ONTNU Multiple hypothesis testing-recent developments and future challenges Ingelin Steinsland ingelins@math.ntnu.no Norwegian University of Science and Technology Multiple hypothesis testing-recent developments and future challenges-p.1/28
NTNUMultiple hypothesis testing - recent developments and future challenges Ingelin Steinsland ingelins@math.ntnu.no Norwegian University of Science and Technology Multiple hypothesis testing - recent developments and future challenges – p.1/28
ONTNU Outline Single hypothesis testing Multiple hypothesis testing Quantities and issues 0 False discovery rates ● Future challenges .Within false discovery rates. Multiple hypothesis tests,the right tool? Multiple hypothesis testing-recent developments and future challenges-p.2/28
NTNU Outline Single hypothesis testing Multiple hypothesis testing Quantities and issues False discovery rates Future challenges Within false discovery rates. Multiple hypothesis tests, the right tool? Multiple hypothesis testing - recent developments and future challenges – p.2/28
ONTNU Single hypothesis testing,example Typical question:Does treatment A give the wished effect? Hypothesis: H=0:Non or negative effect. H=1:Positive effect Multiple hypothesis testing-recent developments and future challenges-p.3/28
NTNU Single hypothesis testing, example Typical question: Does treatment A give the wished effect? Hypothesis: H = 0: Non or negative effect. H = 1: Positive effect Multiple hypothesis testing - recent developments and future challenges – p.3/28
ONTNU Single hypothesis testing,example Typical question:Does treatment A give the wished effect? Hypothesis: I=0:Non or negative effect. H-1:Positive effect Collect data. IF the collected data is very unlikely given H=0; H=0 rejected and H=1 accepted. Treatment A has positive effect. ELSE H=0 accepted. ● Treatment A does not have significant positive effect. Multiple hypothesis testing-recent developments and future challenges-p.3/28
NTNU Single hypothesis testing, example Typical question: Does treatment A give the wished effect? Hypothesis: H = 0: Non or negative effect. H = 1: Positive effect Collect data. IF the collected data is very unlikely given H = 0; H = 0 rejected and H = 1 accepted. Treatment A has positive effect. ELSE H = 0 accepted. Treatment A does not have significant positive effect. Multiple hypothesis testing - recent developments and future challenges – p.3/28
ONTNU Single hypothesis testing ●Hypothesis test: pH=0:0∈曰o versus 。H=1:0∈Θ1（Θ0∩Θ1=0） Test statistics:T(X),observed t. Multiple hypothesis testing-recent developments and future challenges-p.4/28
NTNU Single hypothesis testing Hypothesis test: H = 0 : θ ∈ Θ0 versus H = 1 : θ ∈ Θ1 (Θ0 ∩ Θ1 = ∅). Test statistics: T(X), observed t. Multiple hypothesis testing - recent developments and future challenges – p.4/28