Bayesian confidence in optimal decisions

The optimal way to make decisions in many circumstances is to track the difference in evidence collected in favour of the options. The drift diffusion model (DDM) implements this approach, and provides an excellent account of decisions and response times. However, existing DDM-based models of confidence exhibit certain deficits, and many theories of confidence have used alternative, non-optimal models of decisions. Motivated by the historical success of the DDM, we ask whether simple extensions to this framework might allow it to better account for confidence. Motivated by the idea that the brain will not duplicate representations of evidence, in all model variants decisions and confidence are based on the same evidence accumulation process. We compare the models to benchmark results, and successfully apply 4 qualitative tests concerning the relationships between confidence, evidence, and time, in a new preregistered study. Using computationally cheap expressions to model confidence on a trial-by-trial basis, we find that a subset of model variants also provide a very good to excellent account of precise quantitative effects observed in confidence data. Specifically, our results favour the hypothesis that confidence reflects the strength of accumulated evidence penalised by the time taken to reach the decision (Bayesian readout), with the penalty applied not perfectly calibrated to the specific task context. These results suggest there is no need to abandon the DDM or single accumulator models to successfully account for confidence reports

Optimal Decisions with Limited Information

This thesis considers static and dynamic team decision problems in both stochastic and deterministic settings. The team problem is a cooperative game, where a number of players make up a team that tries to optimize a given cost induced by the uncertainty of nature. The uncertainty is modeled as either stochastic, which gives the stochastic team problem, or modelled as deterministic where the team tries to optimize the worst case scenario. Both the stochastic and deterministic static team problems are stated and solved in a linear quadratic setting. It is shown that linear decisions are optimal in both the stochastic and deterministic framework. The dynamic team problem is formulated using well known results from graph theory. The dynamic interconnection structure is described by a graph. It appears natural to use a graph theoretical formulation to examine how a decision by a member of the team affects the rest of the members. Conditions for tractability of the dynamic team problem are given in terms of the graph structure. Tractability of a new class of information constrained team problems is shown, which extends existing results. For the presented tractable classes, necessary and sufficient conditions for stabilizability are given. The state feedback $mathcal{H}_2$ and $mathcal{H}_{infty}$ dynamic team problems are solved using a novel approach. The new approach is based on the crucial idea of disturbance feedback, which is used to separate the controller effect from the measured output, to eliminate the controller's dual role. Finally, a generalized stochastic linear quadratic control problem is considered. A broad class of team problems can be modeled by imposing quadratic constraints of correlation type. Also, power constraints on the control signals are very common. This motivates the development of a generalized control theory for both the finite and infinite horizon case, where power constraints are imposed. It is shown that the solution can be found using finite dimensional convex optimization

Optimal decisions in two-stage bundling

We develop a generalised framework for pure bundling where buyer tastes for two goods are assumed to follow a normal distribution. In the literature optimal bundling decisions have been considered under the assumption that the weights of the two goods are Öxed and equal. The only consideration is then to choose the proÖt maximising optimal price. Our approach is di§erent and much more realistic. The monopolist Örst decides on the optimal weights of the two goods and in the second stage derives the proÖt maximising bundle price. Welfare and policy implications of our approach are derived and comparisons are made with those of the Öxed weights approach

Optimal Decisions in a Time Priority Queue

Elementary Schoolhttps://egrove.olemiss.edu/phay_jon/1633/thumbnail.jp