Coherency conditions for finite exchangeable inference

Summary We idenify the invertible coherent functional relation between an array of asserted conditional probabilities and the probability distribution for the sum of events that are regarded exchangeably, in the regular case thatP(N _N+1 |S _N =a) ∈ (0, 1) for everya=0, 1, ...,N. The result is used to construct a useful algebraic and geometrical representation of all coherent inferences in the regular case, including those that are nonlinear in the sum of the conditioning events. The special case in which conditional probabilities mimic observed frequencies within (0, 1) receives an exact solution, which allows an easy interpretation of its surprising consequences. Finally, we introduce a new direction in research on prior opinion assessment that this approach, inverse to the usual one, suggests.     

Caffeine intake is not associated with serum testosterone levels in adult men: cross-sectional findings from the NHANES 1999–2004 and 2011–2012

Objective: The association of caffeine intake with testosterone remains unclear. We evaluated the association of caffeine intake with serum testosterone among American men and determined whether this association varied by race/ethnicity and measurements of adiposity.

Methods: Data were analyzed for 2581 men (≥20?years old) who participated in the cycles of the NHANES 1999–2004 and 2011–2012, a cross-sectional study. Testosterone (ng/mL) was measured by immunoassay among men who participated in the morning examination session. We analyzed 24-h dietary recall data to estimate caffeine intake (mg/day). Multivariable weighted linear regression models were conducted.

Results: We identified no linear relationship between caffeine intake and testosterone levels in the total population, but there was a non-linear association (p_nonlinearity?p_nonlinearity?≤?.03 both) and only among men with waist circumference <102?cm and body mass index <25?kg/m² (p_nonlinearity?Conclusion: No linear association was identified between levels of caffeine intake and testosterone in US men, but we observed a non-linear association, including among racial/ethnic groups and measurements of adiposity in this cross-sectional study. These associations are warranted to be investigated in larger prospective studies.     

Estimating hybrid frequency moments of data streams

We consider the problem of estimating hybrid frequency moments of two dimensional data streams. In this model, data is viewed to be organized in a matrix form (A _i,j )_1≤i,j,≤n . The entries A _i,j are updated coordinate-wise, in arbitrary order and possibly multiple times. The updates include both increments and decrements to the current value of A _i,j . The hybrid frequency moment F _p,q (A) is defined as \(\sum_{j=1}^{n}(\sum_{i=1}^{n}{A_{i,j}}^{p})^{q}\) and is a generalization of the frequency moment of one-dimensional data streams.We present the first \(\tilde{O}(1)\) space algorithm for the problem of estimating F _p,q for p∈[0,2] and q∈[0,1] to within an approximation factor of 1±ε. The \(\tilde{O}\) notation hides poly-logarithmic factors in the size of the stream m, the matrix size n and polynomial factors of ε ^?1. We also present the first \(\tilde{O}(n^{1-1/q})\) space algorithm for estimating F _p,q for p∈[0,2] and q∈(1,2].     

Overcoming Language Barriers in the Informed Consent Process: Regulatory and Compliance Issues with the Use of the “Short Form”

Language barriers in the informed consent process can be a significant impediment when recruiting non-English speaking subjects into clinical research studies. Regulatory guidelines indicate that the short form procedure be utilized in such circumstances. In this paper, we examine some of the ambiguities in the regulatory framework, the resulting need for institutional policy guidelines, and compliance issues with the short form process.     

An Application of Operational-Subjective Statistical Methods to Rational Expectations

This article presents a sequential scoring analysis of six econometric forecast distributions for the main components of the annual U.S. gross national product (GNP) accounts—nominal GNP, real GNP, and the implicit price deflator. Analysis of sequential forecasts is presented in terms of proper scoring rules. Computations relevant to the calibration and refinement properties of the forecast distributions are discussed. Annual data are studied for the period 1952–1982. The six forecast distributions are distinguished by the different stances they entail with respect to a subjectivist characterization of the rational-expectations hypothesis.     

Minimum failure explanations for path vector routing changes

Path vector protocols in routing networks convey entire path information to each destination. When links fail, affected paths are replaced by new paths, and by observing the entire path information, one might hope to infer the failed links that caused these changes. However, inferring the exact topological changes behind observed routing changes may not be possible due to limited information, and the same changes may be explained by more than one set of candidate failures. In this paper, using a simple path vector routing model, we present the problem of finding the candidate set with minimum number of failures to explain observed route changes. We call this problem the minimum e-set problem and present algorithms for solving it optimally for certain cases. We also show that the minimum e-set problem is NP-complete in the general case. This material is based upon work supported by the Defense Advanced Research Projects Agency (DARPA) under Contract No N66001-04-1-8926 and by National Science Fundation(NSF) under Contract No ANI-0221453. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the DARPA or NSF. Part of the work was done when Akash Nanavati was at DA-IICT, India     

Defining the Research Category in Pediatric Phase I Oncology Trials

Clinical research studies in children are classified by risk into three major categories. These are as follows: a) minimal risk studies, b) more than minimal risk studies but with benefit, and c) studies with minor increase over minimal risk but with no benefit.

Pediatric Phase I oncology trials, which are conducted in a highly vulnerable population of severely ill children with cancer, are designed to establish safety and to determine the maximum tolerated dose (MTD), as well as establish dose limiting toxicity (DLT). These types of studies can be associated with significant risk. The research design of such high- risk studies, which comprise short-term treatments with varying doses, is generally not associated with any clinical benefit. Classification of the research category in these pediatric studies poses a special problem for the Institutional Review Board (IRB) with major implications for the consenting process. The challenges associated with the classification of such studies are discussed in this article.     

Combining expert probabilities using the product of odds

We resolve a useful formulation of the question how a statistician can coherently incorporate the information in a consulted expert??s probability assessment for an event into a personal posterior probability assertion. Using a framework that recognises the total information available as composed of units available only to each of them along with units available to both, we show: that a sufficient statistic for all the information available to both the expert and the statistician is the product of their odds ratios in favour of the event; that the geometric mean of their two probabilities specifies a contour of pairs of assertions in the unit-square that yield the same posterior probability; that the information-combining function is parameterised by an unknown probability for the event conditioned only on the unspecified information common to both the statistician and the expert; and that an assessable mixing distribution over this unspecified probability allows an integrable mixture distribution to represent a computable posterior probability. The exact results allow the identification of the subclass of coherent probabilities that are externally Bayesian operators. This subclass is equivalent to the class of combining functions that honour the principles of uniformity and compromise.