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Bayesian Optimal Experimental Design

Dominik Strutz, Andrew Curtis

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Bayesian Optimal Experimental Design

Find the experimental design, which is expected to measure data to gain as much information as possible about the desired model parameters.

Dominik Strutz - Bayesian Optimal Experimental Design

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Experimental Design

Find the experimental design, which is expected to measure data to gain as much information as possible about the desired model parameters.

Dominik Strutz - Bayesian Optimal Experimental Design

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Let's start with the first part: Find the experimental design. Formally we can express that as finding the design which maximizes some measure of quality. In the simplest case, we would go through all designs, calculate the quality measure and pick the best one.

But what is a design actually? A design is basically anything that describes your data collection process. It could be the offset of a seismic receiver from some artificial source in the simplest case. But it can be truly anything. A few examples from geophysics are the sensor type (rotational translational), its orientation (vertical or horizontal), the frequency range in the post-processing and, of course, the spatial position. It's also possible to introduce the financial cost of a sensor in this framework.

But what is the measure of quality?

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Information

Find the experimental design, which is expected to measure data to gain as much information as possible about the desired model parameters.

Dominik Strutz - Bayesian Optimal Experimental Design

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C. E. Shannon (1948)

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Information

Find the experimental design, which is expected to measure data to gain as much information as possible about the desired model parameters.

Dominik Strutz - Bayesian Optimal Experimental Design

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Youtube: Huffman Codes: An Information Theory Perspective

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Information Gain

Find the experimental design, which is expected to measure data to gain as much information as possible about the desired model parameters.

Dominik Strutz - Bayesian Optimal Experimental Design

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D. V. Lindley (1956)

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Excepted Information Gain

Find the experimental design, which is expected to measure data to gain as much information as possible about the desired model parameters.

Dominik Strutz - Bayesian Optimal Experimental Design

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D. V. Lindley (1956)

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How to solve this?

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My poster offers details on the methods used to solve this problem in practice!

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This EIG is the quality measure we searched for initially, and it implies solving the optimal design problem in the model space.

With some rearrangement, it is also possible to reformulate the quality measure to solve it in the data space, which is less intuitive but avoids solving an inverse problem. In general this is the preferred way to solve an optimal design problem. This approach is not ideal in the case of many sensors collecting data, cause each sensor will add a data dimension. With only a small number of model parameters for example in the case of seismic source location, the model space approach might be the preferable way.

Again all of the equations are also on my poster if you want to look closer. For more on how to solve this problem in practice, you can also visit my poster. And before I end this, I want to say that I am on the look for projects where I could apply the methods I learned to practical problems. If you think your project could benefit from optimal design, approach me or send me an email.

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How to solve this?

Dominik Strutz - Bayesian Optimal Experimental Design

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My poster offers details on the methods used to solve this problem in practice!

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How to solve this?

Dominik Strutz - Bayesian Optimal Experimental Design

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How to solve this?

Dominik Strutz - Bayesian Optimal Experimental Design

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How to solve this?

Dominik Strutz - Bayesian Optimal Experimental Design

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