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Bayesian and Nonlinear Approaches to Statistics

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Bayesian and Nonlinear Approaches to Statistics

How Bayesian analytics has crossed the threshold from being considered a novelty to a normal technique.

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Someone said years ago that you’ll know Bayesian statistics has become mainstream when people no longer put “Bayesian” in the titles of their papers. That day has come. While the Bayesian approach is still the preferred approach of a minority of statisticians, it’s no longer a novelty. If you want people to find your paper interesting, the substance needs to be interesting. A Bayesian approach isn’t remarkable alone.

You could say the same about nonlinear differential equations. Differential equations are so often nonlinear that the “nonlinear” qualifier isn’t always necessary to say explicitly. Just as a Bayesian analysis isn’t interesting just because it’s Bayesian, a differential equation isn’t necessarily interesting just because it’s nonlinear.

The analogy between Bayesian statistics and nonlinear differential equations breaks down though. Nonlinear equations are intrinsically more interesting than linear ones. But it’s no longer remarkable to solve a nonlinear differential equation numerically.

When an adjective becomes the default, it drops off and the previous default now requires an adjective. Terms like “electronic” and “digital” are fading from use. If you say you’re going to mail someone something, the default assumption is usually that you are going to email it. What used to be simply “mail” is now “snail mail.” Digital signal processing is starting to sound quaint. The abbreviation DSP is still in common use, but digital signal processing is simply signal processing. Now non-digital signal processing requires a qualifier, i.e. analog.

There was no term for Frequentist statistics when it was utterly dominant. Now of course there is. (Some people use the term “classical,” but that’s an odd term given that Bayesian analysis is older.) The term linear has been around a long time. Even when nearly all analysis was linear, people were aware that linearity was a necessary simplification.

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Topics:
bayesian ,nonlinear time series analysis

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