Timeline for Bayesian lighthouse location estimation
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Sep 24, 2019 at 10:54 | vote | accept | Pieter | ||
| Jan 11, 2017 at 18:55 | answer | added | jpneto | timeline score: 6 | |
| Jan 7, 2017 at 0:44 | comment | added | Pieter |
I tried using flashes ~ cauchy(x_loc, y_loc); and this actually gives the perfect result which is a beautiful coincidence :) Still being stubborn here: is there a way to replicate this using a uniform distribution over the angles and then transforming these angles (and locations) to the flash oberservations?
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| Jan 6, 2017 at 22:39 | comment | added | Zen | Check this: bayes.wustl.edu/sfg/why.pdf | |
| Jan 6, 2017 at 22:26 | comment | added | Pieter |
I would prefer something like flashes[i] = x_loc + tan(angle) * y_loc in the Stan model to indicate that it is indeed a deterministic function.
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| Jan 6, 2017 at 22:20 | history | edited | Pieter | CC BY-SA 3.0 |
Update the example to use cauchy distribution and no explicit prior on the angles
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| Jan 6, 2017 at 21:10 | comment | added | Juho Kokkala | @BenGoodrich why would flashes conditional on angle be Gaussian? In the generation code the data is a deterministic function of angle | |
| Jan 6, 2017 at 21:07 | comment | added | Pieter | @JuhoKokkala, thanks, that was a left-over from the other models I tried. Removing does help though. | |
| Jan 6, 2017 at 21:04 | history | edited | Pieter | CC BY-SA 3.0 |
deleted 33 characters in body
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| Jan 6, 2017 at 20:49 | answer | added | Dave Harris | timeline score: 8 | |
| Jan 6, 2017 at 20:08 | comment | added | Ben Goodrich |
Generating the data with a Caucy distribution and modeling it with a normal is the main problem, but your likelihood can simply be written as flashes ~ cauchy(x_loc + tan(angle), 1); if you are using the latest (R)Stan. You don't need to loop and you don't need to explicitly do angles ~ uniform(-pi()/2, pi()/2); because that is already implied by the constraints in the parameter declaration.
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| Jan 6, 2017 at 19:11 | comment | added | Juho Kokkala |
You have an unnecessary vector[N] flashes_ introduced in the model block, unused in the sence that there are no probability statements related to it. Thus, each component of that vector has an improper $U(-\infty, \infty)$ posterior. Does the issue persist after removing this?
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| Jan 6, 2017 at 18:54 | review | Close votes | |||
| Jan 6, 2017 at 19:33 | |||||
| Jan 6, 2017 at 18:27 | comment | added | whuber♦ | As @jpneto hints, the flashes have a Cauchy distribution--which has no expectation and therefore is a challenging thing to model. Please read the excellent post by Douglas Zare at stats.stackexchange.com/a/36037/919. However you go about estimating the location, it should wind up with an estimate very close to a median flash position. | |
| Jan 6, 2017 at 18:10 | comment | added | jpneto | For this problem the normal is not adequate, you should model the flashes with a cauchy. Check D.S.Sivia - Data Analysis, A Bayesian Tutorial (2006), section 2.4. | |
| Jan 6, 2017 at 17:00 | history | asked | Pieter | CC BY-SA 3.0 |