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 Mar 26 awarded Enlightened Mar 26 awarded Nice Answer Mar 9 awarded Yearling Aug 10 comment Linear regression with prior on $\arctan \beta_1$ Found it: projecteuclid.org/euclid.ba/1339616542 Incidentally, the flat prior on the angle transforms to a Cauchy on the slope parameter. Aug 10 comment Linear regression with prior on $\arctan \beta_1$ @Xi'an, that's not true in this case: Jaynes-style invariance arguments lead to a uniform prior on the angle of the slope. IIRC there's an old paper in Bayesian Analysis on priors for the simple errors-in-variables model that IIRC derives such a prior in this fashion. I'm having difficulty tracking down the paper just now... (and as I recall, it doesn't even cite Jaynes.) Aug 10 comment Appropriate priors for truncated regression model Have you considered applying a logarithmic transformation to your dependent variable? Aug 10 comment Do statisticians use the Jeffreys' prior in actual applied work? I like to use Jeffreys' prior as a default/non-informative prior for the simple binomial model ($p\left(\theta\right)\propto\sqrt{\theta\left(1-\theta\right)}$). It's conjugate with weight equivalent to a single datum and it's a 1$^{\rm{st}}$-order probability-matching prior, so I have a good feeling for what it does to the likelihood function and for how to interpret the resulting credible intervals. May 19 awarded Nice Answer Mar 9 awarded Yearling Dec 6 awarded Necromancer Dec 2 comment Unrealistically high significance when marginalizing over large number of parameters To get the noise-only model onto the stage, I guess what you'd have to do is make $N_\rm{obj}$ a model parameter and do inference on it. You'll need proper priors over the object-specific parameters; otherwise, you'll run into the Jeffreys-Lindley thingy. Dec 2 comment Unrealistically high significance when marginalizing over large number of parameters You can expect Bayes to give you the best possible answer under the assumptions you've built into the model. Unless the full model nests the noise-only model within it such that posterior mass can concentrate on the noise-only possibility, Bayes will hallucinate, just as you've told it to. Oct 14 comment What is the decision-theoretic justification for Bayesian credible interval procedures? I've seen procedures that construct intervals from loss functions with univariate action spaces, but these have always struck the doctrinaire Bayesian in me as ad hockeries. My doctrinaire Bayesian self thinks that if you're going to report an interval, then the action space is best abstracted as a set of intervals, period. (The engineer in me is less rigid.) Oct 9 comment What is the decision-theoretic justification for Bayesian credible interval procedures? @RasmusBååth, you're basically asking, "what are the necessary conditions on the loss function for quantile intervals to be the solution to the minimization of posterior expected loss?" My intuition, just from the way the math works in the forward direction, is that this is pretty much it. Haven't proven it, though. Sep 30 awarded Explainer Sep 24 awarded Autobiographer Apr 25 awarded Enlightened Apr 25 awarded Nice Answer Mar 9 awarded Yearling Feb 22 comment On the tractability of posterior distributions Chamberlain Foncha, if you have the covariance matrix, you just calculate a matrix square root (using the Cholesky decomposition, or if $N$ is too big for that to yield stable results, the eigendecomposition) and then use a matrix-affine transformation of a product of standard normal random variates. This will work until $N$ is so big that the eigendecomposition computation outstrips one's computing resources.