# T optimal experimental designs

**URL:** <https://discourse.pumas.ai/t/t-optimal-experimental-designs/574>\
**Category:** model-syntax\
**Created:** [January 13, 2022, 1:33am UTC](https://discourse.pumas.ai/t/t-optimal-experimental-designs/574 "2022-01-13T01:33:33Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![ArnoStrouwen](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/arnostrouwen/32/185_2.png) [@ArnoStrouwen](https://discourse.pumas.ai/u/ArnoStrouwen)\
**Post date:** [January 13, 2022, 1:33am UTC](https://discourse.pumas.ai/t/t-optimal-experimental-designs/574/1 "2022-01-13T01:33:33Z")

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What kind of measure of the FIM do T optimal designs optimize?  
I do not think this is documented currently?

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**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [January 13, 2022, 2:21am UTC](https://discourse.pumas.ai/t/t-optimal-experimental-designs/574/2 "2022-01-13T02:21:34Z")

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The documentation PR exists but it fell through the cracks. Should be merged soon-ish.

T optimal design maximizes the trace of the expected information matrix. In the optimization, negative the trace is actually minimized instead.

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**Author:** ![ArnoStrouwen](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/arnostrouwen/32/185_2.png) [@ArnoStrouwen](https://discourse.pumas.ai/u/ArnoStrouwen)\
**Post date:** [January 13, 2022, 2:50am UTC](https://discourse.pumas.ai/t/t-optimal-experimental-designs/574/3 "2022-01-13T02:50:29Z")

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So A optimal designs minimize the trace of the inverse of the FIM,  
while T optimal designs maximize the trace of the FIM?

When you google “T optimal experimental design” most of the results are about optimal experimental design for model discrimination:

> **[Optimal design | Minimizing the variance of estimators](https://en.wikipedia.org/wiki/Optimal_design#Minimizing_the_variance_of_estimators)**
>
> Experimental designs are evaluated using statistical criteria.
> It is known that the least squares estimator minimizes the variance of mean-unbiased estimators (under the conditions of the Gauss–Markov theorem). In the estimation theory for statistical models with one real parameter, the reciprocal of the variance of an ("efficient") estimator is called the "Fisher information" for that estimator. Because of this reciprocity, minimizing the variance corresponds to maximizing the information.
> Whe...

[https://www.jstor.org/stable/2335364](https://www.jstor.org/stable/2335364)

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<div class="post-metadata">

**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [January 17, 2022, 11:48am UTC](https://discourse.pumas.ai/t/t-optimal-experimental-designs/574/4 "2022-01-17T11:48:15Z")

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> [@ArnoStrouwen](#):
>
> So A optimal designs minimize the trace of the inverse of the FIM,  
> while T optimal designs maximize the trace of the FIM?

Correct. Sorry for the delayed response.