Irrelevant natural extension for choice functions

We consider coherent choice functions under the recent axiomatisation proposed by De Bock and De Cooman that guarantees a representation in terms of binary preferences, and we discuss how to define conditioning in this framework. In a multivariate context, we propose a notion of marginalisation, and its inverse operation called weak (cylindrical) extension. We combine this with our definition of conditioning to define a notion of irrelevance, and we obtain the irrelevant natural extension in this framework: the least informative choice function that satisfies a given irrelevance assessment

Marginal extension in the theory of coherent lower previsions

AbstractWe generalise Walley’s Marginal Extension Theorem to the case of any finite number of conditional lower previsions. Unlike the procedure of natural extension, our marginal extension always provides the smallest (most conservative) coherent extensions. We show that they can also be calculated as lower envelopes of marginal extensions of conditional linear (precise) previsions. Finally, we use our version of the theorem to study the so-called forward irrelevant product and forward irrelevant natural extension of a number of marginal lower previsions

Independent natural extension for sets of desirable gambles

We investigate how to combine a number of marginal coherent sets of desirable gambles into a joint set using the properties of epistemic irrelevance and independence. We provide formulas for the smallest such joint, called their independent natural extension, and study its main properties. The independent natural extension of maximal sets of gambles allows us to define the strong product of sets of desirable gambles. Finally, we explore an easy way to generalise these results to also apply for the conditional versions of epistemic irrelevance and independence

Finitely additive extensions of distribution functions and moment sequences: The coherent lower prevision approach

We study the information that a distribution function provides about the finitely additive probability measure inducing it. We show that in general there is an infinite number of finitely additive probabilities associated with the same distribution function. Secondly, we investigate the relationship between a distribution function and its given sequence of moments. We provide formulae for the sets of distribution functions, and finitely additive probabilities, associated with some moment sequence, and determine under which conditions the moments determine the distribution function uniquely. We show that all these problems can be addressed efficiently using the theory of coherent lower previsions

The Moment Problem for Finitely Additive Probabilities

We study the moment problem for finitely additive probabilities and show that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions

Lexicographic choice functions

We investigate a generalisation of the coherent choice functions considered by Seidenfeld et al. (2010), by sticking to the convexity axiom but imposing no Archimedeanity condition. We define our choice functions on vector spaces of options, which allows us to incorporate as special cases both Seidenfeld et al.'s (2010) choice functions on horse lotteries and sets of desirable gambles (Quaeghebeur, 2014), and to investigate their connections. We show that choice functions based on sets of desirable options (gambles) satisfy Seidenfeld's convexity axiom only for very particular types of sets of desirable options, which are in a one-to-one relationship with the lexicographic probabilities. We call them lexicographic choice functions. Finally, we prove that these choice functions can be used to determine the most conservative convex choice function associated with a given binary relation.Comment: 27 page

Environmental context of endophyte symbioses: Interacting effects of water stress and insect herbivory

Symbiotic associations between grasses and fungal endophytes are generally regarded as mutualistic, yet benefits to host plants may vary with environmental context. Previous studies have emphasized how endophytes influence plant responses to single stressors. In contrast, the outcome of endophyte-grass interactions under simultaneous biotic and abiotic stresses remains poorly explored. We hypothesized that benefits from endophyte symbiosis become most apparent in "complex" environments where hosts experience multiple stresses. We evaluated the performance of endophyte-infected (E+) vs. endophyte-uninfected (E-) Lolium multiflorum plants in a factorial experiment with water supply (control vs. drought) and insect herbivory (with aphids vs. without aphids). Endophyte infection delayed tiller production in well-watered plants, while water stress reduced tillering in E- plants. Endophyte mediation of herbivory tolerance was contingent on water supply. Whereas aphid herbivory was detrimental to E+ plants in well-watered soils, aphids interacted with drought stress in decreasing the reproductive output of E- but not E+ plants. Moreover, endophyte presence decreased aphid densities on drought-stressed plants only. Thus, endophyte symbiosis enhanced host tolerance to overlapping biotic and abiotic stresses, although infected plants failed to outgrow their uninfected counterparts. These results support the view that mutualistic endophyte effects may not arise in low-stress environments. © 2011 by The University of Chicago. All rights reserved.Fil: Miranda, M. Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Omacini, Marina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Chaneton, Enrique Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; Argentin