kb/data/en.wikipedia.org/wiki/Bayesian_experimental_design-1.md

title	chunk	source	category	tags	date_saved	instance
Bayesian experimental design	2/2	https://en.wikipedia.org/wiki/Bayesian_experimental_design	reference	science, encyclopedia	2026-05-05T09:48:59.414261+00:00	kb-cron

of which the latter can be evaluated without the need for evaluating individual posterior probability

    p
    (
    θ
    ∣
    y
    ,
    ξ
    )
  

{\displaystyle p(\theta \mid y,\xi )}

for all possible observations

    y
  

{\displaystyle y}

. It is worth noting that the second term on the second equation line will not depend on the design

    ξ
  

{\displaystyle \xi }

, as long as the observational uncertainty doesn't. On the other hand, the integral of

    p
    (
    θ
    )
    log
    ⁡
    p
    (
    θ
    )
  

{\displaystyle p(\theta )\log p(\theta )}

in the first form is constant for all

    ξ
  

{\displaystyle \xi }

, so if the goal is to choose the design with the highest utility, the term need not be computed at all. Several authors have considered numerical techniques for evaluating and optimizing this criterion. Note that

    U
    (
    ξ
    )
    =
    I
    (
    θ
    ;
    y
    )
    
    ,
  

{\displaystyle U(\xi )=I(\theta ;y)\,,}

the expected information gain being exactly the mutual information between the parameter θ and the observation y. An example of Bayesian design for linear dynamical model identification are given in
. Since

    I
    (
    θ
    ;
    y
    )
    
    ,
  

{\displaystyle I(\theta ;y)\,,}

was difficult to calculate, its lower bound has been used as a utility function. The lower bound is then maximized under the signal energy constraint. Proposed Bayesian design has been also compared with classical average D-optimal design. It was shown that the Bayesian design is superior to D-optimal design. The Kelly criterion also describes such a utility function for a gambler seeking to maximize profit, which is used in gambling and information theory; Kelly's situation is identical to the foregoing, with the side information, or "private wire" taking the place of the experiment.

== See also == Bayesian optimization Optimal design Active Learning Expected value of sample information

== References ==

== Further reading == DasGupta, A. (1996), "Review of optimal Bayes designs" (PDF), in Ghosh, S.; Rao, C. R. (eds.), Design and Analysis of Experiments, Handbook of Statistics, vol. 13, North-Holland, pp. 1099–1148, ISBN 978-0-444-82061-7 Rainforth, Tom; et al. (2023), Modern Bayesian Experimental Design, arXiv:2302.14545