Hierarchical Bayesian inference for concurrent model fitting and comparison for group studies
Fig 12
Performance of the HBI t-test when samples are drawn from a skewed distribution.
A) The skewed distribution (skewness of −0.5). The mean, variance and kurtosis of the distributions are 0, 1 and 3 (i.e. kurtosis of the normal distribution), respectively. This distribution was used to generate the bias parameter, which was then used to generate 20 (A) and 50 (B) subjects according to the biased RL model. B-C) Inference at P <0.05 for the HBI t-test on estimated parameters and t-test on true parameters, as a benchmark, when there is no effect (under the null). Note that this is an unrealistic benchmark because it is based on true parameters that the HBI does not have access to. D-E) Probability of P-value is obtained under the null hypothesis by repeating simulations 2000 times. Under the null hypothesis, the resulting P-value is theoretically expected to have a uniform distribution. Increasing the number of subjects improves the performance of the HBI t-test. The error-bars are 95% confidence intervals for the binomial distribution.