Imprecise probabilistic inference from sequential data.

Although the Bayesian paradigm is an important benchmark in studies of human inference, the extent to which it provides a useful framework to account for human behavior remains debated. We document systematic departures from Bayesian inference under correct beliefs, even on average, in the estimates by experimental subjects of the probability of a binary event following observations of successive realizations of the event. In particular, we find underreaction of subjects' estimates to the evidence ("conservatism") after only a few observations and at the same time overreaction after longer sequences of observations. This is not explained by an incorrect prior nor by many common models of Bayesian inference. We uncover the autocorrelation in estimates, which suggests that subjects carry imprecise representations of the decision situations, with noise in beliefs propagating over successive trials. But even taking into account these internal imprecisions and assuming various incorrect beliefs, we find that subjects' updates are inconsistent with the rules of Bayesian inference. We show how subjects instead considerably economize on the attention that they pay to the information relevant to the decision, and on the degree of control that they exert over their precise response, while giving responses fairly adapted to the task. A "noisy-counting" model of probability estimation reproduces the several patterns we exhibit in subjects' behavior. In sum, human subjects in our task perform reasonably well while greatly minimizing the amount of information that they pay attention to. Our results emphasize that investigating this economy of attention is crucial in understanding human decisions. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Resource-rational account of sequential effects in human prediction.

An abundant literature reports on 'sequential effects' observed when humans make predictions on the basis of stochastic sequences of stimuli. Such sequential effects represent departures from an optimal, Bayesian process. A prominent explanation posits that humans are adapted to changing environments, and erroneously assume non-stationarity of the environment, even if the latter is static. As a result, their predictions fluctuate over time. We propose a different explanation in which sub-optimal and fluctuating predictions result from cognitive constraints (or costs), under which humans however behave rationally. We devise a framework of costly inference, in which we develop two classes of models that differ by the nature of the constraints at play: in one case the precision of beliefs comes at a cost, resulting in an exponential forgetting of past observations, while in the other beliefs with high predictive power are favored. To compare model predictions to human behavior, we carry out a prediction task that uses binary random stimuli, with probabilities ranging from 0.05 to 0.95. Although in this task the environment is static and the Bayesian belief converges, subjects' predictions fluctuate and are biased toward the recent stimulus history. Both classes of models capture this 'attractive effect', but they depart in their characterization of higher-order effects. Only the precision-cost model reproduces a 'repulsive effect', observed in the data, in which predictions are biased away from stimuli presented in more distant trials. Our experimental results reveal systematic modulations in sequential effects, which our theoretical approach accounts for in terms of rationality under cognitive constraints.

Efficient coding of numbers explains decision bias and noise.

Humans differentially weight different stimuli in averaging tasks, which has been interpreted as reflecting encoding bias. We examine the alternative hypothesis that stimuli are encoded with noise and then optimally decoded. Under a model of efficient coding, the amount of noise should vary across stimuli and depend on statistics of the stimuli. We investigate these predictions through a task in which the participants are asked to compare the averages of two series of numbers, each sampled from a prior distribution that varies across blocks of trials. The participants encode numbers with a bias and a noise that both depend on the number. Infrequently occurring numbers are encoded with more noise. We show how an efficient-coding, Bayesian-decoding model accounts for these patterns and best captures the participants' behaviour. Finally, our results suggest that Wei and Stocker's "law of human perception", which relates the bias and variability of sensory estimates, also applies to number cognition.

Human inference in changing environments with temporal structure.

To make informed decisions in natural environments that change over time, humans must update their beliefs as new observations are gathered. Studies exploring human inference as a dynamical process that unfolds in time have focused on situations in which the statistics of observations are history-independent. Yet, temporal structure is everywhere in nature and yields history-dependent observations. Do humans modify their inference processes depending on the latent temporal statistics of their observations? We investigate this question experimentally and theoretically using a change-point inference task. We show that humans adapt their inference process to fine aspects of the temporal structure in the statistics of stimuli. As such, humans behave qualitatively in a Bayesian fashion but, quantitatively, deviate away from optimality. Perhaps more importantly, humans behave suboptimally in that their responses are not deterministic, but variable. We show that this variability itself is modulated by the temporal statistics of stimuli. To elucidate the cognitive algorithm that yields this behavior, we investigate a broad array of existing and new models that characterize different sources of suboptimal deviations away from Bayesian inference. While models with "output noise" that corrupts the response-selection process are natural candidates, human behavior is best described by sampling-based inference models, in which the main ingredient is a compressed approximation of the posterior, represented through a modest set of random samples and updated over time. This result comes to complement a growing literature on sample-based representation and learning in humans. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Biases and Variability from Costly Bayesian Inference.

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 the 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 in 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.