Adaptive Probability Theory: Human Biases as an Adaptation

Humans make mistakes in our decision-making and probability judgments. While the heuristics used for decision-making have been explained as adaptations that are both efficient and fast, the reasons why people deal with probabilities using the reported biases have not been clear. We will see that some of these biases can be understood as heuristics developed to explain a complex world when little information is available. That is, they approximate Bayesian inferences for situations more complex than the ones in laboratory experiments and in this sense might have appeared as an adaptation to those situations. When ideas as uncertainty and limited sample sizes are included in the problem, the correct probabilities are changed to values close to the observed behavior. These ideas will be used to explain the observed weight functions, the violations of coalescing and stochastic dominance reported in the literature

Optimal Remote State Estimation for Self-Propelled Particle Models

We investigate the design of a remote state estimation system for a self-propelled particle (SPP). Our framework consists of a sensing unit that accesses the full state of the SPP and an estimator that is remotely located from the sensing unit. The sensing unit must pay a cost when it chooses to transmit information on the state of the SPP to the estimator; and the estimator computes the best estimate of the state of the SPP based on received information. In this paper, we provide methods to design transmission policies and estimation rules for the sensing unit and estimator, respectively, that are optimal for a given cost functional that combines state estimation distortion and communication costs. We consider two notions of optimality: joint optimality and person-by-person optimality. Our main results show the existence of a jointly optimal solution and describe an iterative procedure to find a person-by-person optimal solution. In addition, we explain how the remote estimation scheme can be applied to tracking of animal movements over a costly communication link. We also provide experimental results to show the effectiveness of the scheme.Comment: a part of the article was submitted to IEEE Conference on Decision and Control 201