Over the years I came to terms with my Bayesian heritage, and I now live my life as a secular Bayesian. I started having thoughts about model misspecification, kind of a taboo topic in the Bayesian church. I worked on weird stuff like loss-calibrated Bayes. I noticed nonparametric Bayesian models weren't automatically more useful than large parametric ones. There were scoring rules, loss functions which couldn't be written as a log-likelihood. I realised the likelihood was important, but not the only thing that exists. Over the years, I started to doubt more and more aspects of my Bayesian faith. I never forgot this encounter, but equally I didn't think much about it since then. You have to think your model really exists somewhere." This, however, only exists if your data and your parameters both exist, in the same $\sigma$-algebra. Then he told me the following, poisoning my pure Bayesian heart forever: "If you use Bayes' rule, you assume that a joint distribution between model parameters and data exist. "Do you believe your model and its parameters exist?" "Well, not really, it's just a model I use to describe reality" I said. "Do you believe your data exists?" - he asked. Possessed by deamonsĪt a convention dominated by Bayesian thinkers I was approached by a frequentist, let's call him Lucifer (in fact his real name is Laci so not that far off). But above all, we believed in our models. We scorned at point estimates, despised p-values. If an algorithm did not work, we shunned its creator for being unfaithful to Bayes. We looked at the world and all we saw the face of Bayes: if something worked, it did because it had a Bayesian interpretation. This particular place practiced the nonparametric Bayesian doctrine. I travelled the world and spent 4 years in a Bayesian monastery in Cambridge, UK. It all started to change when a great scientist took me under his wing and taught me the teachings of Bayes. My parents didn't raise me in a religious tradition. OctoThe secular Bayesian: Using belief distributions without really believing The religious Bayesian
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