# Likelihood tools

Likelihood This procedure will enter an Excel array formula to calculate the negative log likelihood for a set of observed data assuming observational uncertainty. You must first use the spreadsheet to develop an explanatory model. The data ranges (model and observed) must be the same size and shape. Currently only Normal, Poisson, Multinomial  and Binomial likelihoods are allowed. For Multinomial likelihoods, you must choose a range containing the observed data and choose a range containing the cell probabilities. Binomial likelihoods can be specified using Multinomial with two cells, though it would be more efficient to use Excel's built-in formula BINOMDIST.

Bootstrap iteration This routine uses Solver to compute confidence limits for a set of parameters by bootstrapping. You must first enter a PopTools array formula to resample the data. Then use the Likelihood routine (or some other method) to calculate the likelihood for the bootstrap sample. The routine works by replacing the bootstrap sample with fixed values and then calling Solver to fit the parameters. The bootstrap sample is then recalculated to generate a new sample. This is repeated many times, yielding a distribution of parameter estimates, from which confidence limits can be calculated. The output is a new sheet containing the parameter estimates for each iteration. Sort the data and then use the "Summary stats" routine to get the percentiles.

Likelihood profile This routine uses Solver to create a likelihood profile and 95% confidence limits for a single parameter. Before invoking this routine, you must