7 thoughts on “The hinge function provided “a tractable solution to an important and long standing problem in the field of fluvial geomorphology–the prediction of bedload sediment transport in rivers.” How cool is that?”

1. What are the likely gains here over using something like a breakpoint regression? I’m not sure I understand the benefit of the added complexity just to get a single smoothed function.

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   • Olip:

     The hinge function is just smoother. If you want a continuous function with two straight lines intersecting at point, you can do so–it’s a limiting case of the hinge–; the concern is that there can be statistical and computational problems with the discontinuous derivative, and in real life we would not expect the change to happen all at once.

     To put it another way, once it’s implemented, the hinge function is simpler to write and compute than the model with discontinuous derivative.

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     • Thanks Andrew

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2. This reminds me of a physicist friend who advised an ecology grad student on a problem. It turned out that a well-known formula in physics helped solve his problem in ecology. I love it when these interdisciplinary bridges form and keep wondering how to scale up these serendipitous occasions.

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3. Spent two minutes with Claude for https://gist.github.com/soodoku/9c7034df01317312be8bed2302874cc0

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4. A Github gist w/ alternate smoothers

   https://gist.github.com/soodoku/9c7034df01317312be8bed2302874cc0

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5. This is also reminiscent of the smoothly-broken power law formulas used in physics, especially astrophysics. See e.g.,

   https://docs.astropy.org/en/stable/api/astropy.modeling.powerlaws.SmoothlyBrokenPowerLaw1D.html

   I think the smoothly-broken power law in that link might be exactly equal to the hinge function applied in log-log space.

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