Yep, see this paper—Bayesian updating is the same as having all the hypotheses in your head be agents in a prediction market using the Kelly criterion, where their inital wealths are your prior probabilities on those hypotheses, the market price of some observation is your marginal probability over that observation, and the wealths after the bets resolve are the posterior distributions.
Yep, see this paper—Bayesian updating is the same as having all the hypotheses in your head be agents in a prediction market using the Kelly criterion, where their inital wealths are your prior probabilities on those hypotheses, the market price of some observation is your marginal probability over that observation, and the wealths after the bets resolve are the posterior distributions.