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4
votes
Are all probabilities conditional probabilities?
It is possible to develop probability theory taking conditional probability as one of the basic definitions; see section 3.2 in this book and the references mention there. Renyi was one of the first …
1
vote
Bayesian Inference with Student-t likelihood
Section 2.1 of this paper gives expressions for the posterior mean of location parameters. This may be helpful in your context.
0
votes
Quantifying the effect of noise on the posterior variance in Gaussian processes / multivaria...
Consider the joint Gaussian distribution of $(Y, Z, f(x))$. Observe that knowing both $Y$ and $Z$ together is equivalent to knowing $f(\mathbf{x})$ (the noiseless version of $Y$). Then we can compute …