Priors for Random Count Matrices Derived from a Family of Negative Binomial Processes

We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns. The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and beta-negative binomial processes. Because the models lead to closed-form Gibbs sampling update equations, they are natural candidates for nonparametric Bayesian priors over count matrices. A key aspect of our analysis is the recognition that, although the random count matrices within the family are defined by a row-wise construction, their columns can be shown to be i.i.d. This fact is used to derive explicit formulas for drawing all the columns at once. Moreover, by analyzing these matrices' combinatorial structure, we describe how to sequentially construct a column-i.i.d. random count matrix one row at a time, and derive the predictive distribution of a new row count vector with previously unseen features. We describe the similarities and differences between the three priors, and argue that the greater flexibility of the gamma- and beta- negative binomial processes, especially their ability to model over-dispersed, heavy-tailed count data, makes these well suited to a wide variety of real-world applications. As an example of our framework, we construct a naive-Bayes text classifier to categorize a count vector to one of several existing random count matrices of different categories. The classifier supports an unbounded number of features, and unlike most existing methods, it does not require a predefined finite vocabulary to be shared by all the categories, and needs neither feature selection nor parameter tuning. Both the gamma- and beta- negative binomial processes are shown to significantly outperform the gamma-Poisson process for document categorization, with comparable performance to other state-of-the-art supervised text classification algorithms.Comment: To appear in Journal of the American Statistical Association (Theory and Methods). 31 pages + 11 page supplement, 5 figure

High count rate {\gamma}-ray spectroscopy with LaBr3:Ce scintillation detectors

The applicability of LaBr3:Ce detectors for high count rate {\gamma}-ray spectroscopy is investigated. A 3"x3" LaBr3:Ce detector is used in a test setup with radioactive sources to study the dependence of energy resolution and photo peak efficiency on the overall count rate in the detector. Digitized traces were recorded using a 500 MHz FADC and analysed with digital signal processing methods. In addition to standard techniques a pile-up correction method is applied to the data in order to further improve the high-rate capabilities and to reduce the losses in efficiency due to signal pile-up. It is shown, that {\gamma}-ray spectroscopy can be performed with high resolution at count rates even above 1 MHz and that the performance can be enhanced in the region between 500 kHz and 10 MHz by using pile-up correction techniques

A method to correct differential nonlinearities in subranging analog-to-digital converters used for digital gamma-ray spectroscopy

The influence on $\gamma$-ray spectra of differential nonlinearities (DNL) in subranging, pipelined analog-to-digital converts (ADCs) used for digital $\gamma$-ray spectroscopy was investigated. The influence of the DNL error on the $\gamma$-ray spectra, depending on the input count-rate and the dynamic range has been investigated systematically. It turned out, that the DNL becomes more significant in $\gamma$-ray spectra with larger dynamic range of the spectroscopy system. An event-by-event offline correction algorithm was developed and tested extensively. This correction algorithm works especially well for high dynamic ranges

Calibration of the active radiation detector for Spacelab-One

The flight models of the active radiation detector (ARD) for the ENV-01 environmental monitor were calibrated using gamma radiation. Measured sensitivities of the ion chambers were 6.1 + or - 0.3 micron rad per count for ARD S/N1, and 10.4 + or - 0.5 micron rad per count for ARD S/N2. Both were linear over the measured range 0.10 to 500 m/rad hour. The particle counters (proportional counters) were set to respond to approximately 85% of minimum ionizing particles of unit charge passing through them. These counters were also calibrated in the gamma field

Hematological response in sheep given protracted exposures to Co 60 gamma radiation

Leukocyte count changes in sheep after prolonged exposure to gamma irradiation at rate of 1.9 R/h

Symmetries of Abelian Orbifolds

Using the Polya Enumeration Theorem, we count with particular attention to C^3/Gamma up to C^6/Gamma, abelian orbifolds in various dimensions which are invariant under cycles of the permutation group S_D. This produces a collection of multiplicative sequences, one for each cycle in the Cycle Index of the permutation group. A multiplicative sequence is controlled by its values on prime numbers and their pure powers. Therefore, we pay particular attention to orbifolds of the form C^D/Gamma where the order of Gamma is p^alpha. We propose a generalization of these sequences for any D and any p.Comment: 75 pages, 13 figures, 30 table

The VIMOS Public Extragalactic Redshift Survey (VIPERS): On the correct recovery of the count-in-cell probability distribution function

We compare three methods to measure the count-in-cell probability density function of galaxies in a spectroscopic redshift survey. From this comparison we found that when the sampling is low (the average number of object per cell is around unity) it is necessary to use a parametric method to model the galaxy distribution. We used a set of mock catalogues of VIPERS, in order to verify if we were able to reconstruct the cell-count probability distribution once the observational strategy is applied. We find that in the simulated catalogues, the probability distribution of galaxies is better represented by a Gamma expansion than a Skewed Log-Normal. Finally, we correct the cell-count probability distribution function from the angular selection effect of the VIMOS instrument and study the redshift and absolute magnitude dependency of the underlying galaxy density function in VIPERS from redshift $0.5$ to $1.1$. We found very weak evolution of the probability density distribution function and that it is well approximated, independently from the chosen tracers, by a Gamma distribution.Comment: 14 pages, 11 figures, 2 table