Robust Monitoring of Changes in Sequential Bayesian Experimental Design with E-Values

In Sequential BED, an experimenter adaptively selects designs and collects data to learn about the underlying data-generating process (DGP). However, it is typically assumed that the DGP structure is known---for instance, a known parametric family---and that it remains fixed over long, possibly unbounded sequences of experiments. We propose a hypothesis test for detecting changes in the DGP whose type-I error control is not affected by model misspecification. By exploiting recent results in randomized testing for adaptively collected data, we construct a valid test-statistic and convert it into an e-value. Thanks to the properties of e-values, we can easily provide type-I error guarantees even with an unbounded sequence of experiments. We illustrate our hypothesis test with a toy example, also investigating empirically the effect of misspecification on the power of the test.