# Questions tagged [nonparametric-bayes]

Bayesian methods for infinite dimensional parameter spaces.

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196 views

### Marginalizing over a Chinese Restaurant Process prior

I am reading a paper by Kemp et al. and there is a part about marginalising over a Chinese Restaurant Process and I am quite clueless about how could one marginalise over such a prior! The details of ...
48 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), ...
14 views

### Are the Beta and Bernoulli Processes Normalized Random Measures with Independent Increments?

James et al. 2009 introduced the notion of "Normalized Random Measures with Independent Increments." Do the Beta process and Bernoulli process belong to this family?
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### 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 ...
24 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 ?
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53 views

### Bayesian Model Fit for Binary Data

I am looking for methods (and preferably references) for assessing model fit for Bayesian analyses of binary data. Specifically, I am fitting Bayesian parametric and nonparametric item response models ...
49 views

### Bayesian nonparametric estimate of median [closed]

I've been working on estimating the population median of a variable with a complex distribution that is not easily characterized as a parameterized probability distribution. So far, the best I have ...
14 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 ...
27 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 ...
40 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 ...
47 views

### Why are discrete random measures not dominated?

A statement I’ve seen without proof in many books and papers is that random probability measures obtained by normalizing a completely random measure, such as the Dirichlet process, are not dominated ...
362 views

### Bayesian Nonparametric Latent feature model

For quite a long time I've been trying to understand the paper "Bayesian Nonparametric Latent feature model" (by Zoubin Ghahramani et al.) [http://mlg.eng.cam.ac.uk/zoubin/papers/GhaGriSol06.pdf]. In ...
40 views

### Exchangabilty in CRF generative model for HDP

In the HDP Setting, the groups (or documents) are assumed exchangeable between them, and the samples (or words) within each group/topic are also exchangeable. Note the Setting chapter here However, ...
185 views

### Kernel density estimate vs Dirichlet process mixture

Nowadays the Dirichlet process mixture (DPM) seems to be the default Bayesian approach for density estimation. My question is why not simply use the kernel density estimate (KDE) to model the density? ...
119 views

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### Introductory textbook on nonparametric Bayesian models?

I'd like to wrap my head around this topic but learning from white-papers and tutorials is hard because there are many gaps which are usually filled in textbooks. If it is important I have ...
511 views

### Help me understand the Bayesian kernel density estimation (Sibisi and Skilling, 1996)

Sibisi and Skilling (1996, also mentioned in the 1997 paper) define Bayesian kernel density as $$f(x) = \int dx' \,\phi(x')\, K(x, x') \tag{2}$$ Here the kernel $K$ is an assigned smooth ...
2k views

### Normality test for likert scale [duplicate]

I have a questionnaire data that consist of composite Likert scale and discrete Likert items. Likert scales or variables are the sum of few Likert items while the one-item variables are represented ...
197 views

### Dirichlet Process vs. Mixture Models with Many Mixtures

The Dirichlet Process prior is a Bayesian non-parametric prior to model your data as coming from an infinite mixture of distributions. Since your data is finite, only a finite number of these mixture ...
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### 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 ...
35 views

### DPMM asymptotics for finite mixtures?

My understanding is that using a Dirichlet process mixture model for a mixture with finitely many components will result in a misspecified model. Are there any asymptotic results or bounds on the ...
171 views

### Nonparametric topic modeling: hierarchical dirichlet vs. Indian buffet?

The hierarchical dirichlet process (Teh 2005) allows you to discover unlimited topics to describe a document. An alternative process, the Indian Buffet process (Griffiths 2011) is another ...
For an inference problem using a Dirichlet Process prior, one can derive a "basic" Gibbs sampling scheme, where we have a conditional for any parameter $\theta_i$ given the samples $x_i$ and all the ...