Bayesian experimental design for the active nitridation of graphite by atomic nitrogen

TL;DR

This paper develops a Bayesian experimental design approach using information theory to optimize data collection in graphite nitridation experiments, improving parameter inference and detecting conflicting data.

Contribution

It introduces a mutual information-based method for selecting optimal experimental designs and monitors inference quality to determine when to stop data collection.

Findings

Optimal designs maximize statistical dependence between parameters and observables.

Monitoring entropy and KL divergence helps determine the stopping point for data collection.

Sequential Bayesian analysis detects conflicting information between measurements and model predictions.

Abstract

The problem of optimal data collection to efficiently learn the model parameters of a graphite nitridation experiment is studied in the context of Bayesian analysis using both synthetic and real experimental data. The paper emphasizes that the optimal design can be obtained as a result of an information theoretic sensitivity analysis. Thus, the preferred design is where the statistical dependence between the model parameters and observables is the highest possible. In this paper, the statistical dependence between random variables is quantified by mutual information and estimated using a k-nearest neighbor based approximation. It is shown, that by monitoring the inference process via measures such as entropy or Kullback-Leibler divergence, one can determine when to stop the data collection process. The methodology is applied to select the most informative designs on both a simulated data set and on an experimental data set, previously published in the literature. It is also shown that the sequential Bayesian analysis used in the experimental design can also be useful in detecting conflicting information between measurements and model predictions.