All Questions
Tagged with dirichlet-distribution nonparametric-bayes
11
questions
3
votes
0
answers
131
views
A clarification in the original Dirichlet Process paper by Ferguson
I am reading the paper "Bayesian Analysis of Some Nonparametric Problems" by Ferguson where the Dirichlet process is introduced. There is a proposition 5 where the joint distribution of ...
- 1,572
0
votes
2
answers
2k
views
Coding a simple Stick-Breaking Process in Python
I've just red the great 2012 blog post of Edwin Chen about Dirichlet Process with companion code in R and Ruby. Then I'm trying to translate the Stick-Breaking Process from R to Python.
I've got this ...
- 149
2
votes
1
answer
487
views
Proof of neutrality for dirichlet distribution
I am trying to learn the fields of bayesian non-parametric approaches.
I am going thru this manuscript: http://mayagupta.org/publications/FrigyikKapilaGuptaIntroToDirichlet.pdf
I am bit stuck with: ...
- 237
9
votes
1
answer
522
views
What does it mean to integrate over a random measure?
I'm currently looking at a paper of Dirichlet process random effects model and the model specification is as follows:
$$ \begin{align*}y_{i} &= X_{i}\beta + \psi_{i} + \epsilon_{i}\\ \psi_{i} &...
- 1,142
3
votes
1
answer
132
views
Is it possible to define the mean of a varying distribution?
Suppose $(p_1,\ldots,p_k)$ be the vector of multinomial parameters and $$(p_1,\ldots,p_k)\sim \mbox{Dirichlet}(\alpha_1,\ldots,\alpha_k).$$
Let's define a function $f(p_1,\ldots,p_k) \in \mathbb{R}$. ...
- 51
1
vote
1
answer
359
views
For inference of Dirichlet Process Mixture, why the expected value $\int h(x)f(x)$ is desired?
Why the expected value $\int h(x)f(x)$ is desired for inference in Dirichlet Process Mixture?
What is the intuition for MCMC in Dirichlet Process Mixture?
$f(x)$ is the probability density function, ...
- 452
5
votes
1
answer
2k
views
understanding of effect of $\alpha$ in Dirichlet distribution
When reading the topic modeling tutorial written by Blei, KDD 2011 tutorial I was confused about a set of diagrams which aim to show the effect of $\alpha$ in Dirichlet distribution.
For example, for ...
- 5,222
4
votes
1
answer
4k
views
stick breaking model of Dirichlet process
I have a question regarding sticking-breaking model of Dirichlet process, which is defined as follows:
There are further statements that
I am not clear that how to derive equation 1 from that ...
- 5,222
1
vote
1
answer
406
views
How to draw samples from a Bayesian nonparamatric density estimation? [DPpackage]
I am trying to compute a Kernel Density from high dimensional data ($n > 2$). The underlying (generative) model is assumed unknown.
The goal is to draw samples from this estimate, in a sense ...
- 207
6
votes
2
answers
818
views
Understanding the construction of Dirichlet process
I'm trying to understand the construction process of DP, however, with little background in measure theory, the original papers are hard to read, but I believe the ideas behind these papers can be ...
- 442
6
votes
5
answers
5k
views
Simple introduction to MCMC with Dirichlet process prior?
I'm looking for a simple and easy to read introduction to using MCMC with a dirichlet process prior. Or perhaps using MCMC in any machine learning scenario, eg Gaussian Process.
I've been circling ...
- 4,797