Multivariate Hierarchical Frameworks for Modelling Delayed Reporting in Count Data

In many fields and applications count data can be subject to delayed reporting. This is where the total count, such as the number of disease cases contracted in a given week, may not be immediately available, instead arriving in parts over time. For short term decision making, the statistical challenge lies in predicting the total count based on any observed partial counts, along with a robust quantification of uncertainty. In this article we discuss previous approaches to modelling delayed reporting and present a multivariate hierarchical framework where the count generating process and delay mechanism are modelled simultaneously. Unlike other approaches, the framework can also be easily adapted to allow for the presence of under-reporting in the final observed count. To compare our approach with existing frameworks, one of which we extend to potentially improve predictive performance, we present a case study of reported dengue fever cases in Rio de Janeiro. Based on both within-sample and out-of-sample posterior predictive model checking and arguments of interpretability, adaptability, and computational efficiency, we discuss the advantages and disadvantages of each modelling framework.Comment: Biometrics (2019

Monotone Hurwitz numbers in genus zero

Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of the branched covers counted by the Hurwitz numbers, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two results that are reminiscent of those for classical Hurwitz numbers. The first is the monotone join-cut equation, a partial differential equation with initial conditions that characterizes the generating function for monotone Hurwitz numbers in arbitrary genus. The second is our main result, in which we give an explicit formula for monotone Hurwitz numbers in genus zero.Comment: 22 pages, submitted to the Canadian Journal of Mathematic

Hole distribution for (Sr,Ca,Y,La)_14 Cu_24 O_41 ladder compounds studied by x-ray absorption spectroscopy

The unoccupied electronic structure for the Sr_14Cu_24O_41 family of two-leg ladder compounds was investigated for different partial substitutions of Sr^2+ by Ca^2+, leaving the nominal hole count constant, and by Y^3+ or La^3+, reducing the nominal hole count from its full value of 6 per formula unit. Using polarization-dependent x-ray absorption spectroscopy on single crystals, hole states on both the chain and ladder sites could be studied. While for intermediate hole counts all holes reside on O sites of the chains, a partial hole occupation on the ladder sites in orbitals oriented along the legs is observed for the fully doped compound Sr_14Cu_24O_41. On substitution of Ca for Sr orbitals within the ladder planes but perpendicular to the legs receive some hole occupation as well.Comment: 10 pages RevTeX style with 7 embedded figures + 1 table; accepted by Phys. Rev.

Biases in the relationship between dream threats and level of anxiety upon awakening

Objectives:\ud Controlling report length in dream content analysis comprises a significant methodological problem. Individual differences occur in report length which can influence category coding and rating scales. Differences are also found in dream content by sex and age. The aim of this study is to determine the bias of certain variables in dream content analysis when using rating scales, coding systems and questionnaires. As such, an evaluation was performed of the bias of these variables on the relationship between anxiety upon awakening, social threats (ST) and terrifying threats (TT) established in a previous study.\ud Methods: The sample consisted of 215 dreams collected in dreamers' homes (63 belonged to men and 152 to women). The dreamer's level of anxiety upon awakening was assessed with the CEAD. The level of social and terrifying threats in the content of the dreams was also assessed. Other variables entered into the analysis were sex, age, dream length, number of hours before answering the questionnaire, number of hours' sleep and the frequency with which the dreamer suffers nightmares.\ud Results:\ud Use of the Mann Whitney U found significant differences by sex in the dreamer's nightmare frequency (z=-2.53 p=.011), in terrifying threats in the dream (z=-2.03 p= .042) and by dream time (z=-2.51 p=.012). The Spearman Rho correlation coefficient indicated a positive relationship between anxiety upon awakening and nightmare frequency (Rho=.26 p<.001). Social and terrifying threats were also positively correlated with word count and the number of dream characters (Rho=.37 p<.001, Rho=.17 p=.010). Both anxiety upon awakening and social and terrifying threats were negatively correlated with the age of the dreamer (RhoCEAD-AGE=-.20 p=.006, RhoST-AGE=-.30 p<.001, RhoTT-AGE=-.37 p<.001). Possible biases due to sex, age, word count and the number of characters were statistically controlled by means of partial correlation. Through the use of partial correlations, the significance between anxiety upon awakening, social threats and terrifying threats in the dream was observed to be maintained (rCEAD-TS=.17 p=.025, rCEAD-TT=.19 p=.011).\ud Conclusion:\ud The sex, age of the dreamer, the report word count and the number of dream characters must be controlled in research into dream content. In addition, after eliminating these biases, a significant relationship was confirmed between threats which appear in the dream and the dreamer's level of anxiety upon awakening