By generating approximate likelihoods for the mean of observed summary statistics over a grid of parameter values, they determined that the Hausa best fit a growth model beginning ∼1,000 generations ago with a per-generation growth rate α of 0.75×10−3.
We developed an innovative algorithm to solve this task: At first, we simulated a discrete grid of parameter values.
An example of the dependency of the Mahalanobis distance surface for a grid of parameter combination is presented in supplementary figure S1, Supplementary Material online, which shows that indeed the Mahalanobis distance increases as the parameter values are further away from the true set of parameters.
Optimal parameter values, together with the precision of the estimates, were obtained from calculating sum of squares in regular grids of parameter values.
The values can be determined by evaluating the performance over a grid of tuning parameter values using the boostrap or cross-validation.
Iterations using a grid of parameters and initial conditions suggest that, for any parameter values, the frequencies f u, ij will converge for all initial conditions to a unique equilibrium denoted by the frequencies f ^ u, i j.
The parameter space was divided up into a uniform grid and, for each pair of parameter values, the system was simulated for a period of time.
To overcome the limitations of using specific values for a parameter set, we further performed LSA based on MCC over a wide range of parameter values (see Methods).
A given parameter's value is varied along a grid of values while the values of all the other thawed parameters are allowed to float to new best-fit values.
To efficiently search this space and provide a finer density grid in regions with highest likelihoods, we first performed a search on a coarse grid of points over the widest sensible range of parameter values with M = 10,000 samples, then selected a much smaller range of parameter values based on the regions with highest likelihood on the coarse grid.
