multivariate beta distributionmultivariate gamma functionRiesz measureSuppose that the random vector (X1,…,Xq) follows a Dirichlet distribution on Rq+ with parameter (p1,…,pq)∈Rq+. For f1,…,fq>0, it is well-known that E(f1X1+…+fqXq)(p1+…+pq)=fp11…fpqq. In this paper, we ...
Beta-Liouville distributionFacial expressionAction recognitionWe propose a nonparametric Bayesian model for the clustering of proportional data. Our model is based on an infinite mixture of Beta-Liouville distributions and allows a compact description of complex data. The choice of the Beta-Liouville as...
P. Temporal expectation and attention jointly modulate auditory oscillatory activity in the beta band. PLoS ONE 10, e0120288 (2015). Article PubMed PubMed Central Google Scholar Block, N. The puzzle of perceptual precision. Open Mind (2014). Anton-Erxleben, K. & Carrasco, M. Attentional ...
Expectation identityHigh-order momentsFor the variance parameter of the hierarchical normal and inverse gamma model, we analytically calculate the Bayes rule (estimator) with respect to a prior distribution IG(alpha,beta) under Stein's loss function. This estimator minimizes the posterior expected ...
We study the (weak) equilibrium problem arising from the problem of optimally stopping a one-dimensional diffusion subject to an expectation constraint on the time until stopping. The weak equilibrium problem is realized with a set of randomized but purely state dependent stopping times as admissible...
To model the joint distribution over the multi-scale of protein and drug interactions, a few attempts have been developed14,15,16,17. An intuitive approach for learning multi-scale representations is to combine the molecular graph with an interaction network and optimize them jointly. For example...
Thus, we can think of g(y)=E[X|Y=y]g(y)=E[X|Y=y] as a function of the value of random variable YY. We then write g(Y)=E[X|Y].g(Y)=E[X|Y]. We use this notation to indicate that E[X|Y]E[X|Y] is a random variable whose value equals g(y)=E[X|Y=y]g(y...
According to the modern interpretation, which of the following is true of the Phillips curve? a. It has a negative slope in the short run. b. It is vertical in the long run. c. Neither A nor B d. Both A and B Consider the simple linear regression model Yi = \beta_1 + ...
1.One of the more salient effects of listening to music is to create expectations of what is to come next, which may be fulfilled immediately, after some delay, or not at all as the case may be. Th...
To take the example of a real singlet S with mass-squared Lagrangian parameter m 2 S – not to be confused with the pole mass, which we denote MS – and expectation value vS, this means that analagously to Eq. (1.3), m 2 S = m 2 S tree 1 ∂ V − vS ∂S . (1.6) ...