1. A method for model selection, the method comprising: selecting, by one or more processors, a reference model as a possible description of a set of observed data, wherein the reference model includes a reference set of parameters; selecting, by the one or more processors, an alternative model as another possible description of the set of observed data, wherein the alternative model includes an alternative set of parameters; storing, by the one or more processors, an index function for measuring fit of models to data; calculating, by the one or more processors, an observed index difference based on a difference in the index function for fitting the reference model to the set of observed data and for fitting the alternative model to the set of observed data; determining, by the one or more processors, a simulated p-value using an comparison system that determines a threshold-fit simulated index for a first model and, while an early stop condition remains unsatisfied, iteratively compares the observed index difference to a boundary for a simulated index difference, the boundary for the simulated index difference based on a simulated index for a second model, determination of the simulated p-value comprising: generating, by the one or more processors, a set of simulated data; selecting, by the one or more processors, the first model and the second model, wherein the first model is one of the reference model and the alternative model and the second model is the other one of the reference model and the alternative model; performing, by the one or more processors, an operation based on the set of simulated data, wherein the operation includes: performing a simulated threshold-fitting for the first model by the one or more processors, wherein the simulated threshold-fitting for the first model includes varying a set of parameters for the first model for fitting the first model to the set of simulated data and deriving the threshold-fit simulated index for the first model as a value of the index function for the first model that satisfies a threshold criterion; deriving an initial simulated index for the second model as an initial value of the index function for fitting the second model to the set of simulated data; and deriving an initial boundary for the simulated index difference, wherein deriving the initial boundary for the simulated index difference includes calculating a difference between the threshold-fit simulated index for the first model and the initial simulated index for the second model; determining, by the one or more processors, based on a comparison of the initial boundary for the simulated index difference and the observed index difference, whether to update a counter used in calculating the simulated p-value; and selecting, by the one or more processors based on the simulated p-value, one of the reference model and the alternative model for modeling the set of observed data.