Bayesian Prior Sensitivity in Psychological Decision Modeling: Evidence from Loss Aversion Estimation Under Prospect Theory

Abstract

Prior specification is a critical yet frequently neglected decision in Bayesian inference, with potentially severe consequences for behavioral research conclusions, particularly in nonlinear psychological decision models where likelihood surfaces are often flat and parameters are weakly identified. This study presents a simulation-based framework for assessing prior sensitivity in Bayesian psychological decision modeling, using loss aversion estimation under Prospect Theory as a case study. Synthetic binary choice data were generated from the Tversky-Kahneman utility function across four true loss aversion values (λ ∈ {1.5, 2.0, 2.5, 3.0}) and three sample sizes (n ∈ {100, 200, 500}), fitted under three prior specifications: weakly informative diffuse prior, moderate informative, and strongly informative, yielding 1,080 total model fittings from 360 synthetic datasets via Laplace approximation with importance-weighted resampling. Performance was evaluated via posterior mean bias, RMSE, credible interval width, and directional probability P(λ > 2). Three findings emerged. First, diffuse default priors failed to recover the loss aversion parameter when the likelihood was insufficiently informative, regardless of sample size. Second, strongly informative priors introduced systematic bias that persisted independently of sample size when the true parameter deviated from the prior mean. Third, prior choice produced meaningful disagreements in directional behavioral conclusions that larger samples could not eliminate. These findings demonstrate that prior sensitivity is a substantive methodological concern in Bayesian psychological decision modeling that cannot be resolved by increasing sample size alone, and researchers are encouraged to treat prior specification as an explicit analytical choice supported by routine sensitivity analysis.