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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

2 votes
2 answers
1k views

Gaussian expectation of an exponentiated outer product

Given a normal random column vector $\mathbf{x} \sim N(\mu, \Sigma)$, I need the expectation, $$ E\left[ \exp(\mathbf{xx}^\top)\right]$$ where $\exp(\cdot)$ is element-wise exponential function (not …
Memming's user avatar
  • 291
2 votes
Accepted

How to estimate the entropy of a distribution on a power set?

I don't think the power-set structure helps you estimate entropy better. The following extreme cases all give the same entropy for $p_B$, but entropy of the power set observation ranges from 0 to $N$ …
Memming's user avatar
  • 291