Aversion to ambiguity and model misspecification in dynamic stochastic environments

Preferences that accommodate aversion to subjective uncertainty and its potential misspecification in dynamic settings are a valuable tool of analysis in many disciplines. By generalizing previous analyses, we propose a tractable approach to incorporating broadly conceived responses to uncertainty. We illustrate our approach on some stylized stochastic environments. By design, these discrete time environments have revealing continuous time limits. Drawing on these illustrations, we construct recursive representations of intertemporal preferences that allow for penalized and smooth ambiguity aversion to subjective uncertainty. These recursive representations imply continuous time limiting Hamilton–Jacobi–Bellman equations for solving control problems in the presence of uncertainty.Published versio

Discovery-led refinement in e-discovery investigations: sensemaking, cognitive ergonomics and system design.

Given the very large numbers of documents involved in e-discovery investigations, lawyers face a considerable challenge of collaborative sensemaking. We report findings from three workplace studies which looked at different aspects of how this challenge was met. From a sociotechnical perspective, the studies aimed to understand how investigators collectively and individually worked with information to support sensemaking and decision making. Here, we focus on discovery-led refinement; specifically, how engaging with the materials of the investigations led to discoveries that supported refinement of the problems and new strategies for addressing them. These refinements were essential for tractability. We begin with observations which show how new lines of enquiry were recursively embedded. We then analyse the conceptual structure of a line of enquiry and consider how reflecting this in e-discovery support systems might support scalability and group collaboration. We then focus on the individual activity of manual document review where refinement corresponded with the inductive identification of classes of irrelevant and relevant documents within a collection. Our observations point to the effects of priming on dealing with these efficiently and to issues of cognitive ergonomics at the human–computer interface. We use these observations to introduce visualisations that might enable reviewers to deal with such refinements more efficiently

On the contraction method with degenerate limit equation

A class of random recursive sequences (Y_n) with slowly varying variances as arising for parameters of random trees or recursive algorithms leads after normalizations to degenerate limit equations of the form X\stackrel{L}{=}X. For nondegenerate limit equations the contraction method is a main tool to establish convergence of the scaled sequence to the ``unique'' solution of the limit equation. In this paper we develop an extension of the contraction method which allows us to derive limit theorems for parameters of algorithms and data structures with degenerate limit equation. In particular, we establish some new tools and a general convergence scheme, which transfers information on mean and variance into a central limit law (with normal limit). We also obtain a convergence rate result. For the proof we use selfdecomposability properties of the limit normal distribution which allow us to mimic the recursive sequence by an accompanying sequence in normal variables.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000017