Transcript Toy3_Bingham

Some Random Questions
Derek Bingham
Simon Fraser University
Simon Fraser University
Department of Statistics and Actuarial Sciences
Questions I have…many not smart
•
“Parameterization” – Came up several time
– Can be choice for stochastic features in a computer model
– Can be parameters in PDE’s…do these have error? How to account for?
•
Robert and Howard
– How did you generate your ensembles
– Wanted to understand sensitivity to certain parameters? How measure?
Simon Fraser University
Department of Statistics and Actuarial Sciences
Questions I have…many not smart
•
NCAR folks.. What was helpful or what did you learn?
•
Statisticians… new problems or new methodology?
Simon Fraser University
Department of Statistics and Actuarial Sciences
Questions I have…many not smart
•
Regarding PDE’s:
•
y~N(pde( ),)
•
Elaine…interested in maximums (Bo?)….failure models in Engineering
? Build physics right in?
Simon Fraser University
Department of Statistics and Actuarial Sciences
Questions I have…many not smart
•
•
Guillaume – Added stochastic forcing…are models still closed
Seem to have a lot of parameters…are they identifiable?
•
I do not think I understand the data assimilation (Josh? Jeff?)
Simon Fraser University
Department of Statistics and Actuarial Sciences
GP’s have proven effective for emulating computer model
output & data mining
• Gaussian Spatial Process (GP) model frequently used in
modeling response from complex computer codes
• Emulating computer model output
–
–
–
•
output varies smoothly with input changes
output is essentially noise free
GP’s outperform other modeling approaches in this arena (mars,
cart, …)
Data Mining
–
–
compares favorably with other machine learning techniques
noise is a more prominent feature
Simon Fraser University
Department of Statistics and Actuarial Sciences
Gaussian Process Models
•
Emulators to be used as a surrogate for the computer model
1. How to build likely model complexity into design/analysis
– GP models are very complex and hard to interpret
– Even more challenging in calibration/assimilation problems
2. Sample Size Issues
– Do you have enough data to fit these models well?
Simon Fraser University
Department of Statistics and Actuarial Sciences
Complexity
•
Important elicitation problem
•
How complex is the response surface y(x) ?
•
How to build likely model complexity into design/analysis
– GP models are very complex and hard to interpret
– Even more challenging in calibration/assimilation problems
Simon Fraser University
Department of Statistics and Actuarial Sciences
Complexity
Simon Fraser University
Department of Statistics and Actuarial Sciences
Sample Size…Emulating a computer model
Simon Fraser University
Department of Statistics and Actuarial Sciences
Simulation
• p= 27, n=50,100,200,300,500
Random design
Symmetric LHS
Predictions for 100
holdout x’s
Simon Fraser University
Department of Statistics and Actuarial Sciences