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Likelihood-free simulation-based optimal design with an application to spatial extremes.

Markus Hainy¹, Werner G Müller¹, Helga Wagner¹

¹Department of Applied Statistics, Johannes Kepler University, Altenberger Strasse 69, 4040 Linz, Austria.

Stochastic Environmental Research and Risk Assessment : Research Journal

|August 27, 2016

Summary

This summary is machine-generated.

This study introduces a new method for optimal experimental design when likelihood functions are unavailable but simulatable. It uses approximate Bayesian computation to find the best weather station placement for modeling temperature dependence.

Keywords:

Approximate Bayesian computation Importance sampling Max-stable processes Simulation-based optimal design Spatial extremes

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Area of Science:

Statistics
Environmental Science
Spatial Modeling

Background:

Optimal experimental design is crucial for efficient parameter estimation.
Many real-world problems lack analytically available likelihood functions, hindering traditional design methods.
Simulation-based approaches offer a viable alternative when direct likelihood calculation is infeasible.

Purpose of the Study:

To develop and apply a novel method for optimal design in situations requiring simulation-based likelihood approximations.
To optimize the placement of data collection points (e.g., weather stations) for improved model performance.
To enhance the estimation of parameters governing spatial dependence structures in environmental data.

Main Methods:

Utilized approximate Bayesian computation (ABC) to approximate expected utility.
Developed a simulation-based framework for optimal design.
Applied the method to a spatial extremes model for maximum annual summer temperatures.

Main Results:

The proposed method successfully identified an optimal design for weather station placement.
The approach demonstrated efficiency in estimating parameters of spatial dependence.
The application to temperature data provided insights into optimal monitoring network configuration.

Conclusions:

The novel simulation-based optimal design method is effective for problems with intractable likelihoods.
Approximate Bayesian computation provides a powerful tool for utility approximation in design.
The findings have practical implications for environmental monitoring and spatial statistical modeling.