Local limit theorems via Landau-Kolmogorov inequalities

In this article, we prove new inequalities between some common probability metrics. Using these inequalities, we obtain novel local limit theorems for the magnetization in the Curie-Weiss model at high temperature, the number of triangles and isolated vertices in Erd\H{o}s-R\'{e}nyi random graphs, as well as the independence number in a geometric random graph. We also give upper bounds on the rates of convergence for these local limit theorems and also for some other probability metrics. Our proofs are based on the Landau-Kolmogorov inequalities and new smoothing techniques.Comment: Published at http://dx.doi.org/10.3150/13-BEJ590 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Generalized gamma approximation with rates for urns, walks and trees

We study a new class of time inhomogeneous P\'olya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters, a class which includes the Rayleigh, half-normal and gamma distributions. Our main tool is Stein's method combined with characterizing the generalized gamma limiting distributions as fixed points of distributional transformations related to the equilibrium distributional transformation from renewal theory. We identify special cases of these urn models in recursive constructions of random walk paths and trees, yielding rates of convergence for local time and height statistics of simple random walk paths, as well as for the size of random subtrees of uniformly random binary and plane trees.Comment: Published at http://dx.doi.org/10.1214/15-AOP1010 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Total variation error bounds for geometric approximation

We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a coupling between the original distribution and the "discrete equilibrium" distribution from renewal theory. We illustrate the approach in four non-trivial examples: the geometric sum of independent, non-negative, integer-valued random variables having common mean, the generation size of the critical Galton-Watson process conditioned on non-extinction, the in-degree of a randomly chosen node in the uniform attachment random graph model and the total degree of both a fixed and randomly chosen node in the preferential attachment random graph model.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ406 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Author vs. Audience: Bridging the Gap Between Interpretation and Intent

Since Roland Barthes first published his essay “Le mort de l’auteur” (“The death of the author”) in the 1960s, literary critics have reconsidered the role of the author in the interpretation of media. Barthes and others have argued that the author’s intentions matter little after a work of art is handed off for public consumption, and that art is up for interpretation with the audience playing a greater role in its meaning. Others, however, argue that the author is the ultimate authority on the meaning of their work, and that authorial intent is the most important aspect to consider when examining a piece of media. This paper seeks to resolve the conflict between authorial intent and audience interpretation. The reason we might be tempted to lean on the author for guidance, and which viewpoint we should consider in art analysis were examined. Arguments from the perspectives of both a creator and a consumer were compared. While both views have their strengths and weaknesses, one cannot neatly separate the author from the art when examining their work, and so a combination of both authorial intent and audience interpretation should be taken into consideration when analyzing a piece of media

Specialist Legal Clinics: their pedagogy, risks and payoffs as externships

Within clinical legal education there is a great deal of discussion at the moment about externships. Part of the motivation for all this conversation is the desire of law schools to get in on the clinical ‘act’ as inexpensively as possible. Some law Deans have the view that they can outsource clinics to firms and agencies and achieve reputable clinical outcomes with little or no expenditure. We beg to differ and in this article we explain why law school management of an externship experience is resource intensive and nearly as complicated as an in-house clinic. It may be less expensive, but an externship can never be set and forgotten.We also discuss the peculiarities of specialist externships, since many externship sites are in fact specialist legal practices. In fact, the attraction of an externship is the access it provides for students to participate in a specialised area of law, while overseen by specialist lawyers. We set out in detail the advantages and disadvantages of operating such placements and connect these to the recent Australian Best Practices in clinical legal education. To begin with however, we need to define some terms as they are used in an Australian clinical setting

A Quaker Girl

https://digitalcommons.library.umaine.edu/mmb-vp/6093/thumbnail.jp