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Short answer from someone who doesn't know much about Bayesian statistics: You should read about "reference priors". Have a look here: http://arxiv.org/pdf/0904.0156

Consider the following so-called $U$-statistic of order 2: $$U = \frac1{\binom{m}{2}} \sum_{i < j} h(w_i,w_j)$$ where $w_1,\dots,w_m$ are IID from some distribution and $h$ is symmetric. If $|h(w_1,w_ …

I don't quite follow what the reasoning is in the question, but here are some thoughts that don't fit in a comment. Gaussian process regression uses a Gaussian Process (GP) as the prior on the unknown …

I believe you can do something like this: Let $X$ be zero mean. Then the covariance matrix is $ \text{cov}(X) = \mathbb{E}[XX^T]$. Hence, by the same argument: \begin{align*} \text{cov}(X) = \text{ …

Here is an attempt to answer your questions, admitting that I have not read the paper carefully. The generator corresponding to a diffusion satisfying the SDE $dX_t = b(X_t) dt + \sigma(X_t) dB_t$ is …

Consider the special case where $|\mathcal X| = 2$ and $k=1$, that is, if you pick $P_1$ the adversary picks $P_2$ and generates a sample $Y^n = (Y_1,\dots,Y_n)$ drawn i.i.d. from $P_2$, and vice vers …

This question comes up in studying mean parametrization of exponential families of distributions. (See Brown's 1986 book on the subject.) Let $\nu$ be a (Borel) measure on $\mathbb R^d$. Let $p(\cd …