Abstract
We hold this truth to be self-evident, that good principle and good
practice go hand in hand. The principles of Bayesian analysis derive
from elementary symmetries, and nothing more. In sympathy with those
same symmetries, and noting that every invariance broken is generality
forgone, we develop the practice of Bayesian computation. This approach
leads to nested sampling and Galilean Monte Carlo. Nested sampling
is the canonical prior-to-posterior compression algorithm, and Galilean
Monte Carlo (GMC) is the canonical multidimensional exploration strategy.
Though inspired by high dimension, these general methods apply to
problems of all size.
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