Bayesian analysis with conditionally identically distributed sequences
Pier Giovanni Bissiri, Stephen Graham Walker · Electronic Journal of Statistics · 2025
The paper undertakes Bayesian style inference using posterior distributions. The key difference is that we use an assumption of a conditionally identically distributed (c.i.d.) sequence rather than the more common exchangeable sequence. We show that there remains the existence of a prior and posterior while the updating mechanism is achieved through the predictive distributions. This is sufficient given a fundamental result of Doob which explained how posteriors can be constructed in the exchangeable case via predictive distributions. We model the predictive distributions using copulas ensuring the c.i.d. structure.