Experimental Designs

The general experiment process is as follows:

Experimental design refers to the task of choosing the design \(\xi\), i.e. setting the controllable parts of the experiment. The common approach to do this is choose the experiment as \[ \xi^* = \text{argmax}_\xi \mathbb{E}_{p_{true}(y|\xi)}[U(\xi,y)] \]

However, we do not know \(p_{true}(y|\xi)\) and instead we get samples from this distribution. Bayesian Optimal Experimental Design (BOED) is a model-based approach to experimental design which makes use of notions in information theory.

One example application is to know the values of \(x\) for the question "Would you prefer USD \(x\) now or USD 100 in 1 year?", Choose \(x=70\) is a better question than choosing \(x=200\). The role of \(x\) here is that of the design \(\xi\).

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