Win-Stay, Lose-Sample: A Simple Sequential Algorithm for Approximating Bayesian Inference

People can behave in a way that is consistent with Bayesian models of cognition, despite the fact that performing exact Bayesian inference is computationally challenging. What algorithms could people be using to make this possible? We show that a simple sequential algorithm “Win-Stay, Lose-Sample”, inspired by the Win-Stay, Lose-Shift (WSLS) principle, can be used to approximate Bayesian inference. We investigate the behavior of adults and preschoolers on two causal learning tasks to test whether people might use a similar algorithm. These studies use a “mini-microgenetic method”, investigating how people sequentially update their beliefs as they encounter new evidence. Experiment 1 investigates a deterministic causal learning scenario and Experiments 2 and 3 examine how people make inferences in a stochastic scenario. The behavior of adults and preschoolers in these experiments is consistent with our Bayesian version of the WSLS principle. This algorithm provides both a practical method for performing Bayesian inference and a new way to understand people’s judgments.

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Comparing two sequential Monte Carlo samplers for exact and approximate Bayesian inference on biological models

Journal of The Royal Society Interface ◽

10.1098/rsif.2017.0340 ◽

2017 ◽

Vol 14 (134) ◽

pp. 20170340 ◽

Cited By ~ 6

Author(s):

Aidan C. Daly ◽

Jonathan Cooper ◽

David J. Gavaghan ◽

Chris Holmes

Keyword(s):

Bayesian Inference ◽

Bayesian Methods ◽

Sequential Monte Carlo ◽

Model Parameters ◽

Biological Models ◽

Exact Inference ◽

Modelling Studies ◽

Approximate Bayesian ◽

Approximate Bayesian Inference ◽

Abc Methods

Bayesian methods are advantageous for biological modelling studies due to their ability to quantify and characterize posterior variability in model parameters. When Bayesian methods cannot be applied, due either to non-determinism in the model or limitations on system observability, approximate Bayesian computation (ABC) methods can be used to similar effect, despite producing inflated estimates of the true posterior variance. Owing to generally differing application domains, there are few studies comparing Bayesian and ABC methods, and thus there is little understanding of the properties and magnitude of this uncertainty inflation. To address this problem, we present two popular strategies for ABC sampling that we have adapted to perform exact Bayesian inference, and compare them on several model problems. We find that one sampler was impractical for exact inference due to its sensitivity to a key normalizing constant, and additionally highlight sensitivities of both samplers to various algorithmic parameters and model conditions. We conclude with a study of the O'Hara–Rudy cardiac action potential model to quantify the uncertainty amplification resulting from employing ABC using a set of clinically relevant biomarkers. We hope that this work serves to guide the implementation and comparative assessment of Bayesian and ABC sampling techniques in biological models.

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