Sex, lies and self-reported counts: Bayesian mixture models for heaping in longitudinal count data via birth-death processes

Surveys often ask respondents to report nonnegative counts, but respondents may misremember or round to a nearby multiple of 5 or 10. This phenomenon is called heaping, and the error inherent in heaped self-reported numbers can bias estimation. Heaped data may be collected cross-sectionally or longitudinally and there may be covariates that complicate the inferential task. Heaping is a well-known issue in many survey settings, and inference for heaped data is an important statistical problem. We propose a novel reporting distribution whose underlying parameters are readily interpretable as rates of misremembering and rounding. The process accommodates a variety of heaping grids and allows for quasi-heaping to values nearly but not equal to heaping multiples. We present a Bayesian hierarchical model for longitudinal samples with covariates to infer both the unobserved true distribution of counts and the parameters that control the heaping process. Finally, we apply our methods to longitudinal self-reported counts of sex partners in a study of high-risk behavior in HIV-positive youth.Comment: Published at http://dx.doi.org/10.1214/15-AOAS809 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spitzer Mid-Infrared Imaging of Nearby Ultraluminous Infrared Galaxies

We have observed 14 nearby (z<0.16) Ultraluminous Infrared Galaxies (ULIRGs) with Spitzer at 3.6-24 microns. The underlying host galaxies are well-detected, in addition to the luminous nuclear cores. While the spatial resolution of Spitzer is poor, the great sensitivity of the data reveals the underlying galaxy merger remnant, and provides the first look at off-nuclear mid-infrared activity.Comment: To appear in the conference proceedings for Spitzer New Views of the Universe, held Nov. 2004 in Pasadena, C

Birth/birth-death processes and their computable transition probabilities with biological applications

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth(death)/birth-death process, a tractable bivariate extension of the birth-death process. We develop an efficient and robust algorithm to calculate the transition probabilities of birth(death)/birth-death processes using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution

Recent results from COMPTEL observations of Cygnus X‐1

The COMPTEL experiment on the Compton Gamma‐Ray Observatory (CGRO) has now observed Cyg X‐1 on four separate occasions during phase 1 and phase 2 of its orbital mission (April, 1991 to August, 1993). Here we report on the results of the latest analysis of these data, which provide a spectrum extending to energies greater than 2 MeV. A spectral analysis of these data, in the context of a classical Comptonization model, indicates an electron temperature much higher than previous hard X‐ray measurements would suggest (200 keV vs 60–80 keV). This implies either some limitations in the standard Comptonization model and/or the need to incorporate a reflected component in the hard X‐ray spectrum. Although significant variability near 1 MeV has been observed, there is no evidence for any ‘MeV excess.