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Joint probabilities under expected value constraints, transportation problems, maximum entropy in the mean, and geometry in the space of probabilities
Henryk Gzyl
There are interesting extensions of the problem of determining a joint probability with known marginals. On the one hand, one may impose size constraints on the joint probabilities…
A predictive approach to generalized arithmetic means
Henryk Gzyl
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometr…
Prediction in logarithmic distance
Henryk Gzyl
The metric properties of the set in which random variables take their values lead to relevant probabilistic concepts. For example, the mean of a random variable is a best predictor…
Inverse problems for random walks on trees: network tomography
Victor de la Pena, Henryk Gzyl, Patrick McDonald
Let be a finite tree with root and associate to the internal vertices of a collection of transition probabilities for a simple nondegenerate Markov chain. Embedd in…