Reputation
1,900
Top tag
Next privilege 2,000 Rep.
Edit questions and answers
Badges
7 16
Newest
 Nice Answer
Impact
~128k people reached

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.
Jan
30
comment Uniform Random on $(-\infty,\infty)$
Here's a relevant draft article from the arXiv.
Jan
25
awarded  Nice Answer
Jan
11
awarded  Nice Question