How does Random Forest relate to Bayesian model averaging conceptually?

Random Forest approximates model averaging but without explicit Bayesian priors.

Bayesian Model Averaging (BMA) weights models by posterior probability. Random Forest performs uniform averaging over randomized trees, which can be interpreted as an implicit approximation of BMA under a uniform prior over tree structures. However, RF does not compute posterior distributions, making it computationally simpler but theoretically less principled probabilistically.