Biases and Variability from Costly Bayesian Inference

TL;DR

This paper presents a theoretical framework explaining human biases and variability in probabilistic inference as a trade-off between Bayesian reasoning and cognitive costs, with different costs leading to distinct bias patterns.

Contribution

It introduces a novel resource-rational model of Bayesian inference incorporating precision and unpredictability costs, explaining observed biases in sequential probability estimation.

Findings

Precision cost leads to overestimation of small probabilities and fluctuating biases.

Unpredictability cost causes underestimation of small probabilities and persistent biases.

The model predicts slow fluctuations in bias for a fair coin, highlighting complex human inference behaviors.

Abstract

When humans infer underlying probabilities from stochastic observations, they exhibit biases and variability that cannot be explained on the basis of sound, Bayesian manipulations of probability. This is especially salient when beliefs are updated as a function of sequential observations. We introduce a theoretical framework in which biases and variability emerge from a trade-off between Bayesian inference and a cognitive cost of carrying out probabilistic computations. We consider two forms of the cost: a precision cost and an unpredictability cost; these penalize beliefs that are less entropic and less deterministic, respectively. We apply our framework to the case of a Bernoulli variable: the bias of a coin is inferred from a sequence of coin flips. Theoretical predictions are qualitatively different depending on the form of the cost. A precision cost induces overestimation of small probabilities on average and a limited memory of past observations, and, consequently, a fluctuating bias. An unpredictability cost induces underestimation of small probabilities and a fixed bias that remains appreciable even for nearly unbiased observations. The case of a fair (equiprobable) coin, however, is singular, with non-trivial and slow fluctuations of the inferred bias. The proposed framework of costly Bayesian inference illustrates the richness of a 'resource-rational' (or 'bounded-rational') picture of seemingly irrational human cognition.