Elicitation of ambiguous beliefs with mixing bets

I consider the elicitation of ambiguous beliefs about an event and show how to identify the interval of relevant probabilities (representing ambiguity perception) for several classes of ambiguity averse preferences. The agent reveals her preference for mixing binarized bets on the uncertain event and its complement under varying betting odds. Under ambiguity aversion, mixing is informative about the interval of beliefs. In particular, the mechanism allows to distinguish ambiguous beliefs from point beliefs, and identifies the belief interval for maxmin preferences. For ambiguity averse smooth second order and variational preferences, the mechanism reveals inner bounds for the belief interval, which are sharp under additional assumptions. In an experimental study, participants perceive almost as much ambiguity for natural events (generated by the stock exchange and by a prisoners dilemma game) as for the Ellsberg Urn, indicating that ambiguity may play a role in real-world decision making

PROBABILISTIC INFERENCE FOR INTERVAL PROBABILITIES IN DECISION-MAKING PROCESSES

The present paper considers one approach to Bayes’ formula based probabilistic inference under interval values of relevant probabilities; the necessity of it is caused by the impossibility to obtain reliable deterministic values of the required probabilistic evaluations. The paper shows that the approach proves to be the best from the viewpoint of the required amount of calculations and visual representation of the results. The execution of the algorithm of probabilistic inference is illustrated using a classical task of decision making related to oil mining. For visualisation purposes, the state of initial and target information is modelled using probability trees.

Coherent frequentism

By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior distribution. The closure of the set of expected losses corresponding to the dual frequentist posteriors constrains decisions without arbitrarily forcing optimization under all circumstances. This decision theory reduces to those that maximize expected utility when the pair of frequentist posteriors is induced by an exact or approximate confidence set estimator or when an automatic reduction rule is applied to the pair. In such cases, the resulting frequentist posterior is coherent in the sense that, as a probability distribution of the parameter of interest, it satisfies the axioms of the decision-theoretic and logic-theoretic systems typically cited in support of the Bayesian posterior. Unlike the p-value, the confidence level of an interval hypothesis derived from such a measure is suitable as an estimator of the indicator of hypothesis truth since it converges in sample-space probability to 1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly extended to vector parameters of interest. The derivation of upper and lower confidence levels from valid and nonconservative set estimators is formalize

Stochastic models of evidence accumulation in changing environments

Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing world. What effect does such impermanence have on classical results about decision making? To address this question we use sequential analysis to derive a tractable model of evidence accumulation when the correct option changes in time. Our analysis shows that ideal observers discount prior evidence at a rate determined by the volatility of the environment, and the dynamics of evidence accumulation is governed by the information gained over an average environmental epoch. A plausible neural implementation of an optimal observer in a changing environment shows that, in contrast to previous models, neural populations representing alternate choices are coupled through excitation. Our work builds a bridge between statistical decision making in volatile environments and stochastic nonlinear dynamics.Comment: 26 pages, 7 figure