The goal of sequential learning is to draw inference from data that is gathered gradually through time. This is a typical situation in many applications, including finance. A sequential inference procedure is `anytime-valid’ if the decision to stop or continue an experiment can depend on anything that has been observed so far, without compromising statistical error guarantees. A recent approach to anytime-valid inference views a test statistic as a bet against the null hypothesis. These bets are constrained to be supermartingales - hence unprofitable - under the null, but designed to be profitable under the relevant alternative hypotheses. This perspective opens the door to tools from financial mathematics. In this talk I will discuss how notions such as supermartingale measures, log-optimality, and the optional decomposition theorem shed new light on anytime-valid sequential learning. (This talk is based on joint work with Wouter Koolen (CWI), Aaditya Ramdas (CMU) and Johannes Ruf (LSE).)
Finance and Statistics: Trading Analogies for Sequential Learning
A cross-border market model
On the XBID-market 13 European countries can trade electricity between each other. Like other intraday electricity markets, this is handled using a limit order book. However, cross-border trading is limited via the total amount of available transmission capacities during a trading session. We present a cross-border market model between two countries and want to give insight into the interactions on this market. We introduce a so-called reduced-form representation of the market and a capacity process which may restrict cross-border trades in each direction. Assuming that the capacity process is non-restricted, we are able to derive heavy traffic approximations of the standing volumes and the capacity process. We will further motivate a candidate for the heavy traffic approximation of the restricted market model.