Optimal Statistical Blocking Using Zero-suppressed Binary Decision Diagrams

Music City Center 

Statistical blocking is a technique for organizing experimental units into homogeneous groups to reduce the impact of confounding variables when estimating treatment effects.
While there has been considerable work on methods for finding optimal blockings, or more generally, optimal experimental designs, these methods are fairly rigid and do not allow for flexibility in the optimization criterion.
In this talk, we develop a novel optimal blocking technique where we view statistical blocking as a graph partitioning problem, where experimental units are vertices and edges restrict considered blockings.
We then express all partitions as a zero-suppressed binary decision diagram (ZDD), which is a directed acyclic graph in which each path corresponds to a different statistical blocking.
For small experiments, we enumerate all ZDD paths for optimal blocking, while for larger ones, we can find an approximately optimal blocking by sampling paths in the ZDD.
Our approach can accommodate any objective function, and can take into account restrictions on the number of blocks in total and the size of the blocks.
We validate our method through a small simulation study.

Statistical blocking


zero-suppressed binary decision diagram (ZDD)

graph partitioning

optimal blocking

vertices and edges 

Section on Statistics in Epidemiology