Adaptive Gaussian process surrogates for Bayesian inference
This work addresses computational efficiency in Bayesian inference for researchers and practitioners dealing with expensive models, though it appears incremental as it builds on existing Gaussian process and Bayesian optimization techniques.
The paper tackles the problem of Bayesian inference with computationally expensive forward models by developing an adaptive Gaussian process surrogate method that uses expected improvement from Bayesian optimization to construct training designs. Numerical experiments show this approach achieves accurate posterior estimation at a fraction of the cost compared to fixed non-adaptive designs.
We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and utilizes the expected improvement idea from Bayesian global optimization. We adaptively construct training designs by maximizing the expected improvement in fit of the Gaussian process model to the noisy observational data. Numerical experiments on model problems with synthetic data demonstrate the effectiveness of the obtained adaptive designs compared to the fixed non-adaptive designs in terms of accurate posterior estimation at a fraction of the cost of inference with forward models.