1 / 26

Applying False Discovery Rate (FDR) Control in Detecting Future Climate Changes

Applying False Discovery Rate (FDR) Control in Detecting Future Climate Changes. ZongBo Shang SIParCS Program, IMAGe , NCAR August 4, 2009. North American Regional Climate Change Assessment Program (NARCCAP) Predicted Changes in Future Winter Temperature ( °C).

emiko
Download Presentation

Applying False Discovery Rate (FDR) Control in Detecting Future Climate Changes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Applying False Discovery Rate (FDR) Control in Detecting Future Climate Changes ZongBo Shang SIParCS Program, IMAGe, NCAR August 4, 2009

  2. North American Regional Climate Change Assessment Program (NARCCAP)Predicted Changes in Future Winter Temperature ( °C) Note: This figure shows the difference between the mean of future (2040 – 2069 ) winter temperature vs. current (1970 – 1999) winter temperature.

  3. Can We Trust What We See? Note: Those two figures show the means of 10 replicate random fields that are generated from the same Matèrn semi-variogram model, but with different random seeds.

  4. What’s the Problem with PointwiseTwo-sample t Tests?

  5. False Discovery Rate (FDR) Control • FDR controls the expected proportion of incorrectly rejected null hypotheses (type I errors) among the rejected null hypotheses. • Less conservative than Bonferroni procedures, with greater power than Familywise Error Rate (FWER) control, at a cost of increasing the likelihood of obtaining type I errors. Applications of FDR in Functional Magnetic Resonance Imaging Applications of FDR in Genes Expression and Microarray

  6. Definition of False Discovery Rate Let Q = V / (V + S) define the proportion of errors committed by falsely rejecting null hypotheses. Notice Q is an unobservable random variable. Define the FDR to be the expectation of Q:

  7. False Discovery Rates for Spatial Signals • Testing on clusters rather than individual locations • Procedure 1: Weighted Benjamini & Hochberg (BH) procedure • Procedure 2: Weighted two-stage procedure • Procedure 3: Hierarchical testing procedure • Testing stage: control FDR on clusters • Trimming stage: control FDR on selected points Reference: Benjamini, Y. and Heller, R. 2007. False discovery rates for spatial signals. Journal of the American Statistical Association. 102:1272-1281.

  8. Simulation Studies • 1. Random Fields • 2. Random Field Block • 3. Random Field Gradient

  9. Simulation Study I: Two Random Fields Note: Those two figures show the means of 10 replicate random fields that are generated from the same Matèrn semi-variogram model, but with different random seeds.

  10. Pre-defined Clusters

  11. Simulation Study 1: Pointwise vs. False Discover Rate Control

  12. 9 Repeats on Simulation Study I

  13. Simulation Study II: Pre-defined Block Trend 4 -10 -2 2 10 -4

  14. Simulation Study II: Average of 10 Replicates 4 -10 -2 2 10 -4 Random Field (Matèrn, σ = 0.4) Random Field (Matèrn, σ = 0.4) + Block Trends

  15. Simulation Study II: Pointwise vs. False Discover Rate Control

  16. 9 Repeats on Simulation Study II

  17. Study III: Pre-defined Gradient Trend

  18. Study III: Average of 10 Replicates Random Field (Matèrn, σ = 2) Random Field (Matèrn, σ = 2) + Gradient Trends

  19. Simulation Study III: Pointwise vs. False Discover Rate Control

  20. 9 Repeats on Simulation Study III

  21. Applying FDR Control for Detecting Future Climate Changes • Download climate datasets from NARCCAP program • Calculate seasonal average • Construct clusters from EPA Eco-regions • Conduct two-sample t test on temperature/precipitation • Pointwise p-values and corresponding z scores • Build semi-variogram model to estimate spatial autocorrelation • Calculate z score and p-value by cluster • Reject clusters based on FDR control

  22. http://www.epa.gov/wed/pages/ecoregions/na_eco.htm GIS: Vector Dataset, Lambert Equal-Area Projection

  23. H0: Future Winter Temperature Increase by 3 ˚C 61 regions rejected at q=0.25 level 56 regions rejected at q=0.1 level 54 regions rejected at q=0.05 level 51 regions rejected at q=0.01 level

  24. FDR Tests on Winter Temperature H0: Winter Temperature ↑ 1 ˚C H0: Winter Temperature ↑ 2 ˚C H0: Winter Temperature ↑ 3 ˚C H0: Winter Temperature ↑ 4 ˚C H0: Winter Temperature ↑ 5 ˚C H0: Winter Temperature ↑ 6 ˚C

  25. FDR Tests on Winter Precipitation H0: Winter Prec ↓ 20 Kg/ m² H0: ↓ 10 Kg/ m² H0: ↑ 10 Kg/ m² H0: ↑ 20 Kg/ m² H0: Winter Prec ↑ 30 Kg/ m² H0: ↑ 50 Kg/ m² H0: ↑ 75 Kg/ m² H0: ↑ 100 Kg/ m²

  26. Acknowledgement • Dr. Steve Sain, IMAGe, NCAR • Drs. Douglas Nychka, Tim Hoar, IMAGe, NCAR • Dr. Armin Schwartzman, Harvard University • University of Wyoming • SIParCS, IMAGe, NCAR • NARCCAP

More Related