Reddit reviews Algebraic Geometry and Statistical Learning Theory (Cambridge Monographs on Applied and Computational Mathematics)
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My understanding is that certain kinds of discrete random variables can be viewed as algebraic varieties.
There are also books like this.
Whilst I agree with the sentiment, it's worth being careful about:
> If you have much more data than parameters, your posterior would heavily concentrate (see Bayesian Central Limit Theorem) around its mode
In particular, if the mode lies near a singularity of the parameter manifold (e.g. near a symmetry point of a mixture model, but much more general phenomonen exist), then the CLT doesn't really apply.
See https://www.amazon.co.uk/Algebraic-Statistical-Monographs-Computational-Mathematics/dp/0521864674
http://www.amazon.com/Algebraic-Statistical-Monographs-Computational-Mathematics/dp/0521864674