All Questions
8 questions
7
votes
2
answers
269
views
How do we derive the conditional mode as the solution to linear regression, for uniform cost function?
I know that if the cost functions are respectively the least squares ($L^2$) and the absolute deviation ($L^1$), the solution to linear regression is the conditional mean and the conditional median ...
- 629
0
votes
1
answer
337
views
Computing Mode of Prior
How do you compute the mode of a prior with beta distribution $(\alpha, \beta)$?
6
votes
1
answer
489
views
Conditional log-concavity and unimodality
Let $X$ and $Y$ be two random variables (or vectors)
with continuous and "smooth enough" joint distribution. Assume that the two conditional distributions $X|Y=y$
and $Y|X=x$ are log-concave for all $...
- 5,716
8
votes
2
answers
2k
views
Is the MAP the maximum value of the posterior or its mode?
According to the WP definition of MAP:
In Bayesian statistics, a maximum a posteriori probability (MAP)
estimate is an estimate of an unknown quantity, that equals the mode
of the posterior ...
- 4,362
13
votes
2
answers
776
views
Reliability of Mode from an MCMC sample
In his book Doing Bayesian Data Analysis, John Kruschke states that in using JAGS from R
...the estimate of the mode from an MCMC sample can be rather unstable because the estimate is based on a ...
- 1,364
8
votes
1
answer
1k
views
Why not use Beta(1,1) as boundary avoiding prior on a transformed correlation parameter?
In Bayesian Data Analysis, chapter 13, page 317, second full paragraph, in the modal and distributional approximations, Gelman et al. write:
If the plan is to summarize inference by the posterior ...
- 3,925
1
vote
0
answers
114
views
How can you convert Bayesian Information Criterion parameters to a probabilistic interpretation?
I'm working with a general bayesian information criteria to determine if this data exhibits a bimodal, trimodal, quadmodal etc. My existing BIC exhibits clear trimodality, but I'd like a hypothesis ...
- 283
11
votes
4
answers
2k
views
Given a 10D MCMC chain, how can I determine its posterior mode(s) in R?
Question: With a 10 dimensional MCMC chain, let's say I'm prepared to hand you a matrix of the draws: 100,000 iterations (rows) by 10 parameters (columns), how best can I identify the posterior modes?...
- 1,723