| Modeling Relief Consumption Using Heuristics | sT, at the maximum likelihood parameters, 0, of each model. |
| Modeling Relief Consumption Using Heuristics | Mean predicted consumption levels simulated from the maximum likelihood parameterizations of each model over each 10 trials of the experiment for each participant are plotted against the same metric derived from the observed data. |
| Modeling Relief Consumption Using Heuristics | sT, at the maximum likelihood parameterization, 0, of each model. |
| Predicting Consumption from One-Off Choices between Delayed Pains | To estimate the proportion of variance in the observed data accounted for by the models, we found the mean consumption level for each participant across each 10 trials of the experiment, before calculating the same measure by simulating 10000 consumption paths resulting from the maximum likelihood parameterization of the model. |
| Relief Consumption Experiment | Model fitting followed a maximum likelihood framework, using the softmaX policy to generate the probability of observing each possible (rounded) level of relief consumption, given a particular set of model parameters. |
| Relief Consumption Experiment | For each subject 10 iterations of the optimization were performed, and the maximum likelihood estimate across all iterations was selected. |
| Supporting Information | 5, overlaid With consumption simulated (red circles) from the maximum likelihood parameterization, 6, of the Income Maximization model. |
| Supporting Information | Whilst the model fitting process takes account of the observed state of capital on each trial, the simulated paths here are sampled anew from the maximum likelihood parameterization Without reference to the data. |
| Supporting Information | sT, at the maximum likelihood parameterization, 9, of each model overlaid With observed consumption data (White circles). |
| Introduction | We test the neutral null hypothesis using a maximum likelihood approach (using an exact expression [26] for the likelihood of a sample from the SNM), where p-values are evaluated by a parametric bootstrap procedure. |
| Testing the neutral null model | In order to quantify Whether a particular data set is consistent with neutral theory, we adopt a maximum likelihood approach together with a parametric bootstrap as used by Walker and Cyr [45] and Rosindell and Etienne [63]. |
| Testing the neutral null model | We choose the maximized likelihood of the neutral model as our test statistic. |
| Testing the neutral null model | For a test data set XT, we find the maximum likelihood parameter estimates (mMT, GMT , i.e. |