Quantum Physics and Statistical Causal Models

It has been understood for many years that there are connections between constraints such as Bell's inequality and Pearl's instrumental inequalities. This is not surprising since the motivation for Bell's inequality was to test hidden variable theories, and causal models, such as the instrumental variable model, are of this type. In recent years, these connections have grown considerably and now offer many additional areas for research. For example, there is an understanding of causal Bayesian networks in the quantum mechanical setting, there are generalizations of the instrumental inequalities, and general techniques ("inflation") have been developed for deriving constraints from hidden variable models with more general causal structures. These techniques may be very valuable in understanding the properties of statistical models, especially since these methods also describe computationally efficient implementations. Conversely, recent work in statistics on deriving the algebraic closure of latent variable models may offer insights into quantum mechanical systems.

This workshop will provide a setting for these two communities to cross-pollinate.