Bayes vs. the Invaders! Part Four: Convergence

In the previous three posts in our series delving into the cosmic horror of UFO sightings in the United States, we have descended from the deceptively warm and sunlit waters of basic linear regression, through the increasingly frigid, stygian depths of Bayesian inference, generalised linear models, and the probabilistic programming language Stan. In this final post we will explore the implications of the murky realms in which we find ourselves, and consider the awful choices that have led us to this point. We will therefore look, with merciful brevity, at the foul truth revealed by our models, but also consider the arcane philosophies that lie sleeping beneath. […]

Bayes vs. the Invaders! Part Three: The Parallax View

In the previous post of this series unveiling the relationship between UFO sightings and population, we crossed the threshold of normality underpinning linear models to construct a generalised linear model based on the more theoretically satisfying Poisson distribution. On inspection, however, this model revealed itself to be less well suited to the data than we had, in our tragic ignorance, hoped. […]

Bayes vs. the Invaders! Part Two: Abnormal Distributions

This post continues our series on developing statistical models to explore the arcane relationship between UFO sightings and population. The simple linear model developed in the previous post is far from satisfying. It makes many unsupportable assumptions about the data and the form of the residual errors from the model. Most obviously, it relies on an underlying Gaussian (or _normal_) distribution for its understanding of the data. For our count data, some basic features of the Guassian are inappropriate. […]

Bayes vs. the Invaders! Part One: The 37th Parallel

From our earlier studies of UFO sightings, a recurring question has been the extent to which the frequency of sightings of inexplicable otherworldly phenomena depends on the population of an area. Intuitively: where there are more people to catch a glimpse of the unknown, there will be more reports of alien visitors. Is this hypothesis, however, true? Do UFO sightings closely follow population or are there other, less comforting, factors at work? […]