# Questions tagged [nonparametric-bayes]

Bayesian methods for infinite dimensional parameter spaces.

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### 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 ...
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### Gaussian Processes: How to use GPML for multi-dimensional output

Is there a way to perform Gaussian Process Regression on multidimensional output (possibly correlated) using GPML? In the demo script I could only find a 1D example. A similar question on CV that ...
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### Covariance matrix for Gaussian Process and Wishart distribution

I'm reading through this paper on Generalised Wishart Processes (GWP). The paper calculates the covariances between different random variables (following Gaussian Process) using squared exponential ...
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### 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 ...
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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 ...
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### 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 ...
308 views

### Do Stochastic Processes such as the Gaussian Process/Dirichlet Process have densities? If not, how can Bayes rule be applied to them?

The Dirichlet Pocess and Gaussian Process are often referred to as "distributions over functions" or "distributions over distributions". In that case, can I meaningfully talk about the density of a ...
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### 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 ...
235 views

### Default priors for mixtures

Suppose we have $p$ dimensional vectors $Y_i$ which we model with $f_Y (y |\theta) = \sum \pi_k N(y | \mu_k, \Sigma_k)$ with $\theta$ being a catch all for the model parameters (the number of ...
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### 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 ...
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### 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 ...
106 views