Experimental Design: Recent Advances and Challenges for the Future' Paul Darius and Kenneth Portier - PowerPoint PPT Presentation

1 / 24
About This Presentation
Title:

Experimental Design: Recent Advances and Challenges for the Future' Paul Darius and Kenneth Portier

Description:

Experimental Design: Recent Advances and Challenges for the Future. ... place of design in the ... optimal design for linear model is worthless here ... – PowerPoint PPT presentation

Number of Views:243
Avg rating:3.0/5.0
Slides: 25
Provided by: wimco
Category:

less

Transcript and Presenter's Notes

Title: Experimental Design: Recent Advances and Challenges for the Future' Paul Darius and Kenneth Portier


1
Experimental DesignRecent Advances and
Challenges for the Future. Paul Darius and
Kenneth PortierK.U.Leuven , U. Florida
2
Contents
1. Chapter overview 2. Recent advances 3.
Challenges for the future
3
Chapter Overview
place of design in the experimental process
formulation of research question
definition of required precision
model selection
design of experiment
execution of experiment
statistical analysis
interpretation of results
4
elements of a design
starting point research question
units experimental measurement
response variable(s)
explanatory variables treatment
factors covariates blocking factors
levels
replications
randomization
5
analysis model
starting point research question
model response effects error
general linear model Y Xb e
errors assumed N(0,Is2)
responses
parameters
model/design matrix
6
analysis other models
mixed model Y Xa Zb e
errors assumed N(0,R)
random factors b assumed N(O,G)
fixed factors
generalized mixed model Y m e g(m)
Xa Zb
var(e)R
link function
var(b)G
7
analysis procedure
model construction
parameter estimation
checking model assumptions
inference on estimated parameters
hypothesis testing
computation of confidence intervals
8
characteristics of a good design (traditional)
  • allow unbiased estimation of treatment effects
  • allow estimation of underlying variability
  • enough precision to detect differences of
    practical importance
  • control for known sources of extraneous variation
  • allocate treatments to units randomly
  • as simple as possible
  • efficient use of resources

9
constructing a good design (methodological)
subject matter knowledge
research question
resource constraints
elements
cost
model
ease of computing
balance
confounding
rotatability
design
robustness
optimality
in practice often dependence on standard designs
10
Recent Advances
search of Current Index of Statistics for
design in title and keywords hits 1994 478
1995 526 1996 494 1997 358 (lower bound
on the number of methodological articles on
experimental design)
11
Recent Advances broad areas
  • linear/normal models
  • fractional factorials
  • supersaturated designs
  • mean and variance modeling
  • discrimination between models
  • crossover designs
  • sequential and group sequential designs
  • agricultural
  • intra-and interplot competition
  • intercropping

12
Recent Advances broad areas
  • optimal designs
  • (alphabetic) optimality criteria
  • computer construction algorithms
  • for dose-response, immunoassay, toxicokinetic
    studies
  • bayesian approaches
  • correlated error structures
  • temporal and spatial correlation
  • non-normal / non-linear models
  • designs for binary and Poisson data

13
Recent Advances
search of Current Index of Statistics
design design and optim... 1994 478
88 18 1995 526 118 22 1996 494
95 19 1997 358 87 24
14
design optimality principle
for the general linear model
D-optimality minimize (XX)-1 A-optimality
minimize tr(XX)-1 ...
  • finding optimal design
  • analytical
  • select from candidate points

15
D-optimality linear regression
experimental region
16
D-optimality linear regression
experimental region
  • pragmatic solution
  • compromise
  • no longer optimal

17
D-optimality nonlinear regression
1.0
0.8
0.6
y
0.4
0.2
0.0
0.5
1.0
1.5
2.0
2.5
3.0
  • optimal design for linear model is worthless
    here

x
18
D-optimality logistic regression
1.0
0.8
0.6
y
0.4
0.2
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
x
  • example of a generalized linear model
  • same design problem as nonlinear model

19
D-optimality birandomization
2 factor problem, full quadratic model z hard to
change variable, x easy to change gtgt set z, run
all x-combinations for that z d variance ratio
of plot vs subplot errors
x
x
z
z
dgt2.8
0ltdlt2.8
  • example of random factors/correlation structure
  • same design problem optimal design depends on
    guess for
  • the unknown parameters

20
robust optimal designs
Two approaches 1.
initial guess q0
small optimal design
better guess q1
new optimal design
analyze
  • leads to sequential and group-sequential designs
  • problem time span of experiment, confounding
    with time-
  • related factors

21
robust optimal designs
Approach 2
find a design that is not too bad when the
guess is somewhat wrong
set up prior distribution for q use expected
value of optimality criterion as new criterion
q
  • leads to Bayesian approach to optimal design
  • design will depend on prior

22
Challenges for the Future
  • new areas where statistics and/or experimental
    design
  • might/should play a role
  • how to adapt ?
  • will they play a role ?
  • education
  • software

23
New Areas Chemistry
  • chemometrics
  • statistical methods, specially adapted to
    data/methods from
  • analytical chemistry.
  • unusual combinations of variables -
    observations
  • a.o. multivariate calibration problems
  • special methods Partial Least Squares, Neural
    Networks

calibration
new method
conc
conc
conc
?
24
VIS/NIR spectroscopy
  • VIS/NIR-characteristics
  • 380 - 2000 nm
  • 0.5 nm increment

Source VCBT K.U.Leuven
Write a Comment
User Comments (0)
About PowerShow.com