# Questions tagged [nonparametric-bayes]

Bayesian methods for infinite dimensional parameter spaces.

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1answer
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### Likely mean of a multinomial distribution with dirichlet prior

I am working to create a Bayesian non-parametric estimate of the mean of a distribution given a distribution of observations. Ultimately I'd like to get to a credibility interval of the likely mean of ...
1answer
279 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, ...
0answers
37 views

### Is it a problem to have non homogeneus sampling time in Bayes Filter?

I have a doubt related with Recursive State Estimation using Bayes Filter (actually using an aproximation to that through Particle Filters) This algorithm is explained in several sources with ...
3answers
3k views

### Is there a Bayesian approach to density estimation

I am interested to estimate the density of a continuous random variable $X$. One way of doing this that I learnt is the use of Kernel Density Estimation. But now I am interested in a Bayesian ...
1answer
1k views

### Understanding the difference between Supervised and unsupervised learning?

I have been reading about the Supervised and Unsupervised learning. What I came to know through this link is that in case of Supervised learning you have a set of input and a set of labels which are ...
3answers
1k views

### Books for learning non parametric Bayesian model

Having studied parametric Bayesian statistics during the two last years, I plan to begin to self-study non parametric Bayesian model during this summer and look for recommendations. I would like the ...
1answer
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 ...
1answer
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 ...
0answers
32 views

### Is there Bayesian search theory about search through the space of Bayesian models?

Consider we start with a specific Bayesian model, say an infinite mixture model with a Dirichlet Process as a prior. I know there are wildly many variants on this theme, from the Hierarchical ...
0answers
58 views

### How well can the Dirichlet process cluster really small datasets?

I have been debating between a model-based parametric clustering approach (e.g. HMMs), and a hierarchical Dirichlet/Pitman-Yor process for clustering sequential data. I understand the latter has been ...
1answer
395 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 ...
1answer
410 views

### Why semi/nonparametric models?

Increasing the flexibility of models makes it prone to overfitting. On the other hand, it looks to me that, if the space function classes $\mathcal{F}$ is too big, it is hard to prove bounds on ...
2answers
6k views

### PyMC for nonparametric clustering: Dirichlet process to estimate Gaussian mixture's parameters fails to cluster

Problem setup One of the first toy problems I wanted to apply PyMC to is nonparametric clustering: given some data, model it as a Gaussian mixture, and learn the number of clusters and each cluster's ...
0answers
106 views

0answers
1k views

### Non-parametric estimate of conditional expectation

I have a (fairly smooth) function $f$ and a sample $\{(x_i,y_i)\}_{i=1,\ldots,N}$ from the joint distribution of the random variables $X$ and $Y$. I would like to estimate the conditional expectation ...
0answers
158 views

### Points to keep in mind while implementing a nonparametric bayesian inference procedure from scratch

I have been trying to implement a Bayesian inference procedure from scratch for a specific problem, but I have implemented the procedure, and it doesn't seem to work. Since, I can't just post the ...
1answer
2k views

2answers
2k views

### How adding covariance noise in Gaussian processes to prevent overfitting?

I am told, in Gaussian Processes, adding covariance function noise to others, say SEiso or Materns, cause a better result, since it prevents from over fitting. I appreciate if someone could put more ...
1answer
1k views

### Pitman-Yor processes in R or Python

I am looking for a good tool in R or Python or any other implementation that can help to me generate sampling from hierarchical Pitman-Yor processes (HPY) (one of the recent and popular nonparametric ...
5answers
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 ...
2answers
302 views

### How do I compare multiple arbitrary predictions for a given data set?

Background: I am developing a Python Statistics Framework, not because the ones out there are bad but because it will help me learn Python and Statistics. I have taken AP Stats, and read scattered ...
2answers
1k views

### What are some applications of Chinese restaurant processes?

What are some applications of Chinese restaurant processes? I'm trying to learn a bit about non-parametric Bayesian methods, starting with Dirichlet processes and CRPs, but all the tutorials I've ...
1answer
5k views

### How do I use the GPML package for multi dimensional input?

I have downloaded the Gaussian Processes for Machine Learning (GPML) package (gpml-matlab-v3.1-2010-09-27.zip) from the website, and I can run the regression example (demoRegression) in Octave. It ...