Conformal Exchangeability Martingale

Conformal exchangeability martingales are defined in the article conformal testing. The notion of a conformal exchangeability martingale has several pitfalls:

• Conformal exchangeability martingales are randomized: they depend not only on the observations but also on independent random numbers taking values in 0,1\$.
• Each conformal exchangeability martingale is a martingale only in the sense of satisfying . It does not satisfy (where is the past including the observations ) except in trivial cases.
• Therefore, the sum of two conformal exchangeability martingales does not have to be a conformal exchangeability martingale.

The main open question about conformal exchangeability martingales is whether they exhaust the class of exchangeability martingales.