Questions tagged [nonparametric-bayes]
Bayesian methods for infinite dimensional parameter spaces.
83 questions
1 vote
0 answers
65 views
How to interpret Bayes Factors from Bayesian Mann Whitney U Test?
I am comparing the cognitive performance of two different clinical groups. I used the DFBA R package to compute Bayesian Mann-Whitney Tests and am having difficulty interpreting the results. I know ...
- 11
2 votes
0 answers
178 views
Stick-breaking: break sticks of decreasing lengths
The stick-breaking construction used for Dirichlet Processes can create an infinite sequence of probabilities $ \boldsymbol{\pi} $ (stick lengths) that sum to 1 via the following formulae: $\nu_i \sim ...
- 133
10 votes
4 answers
2k views
How would a bayesian estimate a mean from a large sample?
What would a bayesian do if she wanted to do inference for the mean with a large sample but has no idea of the underlying distributions? A frequentist statitician would use the sample mean as a point ...
- 1,709
2 votes
0 answers
101 views
How to interpret this plot?
Please give me an explanation based on this Non-linear estimation results from the aggregate model (HOSP). This figure shows the non-linear effect of age (AGE), education (EDU), family size (FAMSZ), ...
- 21
0 votes
1 answer
64 views
what does z|G mean in nonparametric bayes?
when saying z is distributed according to G, where G comes from a dirichlet process, i saw this expression: z|G ~ G is this same meaning with z ~ G ?
- 3
1 vote
0 answers
117 views
Online Stochastic Variational Inference for Dirichlet Process Mixture Models
There's a 2013 NeurIPS paper I'm trying to understand, Online Learning of Nonparametric Mixture Models via Sequential Variational Approximation. I have a few questions: Equation 2, which defines a ...
- 1,088
0 votes
1 answer
223 views
Mean of draws of Dirichlet Process
Lets assume a Dirichlet process random measure in stick-breaking notation $G=\sum^\infty_{i=1} p_i \delta_{\lambda_i}$, such that $\lambda_i\sim H$ from some base distribution H, with point mass $\...
- 3
3 votes
1 answer
242 views
Why nonparametric maximum likelihood of mixture is convex
Consider $x_i \sim N(\mu_i, 1)$ where $i = 1, \ldots, n$ and assume $\mu_i$ is generated i.i.d. from an unknown distribution $F$. We are interested in estimating the unknown $\mu_i$. One way to solve ...
- 75
2 votes
1 answer
107 views
Expected Number of Dishes in Indian Buffet Process?
I'm sure this question has an answer somewhere online, but I can't find it. Suppose I have an Indian Buffet Process with $T$ customers and concentration parameter $\alpha$. For those unfamiliar with ...
- 1,088
3 votes
1 answer
501 views
Why does Chinese Restaurant Table Distribution look like a Gaussian Distribution?
The Chinese Restaurant Table Distribution describes the probability distribution for the number of non-empty tables in the Chinese Restaurant Process after $T$ customers have been seated. Specifically,...
- 1,088
2 votes
1 answer
775 views
Chinese Restaurant Process: Expected cardinality (number of customers) of each block (table)?
Short version of the question: The Chinese Restaurant Process defines a distribution over partitions of $[T] := \{1, ...., T\}$. What is the expected cardinality of the $t$th block, where $t \in \{1, ....
- 1,088
3 votes
0 answers
161 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 ...
- 1,622
1 vote
1 answer
150 views
R fitted() function applied to rbart (Bayesian Additive Regression Trees w/ random effects) object in the dbarts package
I'm having a hard time figuring out what the output of fitted() applied to a rbart object means. Specifically, I fit my data ...
- 93
1 vote
0 answers
65 views
Dirichlet Process vs Hierarchical Dirichlet Process: coupling among transitions on infinite HMM
I'm new to nonparametric Bayesian, and I am reading a paper about beam sampling for the infinite hidden Markov model. In the paper, it is mentioned that since there is no coupling among the ...
- 11
2 votes
1 answer
262 views
What is the Dirichlet Proces Mixture Models posterior
I am trying to understand Dirichlet Process Mixture models. One of the videos I have been watching is by Tamara Broderick. I think it is a very good introductory video to Dirichlet Process mixture ...
- 1,136