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Joe Thorley

Note the current version of ssdtools soft-deprecated burr III because “poorly defined” where it means unclear which parameterization to use and because issues with convergence.

Carl Schwarz

Some wordsmithing needed. Maximum likelihood, method of moments, or non-linear fits using the cdf are ways to estimating the parameters of the underlying distribution. This is a wealth of statistical literature on the pros and cons of each (computations simplicity, unbiased estimates of parameters etc) and I don’t think we want to go there.

Cdf linearization is method of finding se for the quantiles. This is different from fitting the distributions.

Bayesian methods are overlaid on maximum likelihood methods. Key advantages is the ability to incorporate prior information (e.g. you may have prior information based on other chemicals), or for more complex situation (e.g. individual endpoints have uncertainty, are censored) for which MLE are numerically complex to define (require integration) but MCMC does a numerical integration.

David Fox

Given we’re already over the word count and that we’ve been asked to expand on qute a few topics, I suggest we just point to some references on Bayesian methods. Fox (2010) is already in our references but we could add one or two more.