#xtze.;om0;License:GPL-3Author(s)ThomasLotzeandMarkusLoecher best_binomial_banditbest_binomial_bandit DescriptionComputetheBayesianprobabilitiesforeacharmbeingthebestbinomialbandit.Usagebest_binomial_bandit(x,n,alpha=1,beta=1)Argumentsxasinprop.test,avectorofthenumberofsuccessesnasinprop.test,avectorofthenumberoftrialsalphashapeparameteralphaforthepriorbetadistribution.betashapeparameterbetaforthepriorbetadistribution. 4best_binomial_bandit_simUsagebest_binomial_bandit_sim(x,n,alpha=1,beta=1,ndraws=5000)Argumentsxasinprop.test,avectorofthenumberofsuccessesnasinprop.test,avectorofthenumberoftrialsalphashapeparameteralphaforthepriorbetadistribution.betashapeparameterbetaforthepriorbetadistribution.ndrawsnumberofrandomdrawsfromtheposteriorValueavectorofprobabilitiesforeacharmbeingthebestbinomialbandit;thiscanbeusedforfuturerandomizedallocationAuthor(s)ThomasLotzeandMarkusLoecherReferencesStevenL.Scott,AmodernBayesianlookatthemulti-armedbandit,Appl.StochasticModelsBus.Ind.2010;26:639-658.(http://www.economics.uci.edu/~ivan/asmb.874.pdf)SeeAlsoprop.testExamplesx=c(10,20,30,33)n=c(100,102,120,130)best_binomial_bandit_sim(x,n,ndraws=1000)round(best_binomial_bandit(x,n),3)best_binomial_bandit_sim(c(2,20),c(100,1000))best_binomial_bandit_sim(c(2,20),c(100,1000),alpha=2,beta=5)#quicklookatthevariousshapesofthebetadistributionaswechangetheshapeparams:AlphaBeta=cbind(alpha=c(0.5,5,1,2,2),beta=c(0.5,1,3,2,5))M=nrow(AlphaBeta)y=matrix(0,100,ncol=M)x=seq(0,1,length=100)for(iin1:M)y[,i]=dbeta(x,AlphaBeta[i,1],AlphaBeta[i,2])matplot(x,y,type="l",ylim=c(0,3.5),lty=1,lwd=2) distribution_estimate7}else{print("Nosignificanttime-basedfactor")} distribution_estimatesummarize_metrics DescriptionAconveniencefunctiontoperformoverallmetricanalysis:mean,median,CI.Usagedistribution_estimate(v,successes=NULL,num_quantiles=101,observed=FALSE)Argumentsvavectorofvaluestobeanalyzed(fornonbinarydata),ornumberoftrials(forbinarydata)successesnumberofsuccesses(forbinarydata)num_quantilesnumberofquantilestosplitintoobservedwhethertogeneratetheobserveddistribution(ratherthantheestimateddistri-butionofthemean);defaultFALSEValueadataframewiththefollowingcolumns:quantilestheestimatedquantiles(0,0.01,0.02,...,1)forthemean,usingaBeta-binomialestimateofpforbinomialdata,abootstrappedquantiledistributionforreal-valuednumbersxxvaluesforplottingalineplotoftheestimateddistributionyyvaluesforplottingalineplotoftheestimateddistributionmidsmidvaluesforplottingabarplotoftheestimateddistributionleftsleftvaluesforplottingabarplotoftheestimateddistributionrightsrightvaluesforplottingabarplotoftheestimateddistributionwidthswidthvaluesforplottingabarplotoftheestimateddistributionheightsheightvaluesforplottingabarplotoftheestimateddistributionprobabilitiesprobabilitiesindicatinghowmuchprobabilityiscontainedineachbarplotAuthor(s)ThomasLotze&#xthom; slo;&#xtze@;&#xthom; slo;&#xtze.;om0; signicance_analysis9 significance_analysissignicance_analysis DescriptionAconveniencefunctiontoperformoverallproportioncomparisonusingprop.test,beforedoingpairwisecomparisons,toseewhatoutcomesseemtobebetterthanothers.Usagesignificance_analysis(x,n)Argumentsxasinprop.test,avectorofthenumberofsuccessesnasinprop.test,avectorofthenumberoftrialsValueadataframewiththefollowingcolumns:successesxtotalsnestimated_proportionx/nlower0.95condenceintervalontheestimatedamountbywhichthisalternativeout-performsthenext-loweralternativeupper0.95condenceintervalontheestimatedamountbywhichthisalternativeout-performsthenext-loweralternativesignificancep-valueforthetestthatthisalternativeoutperformsthenext-loweralternativeorderorder,byhighestsuccessproportionbest1ifitispartofthe'highestperforminggroup'–thosegroupswhichwerenotsignicantlydifferentfromthebestgroupp_bestBayesianposteriorprobabilitythatthisalternativeisthebestbinomialbanditNoteThisisintendedforuseinA/Bsplittesting–sosizesofnshouldberoughlyequal.Also,notethatalternativeswhichhavethesamerankaregroupedtogetherforanalysiswiththe'next-lower'alternative,soyoumaywanttochecktoseeifranksareequal.Author(s)ThomasLotze&#xthom; slo;&#xtze@;&#xthom; slo;&#xtze.;om0; summarize_metrics11Examplesx=c(10,20,30,50)n=c(100,102,120,130)sim_post(x,n) summarize_metricssummarize_metrics DescriptionAconveniencefunctiontoperformoverallmetricanalysis:mean,median,CI.Usagesummarize_metrics(v,successes=NULL)Argumentsvavectorofvaluestobeanalyzed(fornonbinarydata),ornumberoftrials(forbinarydata)successesnumberofsuccesses(forbinarydata)Valuealistwiththefollowingitems:meanmeanmedianmedianlower0.95condenceintervalonthemeanupper0.95condenceintervalonthemeannum_obsnumberofobservationsofthismetrictotalthesumofallvaluesofthismetric(mean*num_obs)Author(s)ThomasLotze&#xthom; slo;&#xtze@;&#xthom; slo;&#xtze.;om0;Examplesmetric_list=list(rbinom(n=100,size=1,prob=0.5),rbinom(n=100,size=1,prob=0.7),rpois(n=100,lambda=5))summarize_metrics(length(metric_list[[1]]),sum(metric_list[[1]]))summarize_metrics(length(metric_list[[2]]),sum(metric_list[[2]]))summarize_metrics(metric_list[[3]]) IndexTopicdesignbest_binomial_bandit,2best_poisson_bandit,5significance_analysis,9Topichtestbest_binomial_bandit,2best_poisson_bandit,5deseasonalized_trend,6distribution_estimate,7significance_analysis,9summarize_metrics,11Topicpackagebandit-package,2bandit(bandit-package),2bandit-package,2bbb(best_binomial_bandit),2best_binomial_bandit,2best_binomial_bandit_sim,3best_poisson_bandit,5bpb(best_poisson_bandit),5deseasonalized_trend,6distribution_estimate,7prob_winner,8prop.test,3–5,10significance_analysis,9sim_post,10summarize_metrics,11value_remaining,1213