Approximate inference and Bayesian decision theory

Solving a decision problem is a two-step procedure: firstly, one performs inference to obtain the approximate posterior distribution, which, secondly, is used to solve said decision problem. The beauty of breaking down Bayesian decision theory in this way, it is usually lectured, is that the two steps can be implemented independently. In reality, however, the inference step can only be performed in an approximate manner; as a consequence, the second step will depend on properties of the approximation in the first step. hence the two steps become coupled. We propose to investigate this coupling.
The project aims to research approximate inference in the context of Bayesian decision theory. We hope to enable the application of Bayesian decision theory in combination with well-established approximate-inference schemes; to qualitatively and quantitatively identify biases in decisions due to performing inference approximately; and to develop techniques that alleviate these biases.