Barbara Heller, Ph.D.
Inference problems in the field of Mathematical Statistics; the use of generalized coherent states for the purpose of creating parametric families of probability distributions; statistical modelling via group theoretic methods; posterior distributions via coherent states; operational approach to quantum physics; probability operator valued measures.
- Special functions and characterizations of probability distributions by zero regression properties, Journal of Multivariate Analysis 13, 473-487 (1980).
- Use of the hyperbolic differential operator to find a scalar statistic which hss constant regression on the mean of a sample of Wishart matrices, Journal of Multivariate Analysis 14, issue 1, pp. 101-104 (1984).
- Posterior distributions on certain parameter spaces obtained by using group theoretic methods adopted from quantum physics, with M. Wang, Technical Report No. 546, The University of Chicago, Department of Statistics, April, 2004.
- Group invariant inferred distributions via noncommutative probability, with M. Wang, arXiv:math/0611675 IMS Lecture Notes Monograph Series, Vol. 50 (2006), 1-19.
- Posterior Distribution for Negative Binomial Parameter p Using a Group Invariant Prior, with M. Wang, Statistics and Probability Letters, 77, 1542-1548 (2007).
- Coherent States and Bayesian Duality, with S.T. Ali and J.-P. Gazeau, arXiv:0803.2269v1[math-ph] (2008), Journal of Physics A Math. Theor. 41, (2008) 365302 (22pp).
- POVM quantization, with J.P.Gazeau, arXiv:1408.6090v1 [quant-ph] 26 Aug. 2014
- Positive-operator valued measure (POVM) quantization, with J. P. Gazeau, Axioms ISSN 2075-1680 (2015), 4,1-29.