Autoregressive Large Language Models (LLMs) trained for next-word prediction have demonstrated remarkable proficiency at producing coherent text. But are they equally adept at forming coherent probability judgments? We use probabilistic identities and repeated judgments to assess the coherence of probability judgments made by LLMs. Our results show that the judgments produced by these models are often incoherent, displaying human-like systematic deviations from the rules of probability theory. Moreover, when prompted to judge the same event, the mean-variance relationship of probability judgments produced by LLMs shows an inverted-U-shaped like that seen in humans. We propose that these deviations from rationality can be explained by linking autoregressive LLMs to implicit Bayesian inference and drawing parallels with the Bayesian Sampler model of human probability judgments.

Simulating sampling algorithms with people has proven a useful method for efficiently probing and understanding their mental representations. We propose that the same methods can be used to study the representations of Large Language Models (LLMs). While one can always directly prompt either humans or LLMs to disclose their mental representations introspectively, we show that increased efficiency can be achieved by using LLMs as elements of a sampling algorithm. We explore the extent to which we recover human-like representations when LLMs are interrogated with Direct Sampling and Markov chain Monte Carlo (MCMC). We found a significant increase in efficiency and performance using adaptive sampling algorithms based on MCMC. We also highlight the potential of our method to yield a more general method of conducting Bayesian inference with LLMs.

People systematically deviate from the rational Bayesian updating of beliefs, as notably evidenced by conservatism and base-rate neglect. The primary cognitive models that explain these biases include simple heuristics (Woike et al., 2023, https://doi.org/10.1016/j.cogpsych.2023.101564) and stochastic sampling approximations of the Bayesian solution, like the Bayesian Sampler (Zhu et al., 2020, https://doi.org/10.1037/rev0000190). However, neither type of explanation appears entirely complete, as the data fall between the two; only about half of participants' responses align with heuristics. Could these results be explained by a new class of models that blend heuristics with Bayesian models? We test both simple mixtures of heuristics and the Bayesian Sampler, as well as a hybrid model in which heuristics are used to set a prior that improves estimates based on stochastic samples. Our analysis indicates that neither heuristics nor the Bayesian Sampler alone are sufficient to explain the data.

When faced with delayed, uncertain rewards, humans andother animals usually prefer to know the eventual outcomesin advance. This preference for cues providing advance infor-mation can lead to seemingly suboptimal choices, where lessreward is preferred over more reward. Here, we introduce areinforcement-learning model of this behavior, the anticipatedprediction error (APE) model, based on the idea that predic-tion errors themselves can be rewarding. As a result, animalswill sometimes pick options that yield large prediction errors,even when the expected rewards are smaller. We compare theAPE model against an alternative information-bonus model,where information itself is viewed as rewarding. These mod-els are evaluated against a newly collected dataset with humanparticipants. The APE model fits the data as well or betterthan the other models, with fewer free parameters, thus provid-ing a more robust and parsimonious account of the suboptimalchoices. These results suggest that anticipated prediction er-rors can be an important signal underpinning decision making.

Effectively updating one’s beliefs requires sufficient empirical evidence (i.e., data) and the computational capacity to process it. Yet both data and computational resources are limited for human minds. Here, we study the problem of belief updating under limited data and limited computation. Using information theory to characterize constraints on computation, we find that the solution to the resulting optimization problem links the data and computational limitations together: when computational resources are tight, agents may not be able to integrate new empirical evidence. The resource-rational belief updating rule we identify offers a novel interpretation of conservative Bayesian updating.

Sampling-based models, which assume that people remember or simulate instances of events and count outcome propor-tions to make probability judgments, account for many apparent biases in human judgment. The success of such modelsis generally dependent on sample size, as particularly large or particularly small samples are often required for a modelto reproduce effects observed in data. Thus, systematically exploring the actual number of instances that people tend tosample is an important criterion in evaluating model credibility. Here we propose a method of estimating sample size byway of inter-judgment variance. We show through model recovery that this method will reliably recover the correct samplesize and subsequently apply the method to two well-supported models of human probability judgment, Probability TheoryPlus Noise and the Bayesian Sampler. Results indicate, in both cases, that human probability judgments are based on arelatively plausible (¡ 10) number of sampled instances.

The judgments that people make are not independent –initial decisions can bias later perception. This has beenshown in tasks in which participants first decide whetherthe direction of moving dots is to one side or the otherof a reference line: their subsequent estimates are biasedaway from this reference line. This interesting bias has beenexplained in past work as either a consequence of weightingsensory neurons, or as a consequence of participants adjustingtheir estimate to match their decision. We propose anew explanation: that people sequentially sample evidenceto make their decision, and reuse these samples to maketheir estimate (i.e., amortised inference). Because optimalstopping leads to samples that strongly favor one or anotherdecision alternative, the subsequent estimates are also biasedaway from the reference line. We introduce a sequentialsampling model for posterior samples that does not assumeconstant thresholds, and provide evidence for our explanationin a new experiment that generalizes the perceptual bias to anew domain.

When making financial forecasts, individuals often overreact to recent information, as consistently observed in both laboratory studies with naïve participants and professional consensus real-world forecasting. Current models attribute this overreaction to either an overestimation of recent information or memory constraints favoring more accessible information. An alternative explanation suggests individuals accurately integrate all available information into their mental posterior probability distribution for forecasting, but are unable to directly access this distribution, leading to dependence on approximation methods such as sampling. Local sampling algorithms have received recent support in other forecasting contexts and may introduce overreaction as a consequence of a starting point bias. By reanalyzing existing data from a price prediction task with a random walk price series, we observe increasing variability in predicted values and forecast errors as the horizon expands. Employing this heightened variability and overreaction, we differentiate between competing explanations for the observed forecasting behavior.

There has been considerable interest exploring how the utility of an outcome impacts the probability with which it is mentally simulated. Earlier studies using varying methodologies have yielded divergent conclusions with different directions of the influence. To directly examine such mental process, we employed a random generation paradigm in which all the outcomes were either equally (i.e., followed a uniform distribution) or unequally (i.e., a binomial distribution) probable. While our results revealed individual differences in how the utility influenced responses, the overall findings suggested that it is the outcomes' probabilities, not their utilities, that guide this process. Notably, an initial utility-independent bias emerged, with individuals displaying a tendency to start with smaller values when all outcomes are equally likely. Our findings offer insights into the benefits of studying the mental sampling processes and provide empirical support for particular sampling models in this domain.

Recent decision making theories have explained behaviour using mental sampling mechanisms where people imagine possible outcomes to guide their choices. Simultaneously, work in other domains has found evidence of particular mental sampling patterns, such as autocorrelations between samples and moderation by prior assumptions, which current decision making theories do not generally consider. Here, we seek to unify this work, developing a new sampling model of preferential choice incorporating these findings in other domains. Our model, based on the Autocorrelated Bayesian Sampler, predicts choice, reaction time, confidence and valuation from a common underlying process. We find a strong correspondence between our model's predictions and empirical choice data, though performance remains below leading explanations for such tasks. Our model does however cover a broader set of response types than existing theories, suggesting the advantages of considering of a wider range of behaviours than are commonly examined in current decision making studies.