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Wen et al. show two forecasters with identical marginal predictions can make arbitrarily different decisions. A disjoint contextual bandit (one model per arm) is exactly their independence forecaster. In conjugate linear models the joint is exact and free, and partial pooling through a shared component gets it back.
If you’re running a Bayesian model in a non-stationary environment, you need to forget old data. The obvious approach – scale the precision matrix by a constant – has a failure mode called covariance windup. This post works through three forgetting rules, ending with one borrowed from adaptive control that dominates the others.
I probably overuse the normal-inverse-gamma posterior. Every time I build a bandit system, every time I need uncertainty quantification for sequential decisions, I end up back at conjugate linear regression.
Suppose you’re choosing a continuous value x and observing a noisy reward y. The reward depends on x through some unknown function f(x), and you’re making decisions repeatedly—learning as you go. This post explores how to build scalable Bayesian models for this problem using principled approximations.