Example Problem for Experimental Design - Revision history

Admin at 16:33, 16 December 2017

2017-12-16T16:33:05Z

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			See code at [[ToyProblem_cmr.m]]

	=Problem Description=		=Problem Description=

Admin: /* Problem Description */

2017-12-16T12:44:09Z

Problem Description

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	=Problem Description=		=Problem Description=

			<s>
	Problem description: http://files.charlesmartinreid.com/ExperimentalDesign/VUQ_Toy_Problem.pdf		Problem description: http://files.charlesmartinreid.com/ExperimentalDesign/VUQ_Toy_Problem.pdf
			</s>

	=Inputs and Outputs=		=Inputs and Outputs=

Admin at 19:04, 30 June 2011

2011-06-30T19:04:00Z

Show changes

Admin: /* Selecting a Model */

2011-06-30T08:25:42Z

Selecting a Model

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	==Selecting a Model==		==Selecting a Model==

	~~In order to select a~~ model ~~from the categories above~~, you must first ~~consider~~ your ~~selected~~ [[Experimental Design Lecture\|experimental design]]. ~~In order~~ to ~~sample the function as few number of times as possible~~ (~~which is the case unless you are running~~ a ~~Monte Carlo simulation~~)~~, one typically assumes a~~ form of the model output(s) as a function of the model input(s). If a Monte Carlo simulation is being run, any linear model from above may be selected and fit to the data (in this case, it is useful to explore different models of different forms and degrees).		Before selecting the form of the surrogate model, you must first select your [[Experimental Design Lecture\|experimental design]]. Typically the experimental design is selected to regress some particular functional form (e.g. a polynomial).

			A form of the model output(s) as a function of the model input(s) is assumed in order to sample the function as few number of times as possible.

			If a Monte Carlo simulation is being run, the cost is very high, but the method is very flexible - any linear model from above may be selected and fit to the data (in this case, it is useful to explore different models of different forms and degrees).

	For more information on the experimental design step, see the [[Experimental Design Lecture]].		For more information on the experimental design step, see the [[Experimental Design Lecture]].

Admin at 09:20, 29 June 2011

2011-06-29T09:20:18Z

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	~~[[Category:Experimental Design]]~~

			{{ExperimentalDesign}}

Admin at 08:43, 29 June 2011

2011-06-29T08:43:42Z

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	For more information on the experimental design step, see the [[Experimental Design Lecture]].		For more information on the experimental design step, see the [[Experimental Design Lecture]].

			=See Also=

			* [[Experimental Design Lecture]]




			[[Category:Experimental Design]]

Admin: /* Problem Description */

2011-06-29T08:42:32Z

Problem Description

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	=Problem Description=		=Problem Description=

	Problem description: http://files.charlesmartinreid.com/VUQ_Toy_Problem.pdf		Problem description: http://files.charlesmartinreid.com/ExperimentalDesign/VUQ_Toy_Problem.pdf

	=Inputs and Outputs=		=Inputs and Outputs=

Admin: /* Linear Model Classification */

2011-06-29T07:07:48Z

Linear Model Classification

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	==Linear Model Classification==		==Linear Model Classification==

			A very helpful guide, given by Matlab, that describes and illustrates various regression analysis techniques: http://www.mathworks.com/help/toolbox/stats/bq_676m-2.html

	===Generalized Linear Models===		===Generalized Linear Models===

Admin at 07:06, 29 June 2011

2011-06-29T07:06:42Z

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 '''NOTE''': there is a more general discussion of experiment design, of which the response surface methodology is only one of several, at the following page:
-[[ExperimentDesignLecture]]
+[[Experimental Design Lecture]]
 ==Linear Model Classification==
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 * http://en.wikipedia.org/wiki/Multivariate_regression_model
 * Nelder and Wedderburn (1972)
 ===Multiple Linear Regression===
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 ===Response Surface Models (Multivariate)===

Admin: /* Analysis of Results and Construction of Response Surface */

2011-06-29T07:00:37Z

Analysis of Results and Construction of Response Surface

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	The ultimate reason for sampling the function is to construct a response surface, and in order to construct a response surface, some kind of generalized linear model will have to be used.		The ultimate reason for sampling the function is to construct a response surface, and in order to construct a response surface, some kind of generalized linear model will have to be used.

	==Model Classification==		'''NOTE''': there is a more general discussion of experiment design, of which the response surface methodology is only one of several, at the following page:

			[[ExperimentDesignLecture]]

			==Linear Model Classification==

	===Generalized Linear Models===		===Generalized Linear Models===