Intersection types for unbind and rebind

We define a type system with intersection types for an extension of lambda-calculus with unbind and rebind operators. In this calculus, a term with free variables, representing open code, can be packed into an "unbound" term, and passed around as a value. In order to execute inside code, an unbound term should be explicitly rebound at the point where it is used. Unbinding and rebinding are hierarchical, that is, the term can contain arbitrarily nested unbound terms, whose inside code can only be executed after a sequence of rebinds has been applied. Correspondingly, types are decorated with levels, and a term has type decorated with k if it needs k rebinds in order to reduce to a value. With intersection types we model the fact that a term can be used differently in contexts providing different numbers of unbinds. In particular, top-level terms, that is, terms not requiring unbinds to reduce to values, should have a value type, that is, an intersection type where at least one element has level 0. With the proposed intersection type system we get soundness under the call-by-value strategy, an issue which was not resolved by previous type systems.Comment: In Proceedings ITRS 2010, arXiv:1101.410

Trees from Functions as Processes

Levy-Longo Trees and Bohm Trees are the best known tree structures on the {\lambda}-calculus. We give general conditions under which an encoding of the {\lambda}-calculus into the {\pi}-calculus is sound and complete with respect to such trees. We apply these conditions to various encodings of the call-by-name {\lambda}-calculus, showing how the two kinds of tree can be obtained by varying the behavioural equivalence adopted in the {\pi}-calculus and/or the encoding

Modelling Bird Migration with Motus Data and Bayesian State-Space Models

Bird migration is a poorly-known yet important phenomenon, as understanding movement patterns of birds can inform conservation strategies and public health policy for animal-borne diseases. Recent advances in wildlife tracking technology, in particular the Motus system, have allowed researchers to track even small flying birds and insects with radio transmitters that weigh fractions of a gram. This system relies on a community-based distributed sensor network that detects tagged animals as they move through the detection nodes on journeys that range from small local movements to intercontinental migrations. The quantity of data generated by the Motus system is unprecedented, is on its way to surpass the size of all other centralized databases of animal detection and requires novel statistical methods. Building from the bsam package in R, I propose two new biologically informed Bayesian state-space models for animal movement in JAGS that include informed assumptions about songbird behavior. I evaluate the models using a simulation study in realistic conditions of data missingness. One of these models is generalized to a hierarchical version that fits population-level movement through joint estimation of movement parameters over multiple animal tracks. To apply the models, I then employ a localization routine on a Motus data set from migrating songbirds (Red-eyed Vireos - Vireo olivaceus) from the Eastern coast of North America. This allows me to apply the new hierarchical model and its predecessor to estimate unobserved locations and behaviors. Migratory flights were observed to occur mostly in the evenings along the coast and directed migratory flights were detected over water over e.g. the Bay of Fundy, the Long Island Sound and the New York Bight. Area-restricted searches were confined to coastal areas, in particular the Gulf of Maine, Long Island and Cape May

Extending Valuation to Controlled Value Functions and Non- Uniform Scaling with Generalised Unobserved Variances

A common by-product of discrete choice models is the marginal rate of substitution between two attributes (one usually measured in monetary units). The typical output is a point estimate value. In reality there is a distribution of values around a mean which is the product of non-linearities in the role of each attribute in utility space, as well as covariate influences that condition the role of taste weights in dimensioning the relative importance of each attribute in a choice setting. This paper considers the broad issue of breaking away from valuation to valuation functions, the need to use appropriate experimental design procedures and mean centering or orthogonal codes in estimation with translation back to the real attribute levels in order to reveal the appropriate evaluation distributions. By relaxing the strict constant variance condition in practical discrete choice models, we are able further to absorb unobserved sources of behavioural variability which if not allowed for tend to produce an overvaluation. We illustrate the methods discussed above with a case study on choice of existing and potential commuter modes in six Australian capital cities

Relational Parametricity for Computational Effects

According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricity provides a powerful tool for establishing data abstraction properties, proving equivalences of datatypes, and establishing equalities of programs. Such properties have been well studied in a pure functional setting. Many programs, however, exhibit computational effects, and are not accounted for by the standard theory of relational parametricity. In this paper, we develop a foundational framework for extending the notion of relational parametricity to programming languages with effects.Comment: 31 pages, appears in Logical Methods in Computer Scienc

An Introduction to Inductive Statistical Inference: from Parameter Estimation to Decision-Making

These lecture notes aim at a post-Bachelor audience with a background at an introductory level in Applied Mathematics and Applied Statistics. They discuss the logic and methodology of the Bayes-Laplace approach to inductive statistical inference that places common sense and the guiding lines of the scientific method at the heart of systematic analyses of quantitative-empirical data. Following an exposition of exactly solvable cases of single- and two-parameter estimation problems, the main focus is laid on Markov Chain Monte Carlo (MCMC) simulations on the basis of Hamiltonian Monte Carlo sampling of posterior joint probability distributions for regression parameters occurring in generalised linear models for a univariate outcome variable. The modelling of fixed effects as well as of correlated varying effects via multi-level models in non-centred parametrisation is considered. The simulation of posterior predictive distributions is outlined. The assessment of a model's relative out-of-sample posterior predictive accuracy with information entropy-based criteria WAIC and LOOIC and model comparison with Bayes factors are addressed. Concluding, a conceptual link to the behavioural subjective expected utility representation of a single decision-maker's choice behaviour in static one-shot decision problems is established. Vectorised codes for MCMC simulations of multi-dimensional posterior joint probability distributions with the Stan probabilistic programming language implemented in the statistical software R are provided. The lecture notes are fully hyperlinked. They direct the reader to original scientific research papers, online resources on inductive statistical inference, and to pertinent biographical information.Comment: 161 pages, 22 *.eps figures, LaTeX2e, hyperlinked references. First thorough revision, extended list of reference

Pension Portability and Labour Mobility in the United States. New Evidence from SIPP Data

We explore the role of employer provided pensions on job mobility choices using data from the Survey of Income and Program Participation. Defined benefit plans are found to have a significant negative effect on mobility. However, we find no significant evidence that the potential pension portability losses deter job mobility among workers covered by these plans. We also find that the portability policy change implemented by the Tax Reform Act of 1986 had only minor effects on mobility. Puzzlingly, defined contribution plans, although fully portable, are found to have an impact similar to defined benefit plans. Evidence of compensation premiums accruing to workers in pension, union and health insurance covered jobs supports the view that workers are less likely to leave 'good jobs'.Labour mobility ; Pension portability ; Switching regression models