Abstract: Given sequentially observed data, anytime-valid methods guarantee valid inference at adaptively chosen sample sizes, as opposed to pre-specified sample sizes, thereby allowing the experimenter to stop experiments early. Furthermore, when using anytime-valid confidence intervals, also known as confidence sequences, the experimenter can repeatedly peek at the results over time (referred to as "continuous monitoring") without compromising validity.

In this talk, I will discuss two recent advances in the field of anytime-valid inference. First, I will introduce anytime-valid approaches to the problem of comparing sequential forecasters under continuous monitoring, commonly found in meteorology, sports, and finance. In particular, I will derive tight confidence sequences that can track the time-varying mean expected score difference between any two forecasters, without requiring restrictive assumptions such as stationarity.

Second, I will introduce a general approach to combining anytime-valid statistical evidence ("e-process") for a null hypothesis, where the evidence is constructed in different information sets (filtrations). This is motivated by a common challenge arising in various sequential inference problems, including sequential tests of randomness and independence, as well as the sequential comparison of k-step-ahead forecasters. I will show how a simple approach based on adjusters allows us to combine arbitrary e-processes across filtrations with an asymptotically logarithmic cost.

https://yjchoe.github.io/