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Results tagged with bayesian
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user 1146
Bayesian inference is a method of statistical inference that relies on treating the model parameters as random variables and applying Bayes' theorem to deduce subjective probability statements about the parameters or hypotheses, conditional on the observed dataset.
25
votes
4
answers
7k
views
Weakly informative prior distributions for scale parameters
I have been using log normal distributions as prior distributions for scale parameters (for normal distributions, t distributions etc.) when I have a rough idea about what the scale should be, but wan …
- 4,590
24
votes
1
answer
8k
views
What MCMC algorithms/techniques are used for discrete parameters?
I know a fair amount about fitting continuous parameters particularly gradient-based methods, but not much about fitting discrete parameters.
What are commonly used MCMC algorithms/techniques for fi …
- 4,590
17
votes
2
answers
3k
views
What is a 'message passing method'?
I have a vague sense of what a message passing method is: an algorithm that builds an approximation to a distribution by iteratively building approximations of each of the factors of the distribution …
- 4,590
16
votes
2
answers
3k
views
What's a good prior distribution for degrees of freedom in a t distribution?
I want to use a t distribution to model short interval asset returns in a bayesian model. …
- 4,590
13
votes
2
answers
541
views
What should I know about designing a good Hybrid/Hamiltonian Monte Carlo algorithm?
I am designing a Hybrid Monte Carlo sampling algorithm for PyMC, and I am trying to make it as fuss free and general as possible, so I am looking for good advice on designing an HMC algorithm. I have …
11
votes
3
answers
2k
views
Textbook deriving Metropolis-Hastings and Gibbs Sampling
I have fairly good practical experience with Metropolis-Hastings and Gibbs sampling, but I want to get a better mathematical understanding of these algorithms. What are some good textbooks or articles …
- 4,590
9
votes
4
answers
1k
views
Standard algorithms for doing hierarchical linear regression?
Are there standard algorithms (as opposed to programs) for doing hierarchical linear regression? Do people usually just do MCMC or are there more specialized, perhaps partially closed form, algorithms …
- 4,590
8
votes
Accepted
What methods can be used to specify priors from data?
If you have all this data, I think the best answer is to actually fit a single large model, using Hierarchical Modeling rather than do it in two steps (generating a prior then fitting a model). This i …
- 4,590
8
votes
5
answers
770
views
Papers on Bayesian factor analysis?
I am interested in fitting a factor analysis-like model on asset returns or other similar latent variable models. What are good papers to read on this topic? I am particularly interested in how to han …
- 4,590
8
votes
1
answer
540
views
Estimating a sparse inverse covariance matrix with known sparsity
If the distribution in question is the posterior of a Bayesian graphical model, many or most of the variables will be conditionally independent of each other. …
- 4,590
7
votes
Accepted
What's a good prior distribution for degrees of freedom in a t distribution?
On page 372 of ARM, Gelman and Hill mention using a uniform distribution on the inverse of DF between 1/DF = .5 and 1/DF = 0.
Specifically, in BUGS, they use:
nu.y <- 1/nu.inv.y
nu.inv.y ~ dunif( …
- 4,590
7
votes
4
answers
1k
views
What are good techniques and resources for teaching Bayes theorem?
My friend and I want to do a hands on tutorial on Bayes theorem for the Seattle LessWrong group. Neither of us have done this before, so we're searching for prior art; techniques that other people hav …
- 4,590
6
votes
Accepted
What is the Bayesian counterpart to a two-sample t-test with unequal variances?
While you can do this in a Bayesian way, have you considered whether it would actually be better to estimate the difference in the means rather than test whether they are different? …
- 4,590
6
votes
3
answers
5k
views
5
votes
Accepted
Estimating distribution parameters from few data points
I believe that Gelman's books (Bayesian Data Analysis and Data Analysis Using Regression and Multilevel/Hierarchical Models) talk quite a bit about this kind of thing (though perhaps not a lot for variance …
- 4,590