Correlation parameterization in random function models to improve normal approximation of the likelihood or posterior
Béla Nagy, Jason L. Loeppky, William J. Welch · 2007
Transformations can help small sample likelihood/Bayesian inference by improving the approximate normality of the likelihood/posterior. In this a rticle we investigate when one can expect an improvement for a one-dimensional random function (Gaussian process) model. The log transformation of the range parameter is compared with an alternative (the logexp) for the family of Power Exponential correlations. Formulas are developed for measuring nonnormality based on Sprott (1973). The effect of transformations on non-normality is evaluated analytically and by simulations. Results show that, on average, the log transformation improves approximate normality for the Squared Exponential (Gaussian) correlation function, but this is not always the case for the other members of the Power Exponential family.