An Alternative Uncertainty Calculator

Rather than using the bootstrap method, an alternative way to calculate the uncertainty in fitted parameters is to use the tau-squared grid, in a way very similar to standard Bayesian analysis. By converting each pixel's tau-squared into a probability, one can create a relative probability grid, and if you divide by the sum of all pixels, they become absolute probabilities. One can then sum all the probability below a given tau-squared to obtain a plot of tau-squared against probability. All you then need to do is choose the tau-squared level which corresponds to (say) 67 percent, and use this as a confidence limit.

I have implemented this method in the program uncer. In principle one must extend the grid over the full (potentially infinite) range of all the parameters, but for reasonable ranges of the parameters the error introduced seems to be negligible (though I'm still experimenting). This method gives very similar answers to the bootstrap for 67 percent confidence, but by 95 percent the answers are significantly different for reasons I have yet to fathom.