Natural statistics for spectral samples

Spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric functions, k-statistics and polykays. We construct spectral k-statistics as unbiased estimators of cumulants of trace powers of a suitable random matrix. Moreover we define normalized spectral polykays in such a way that when the sampling is from an infinite population they return products of free cumulants.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1107 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Distributed utterances

I propose an apparatus for handling intrasentential change in context. The standard approach has problems with sentences with multiple occurrences of the same demonstrative or indexical. My proposal involves the idea that contexts can be complex. Complex contexts are built out of (“simple”) Kaplanian contexts by ordered n-tupling. With these we can revise the clauses of Kaplan’s Logic of Demonstratives so that each part of a sentence is taken in a different component of a complex context. I consider other applications of the framework: to agentially distributed utterances (ones made partly by one speaker and partly by another); to an account of scare-quoting; and to an account of a binding-like phenomenon that avoids what Kit Fine calls “the antinomy of the variable.

Healthcare provider perceptions of clinical prediction rules

Objectives: To examine internal medicine and emergency medicine healthcare provider perceptions of usefulness of specific clinical prediction rules. Setting: The study took place in two academic medical centres. A web-based survey was distributed and completed by participants between 1 January and 31 May 2013. Participants: Medical doctors, doctors of osteopathy or nurse practitioners employed in the internal medicine or emergency medicine departments at either institution. Primary and secondary outcome measures: The primary outcome was to identify the clinical prediction rules perceived as most useful by healthcare providers specialising in internal medicine and emergency medicine. Secondary outcomes included comparing usefulness scores of specific clinical prediction rules based on provider specialty, and evaluating associations between usefulness scores and perceived characteristics of these clinical prediction rules. Results: Of the 401 healthcare providers asked to participate, a total of 263 (66%), completed the survey. The CHADS2 score was chosen by most internal medicine providers (72%), and Pulmonary Embolism Rule-Out Criteria (PERC) score by most emergency medicine providers (45%), as one of the top three most useful from a list of 24 clinical prediction rules. Emergency medicine providers rated their top three significantly more positively, compared with internal medicine providers, as having a better fit into their workflow (p=0.004),helping more with decision-making (p= 0.037), better fitting into their thought process when diagnosing patients (p= 0.001) and overall, on a 10-point scale, more useful (p= 0.009). For all providers, the perceived qualities of useful at point of care, helps with decision making, saves time diagnosing, fits into thought process, and should be the standard of clinical care correlated highly (\u3e= 0.65) with overall 10-point usefulness scores. Conclusions: Healthcare providers describe clear preferences for certain clinical prediction rules, based on medical specialty

Generalized monotonic functional mixed models with application to modelling normal tissue complications

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73586/1/j.1467-9876.2007.00606.x.pd

CAR-Net: Clairvoyant Attentive Recurrent Network

We present an interpretable framework for path prediction that leverages dependencies between agents' behaviors and their spatial navigation environment. We exploit two sources of information: the past motion trajectory of the agent of interest and a wide top-view image of the navigation scene. We propose a Clairvoyant Attentive Recurrent Network (CAR-Net) that learns where to look in a large image of the scene when solving the path prediction task. Our method can attend to any area, or combination of areas, within the raw image (e.g., road intersections) when predicting the trajectory of the agent. This allows us to visualize fine-grained semantic elements of navigation scenes that influence the prediction of trajectories. To study the impact of space on agents' trajectories, we build a new dataset made of top-view images of hundreds of scenes (Formula One racing tracks) where agents' behaviors are heavily influenced by known areas in the images (e.g., upcoming turns). CAR-Net successfully attends to these salient regions. Additionally, CAR-Net reaches state-of-the-art accuracy on the standard trajectory forecasting benchmark, Stanford Drone Dataset (SDD). Finally, we show CAR-Net's ability to generalize to unseen scenes.Comment: The 2nd and 3rd authors contributed equall