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Results tagged with bayesian-probability
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user 11260
7
votes
Who introduced the term hyperparameter?
In 1996 Irving Good himself recalls:
One of the related problems close to philosophy is the estimation of the probability of one category of a multinomial when the order of the cells is irrelevant. [ …
- 188k
3
votes
Accepted
Parametrising a sparse orthogonal matrix
The smallest number of nonzero entries in an $n\times n$ fully indecomposable$^*$ orthogonal matrix is $4n−4$. A method to construct such a matrix is described in Sparse orthogonal matrices (2003).
$ …
- 188k
0
votes
Accepted
The expectation of binary logistics regression with respect to Gaussian distribution
Notice that $g(s,x)=(s-1)x+\ln\sigma(x)$. So
$$\langle g(s,x)\rangle_q=(s-1)m+\langle \ln\sigma(x)\rangle_q$$
and the entire $s$-dependence is trivial. Now for the second identity we perform a partia …
- 188k
1
vote
Accepted
Bayesian estimation with lower dimensional prior
Here is one approach, Optimal low-rank approximations of Bayesian linear inverse problems, see also reference 56. Typically, you construct a reduced basis for the parameter space.
- 188k
1
vote
Accepted
Adaptive priors
The modification of the traditional Bayes method where the prior distribution is determined by the data goes by the name empirical Bayes method. The motivation for the empirical approach is a practica …
- 188k
4
votes
Bayes statistics precisely formulated
Disclaimer: this refers to the situation described in these lecture notes, where Bayes theorem is applied to events. It seems this is not what the OP has in mind, so I'm just leaving my answer for the …
- 188k