A hierarchy of twofold resource allocation automata supporting optimal sampling

We consider the problem of allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. More specifically, the user is presented with 'n' sets of data points, S 1, S 2, ..., S n , where the set S i has N i points drawn from two classes {ω 1, ω 2}. A random sample in set S i belongs to ω 1 with probability u i and to ω 2 with probability 1∈-∈u i , with {u i }. i∈=∈1, 2, ...n, being the quantities to be learnt. The problem is both interesting and non-trivial because while both n and each N i are large, the number of samples that can be drawn is bounded by a constant, c. We solve the problem by first modelling it as a Stochastic Non-linear Fractional Knapsack Problem. We then present a completely new on-line Learning Automata (LA) system, namely, the Hierarchy of Twofold Resource Allocation Automata (H-TRAA), whose primitive component is a Twofold Resource Allocation Automaton (TRAA), both of which are asymptotically optimal. Furthermore, we demonstrate empirically that the H-TRAA provides orders of magnitude faster convergence compared to the LAKG which represents the state-of-the-art. Finally, in contrast to the LAKG, the H-TRAA scales sub-linearly. Based on these results, we believe that the H-TRAA has also tremendous potential to handle demanding real-world applications

The impact of information about different absolute benefits and harms on intention to participate in colorectal cancer screening: A think-aloud study and online randomised experiment

Background There is considerable heterogeneity in individuals’ risk of disease and thus the absolute benefits and harms of population-wide screening programmes. Using colorectal cancer (CRC) screening as an exemplar, we explored how people make decisions about screening when presented with information about absolute benefits and harms, and how those preferences vary with baseline risk, between screening tests and between individuals. Method We conducted two linked studies with members of the public: a think-aloud study exploring decision making in-depth and an online randomised experiment quantifying preferences. In both, participants completed a web-based survey including information about three screening tests (colonoscopy, sigmoidosc