A note on antidata.

Antidata in Bayesian inference was claimed in [1]. The idea was that when an entropic 1-prior (as defined in [1]) encodes an estimate of the unknown distribution parameters (for example the parameters of a Gaussian), this estimate could reduce the degrees of freedom in the posterior pdf (probability density function) of the parameters, as if it annihilated information in the likelihood. This would be in contrast to the (natural conjugate) 0-prior, where typically the estimate with weight α>0 acts like an additional α data points combined with the actual n data samples, thus increasing the degrees of freedom in the posterior by α and making the 0-posterior more informative. I became skeptical of antidata when I failed to see it in plots that I produced. I found that antidata, in the clearest scenario (when the sample statistic coincides with the parameter estimate), does not occur with the Bernoulli, Exponential, or Gaussian (when only ν is unknown or when μ and ν are both unknown) models. This was measured in terms of the parametrization-neutral information gain of the posteriors relative to a Uniform prior (or virtual Uniform prior). We correct some computations of the 1-prior published in [1]. These computations were not the source of the appearance of antidata; rather, an approximation to the 1-posterior and possibly the choice of parametrization were what allowed that. It remains to find antidata in other probability models, or to prove it does not occur at all. Our computations and reasoning suggest that usually (but not always) the 1-prior is actually the more informative entropic prior for inference. [ABSTRACT FROM AUTHOR]