Essays in Likelihood-Based Computational Econometrics

The theory of probabilities is basically only common sense reduced to a calculus. Pierre Simon Laplace, 1812 The quote above is from Pierre Simon Laplace’s introduction to his seminal work Th´eorie analytique des probabilit´es, in which he lays the groundwork for what is currently known as Bayesian analysis. He proceeds to describe probability theory, and statistical inference, as a method that makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it. (translation from French: Dale, 1995) This statement contains a profound truth and insight: Probability theory offers a clean and simple recipe for reasoning under uncertainty which I experienced as eyeopening when I first learned about it. As my knowledge of probability theory increased, however, I also realized that in isolation this quote presents things to be much simpler than they actually are: Reducing common sense to a calculus is extremely difficult to do well in practice. Translating our common sense into the language of probabilities takes a lot of practice, and if done accurately it often leads to a calculus without any exact solutions. It is therefore the task of statisticians and econometricians to find practical ways of reducing our common sense to calculus, and to devise smart new methods for efficiently doing the resulting calculations. This work represents my contribution towards these goals.

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