The problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models is considered. While recursive formulae for evaluating ...the joint cumulative distribution function of such order statistics exist, their numerical implementation remains a challenging task. This task is tackled by presenting novel generalizations of known recursions. They are utilized to obtain exact results (calculated in rational arithmetic) as well as faithfully rounded results. Finally, some applications in goodness-of-fit testing, step-wise multiple hypothesis testing, and sample size calculation for studies with multiple endpoints are discussed.
•Recursions for the joint distribution function of order statistics are generalized.•Numerically stable and runtime-efficient implementations are provided.•Applications in statistical testing and sample size planning are described.
We give an adequate denotational semantics for languages with recursive higher-order types, continuous probability distributions, and soft constraints. These are expressive languages for building ...Bayesian models of the kinds used in computational statistics and machine learning. Among them are untyped languages, similar to Church and WebPPL, because our semantics allows recursive mixed-variance datatypes. Our semantics justifies important program equivalences including commutativity.
Our new semantic model is based on `quasi-Borel predomains'. These are a mixture of chain-complete partial orders (cpos) and quasi-Borel spaces. Quasi-Borel spaces are a recent model of probability theory that focuses on sets of admissible random elements. Probability is traditionally treated in cpo models using probabilistic powerdomains, but these are not known to be commutative on any class of cpos with higher order functions. By contrast, quasi-Borel predomains do support both a commutative probabilistic powerdomain and higher-order functions. As we show, quasi-Borel predomains form both a model of Fiore's axiomatic domain theory and a model of Kock's synthetic measure theory.
Recursion and self-embedding are at the heart of our ability to formulate our thoughts, articulate our imagination and share with other human beings. Nonetheless, controversy exists over the extent ...to which recursion is shared across all domains of syntax. A collection of 18 studies are presented here on the central linguistic property of recursion, examining a range of constructions in over a dozen languages representing great areal, typological and genetic diversity and spanning wide latitudes. The volume expands the topic to include prepositional phrases, possessives, adjectives, and relative clauses - our many vehicles to express creative thought - to provide a critical perspective on claims about how recursion connects to broader aspects of the mind. Parallel explorations across language families, literate and non-literate societies, children and adults are investigated and constitutes a new step in the generative tradition by simultaneously focusing on formal theory, acquisition and experimentation, and ecologically-sensitive fieldwork, and initiates a new community where these diverse experts collaborate.
The questions of the Lithuanian olympiad-2005 are presented and solutions are given.
Straipsnyje pateikiamos LIV Lietuvos moksleivių matematikos olimpiados (Visaginas, 2005–03–31) uždavinių sąlygos, ...sprendimas bei analizė.
We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new ...rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible.
Hjorth and Nies proposed notions of randomness corresponding to the higher recursion setting. In particular, they defined the notion of -Martin-Lof randomness. In this article we present examples of ...-Martin-Lof random reals which are obtained as measures of open sets.
PDF
