Group invariant inferred distributions via noncommutative probability

One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance method for constructing inferred distributions on parameter spaces given observed results. These inferred distributions are obtained without using Bayes' method and in particular without using a joint distribution of random variable and parameter. In the Poisson and binomial cases, the final formulas for inferred distributions coincide with the formulas for Bayes posteriors with uniform priors.Comment: Published at http://dx.doi.org/10.1214/074921706000000563 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Optical properties of TlNi2Se2: Observation of pseudogap formation

The quasi-two-dimensional nickel chalcogenides $TlNi_2Se_2$ is a newly discovered superconductor. We have performed optical spectroscopy study on $TlNi_2Se_2$ single crystals over a broad frequency range at various temperatures. The overall optical reflectance spectra are similar to those observed in its isostructure $BaNi_2As_2$. Both the suppression in $R(\omega)$ and the peaklike feature in $\sigma_1(\omega)$ suggest the progressive formation of a pseudogap feature in the midinfrared range with decreasing temperatures, which might be originated from the dynamic local fluctuation of charge-density-wave (CDW) instability. We propose that the CDW instability in $TlNi_2Se_2$ is driven by the saddle points mechanism, due to the existence of van Hove singularity very close to the Fermi energy.Comment: 5 pages, 4 figure