All Questions
Tagged with nonparametric bayesian
60
questions
3
votes
1
answer
111
views
Robbins estimate Empirical Bayes
From the compound sampling model where:
$Y_i | \theta_i \sim Poi(\theta_i)$
The marginal distribution of $\theta_i$ is $G$, non-parametric.
We get that the Bayes estimate of $\theta_i$ under ...
- 347
2
votes
1
answer
195
views
Reference for poor sampler mixing in large bayesian models
I keep seeing this in various presentations, but never saw a reference for it. Although it makes an intuitive sense why samplers potentially can face mixing issue when operating on large space of ...
- 1,502
1
vote
0
answers
31
views
Estimating Gamma PDF parameters from data with negative increments
Say we have collected data, and from a physical perspective we know that the collected data should increase positively with time. However the data looks more like this:
This data shown in the figure ...
- 565
1
vote
1
answer
18
views
Measuring quality of random items - probability that quality exceeds a without any assumptions
Say I draw $n$ random items and measure their quality in the interval $[0,1]$. Now I would like to know: If I draw another item, what is the probability that this item has a quality larger than $0.5$? ...
- 103
2
votes
1
answer
895
views
Combining triangular distributions
Vose (in Risk analysis a quantitative guide, 2008) argues that it is preferable to use non-parametric distributions when eliciting knowledge about an unknown distribution from experts. The argument is ...
- 33
31
votes
2
answers
10k
views
Is it true that Bayesian methods don't overfit?
Is it true that Bayesian methods don't overfit? (I saw some papers and tutorials making this claim)
For example, if we apply a Gaussian Process to MNIST (handwritten digit classification), but only ...
- 1,337
6
votes
1
answer
2k
views
What does the base distribution of the Dirichlet Process mean?
So far I only really understand the Dirichlet Process through its various metaphors. For the Polya Urn scheme, my understanding is that the "base distribution" is the original distribution of colors ...
- 1,002
8
votes
2
answers
2k
views
Bayesian nonparametric answer to deep learning?
As I understand it, deep neural networks are performing "representation learning" by layering features together. This allows learning very high dimensional structures in the features. Of course, it's ...
- 1,002
1
vote
0
answers
53
views
Nonparametric density estimation, individual probablities
Consider the problem of doing nonparametric density estimation using kernel density estimator in the common form
$k(\frac{\textbf{x} - \mathbf{x_{j}}}{h})$,
$k(\textbf{u}) = \begin{cases}
1 & \...
- 121
0
votes
1
answer
267
views
Understanding Gaussian Process and their Priors
I am very interested to understand the motivation behind why are we using these priors let's say in the context of regression. I know that the kernel depicts the distance between the points or let's ...
- 3
8
votes
1
answer
1k
views
Nonparametric nonlinear regression with prediction uncertainty (besides Gaussian Processes)
What are state-of-the-art alternatives to Gaussian Processes (GP) for nonparametric nonlinear regression with prediction uncertainty, when the size of the training set starts becoming prohibitive for ...
- 5,226
8
votes
1
answer
276
views
Dirichlet process mixture MCMC
I'm reading Markov Chain Sampling Methods for Dirichlet Process Mixture Models by Radford M. Neal. Equation (3.6) states that
$$
\text{If } c=c_{j} \text{ for some } j\neq i: P\left(c_{i}=c\;|\;c_{-i}...
- 1,142
1
vote
0
answers
444
views
Need for iid in MLE
I am studying about parametric estimation in supervised learning using maximum likelihood estimation. Here is what I learned:
Separate our training data according to class; i.e., we have c data sets ...
- 235
4
votes
0
answers
44
views
German tank variant: estimate resolution of camera given cropped photo sizes
Make whatever assumptions you like, but I like the flavor of nonparametric techniques.
I have a list of the $x_i$ by $y_i$ resolutions of a number of photos, all cropped from photos taken at the same ...
- 2,121
4
votes
0
answers
408
views
Is this how a Bayesian bootstrap works?
I am a bit new to the whole nonparametric and Bayesian idea, so tell me if this is correct: to estimate, say, the mean of a dataset's population we do the following:
We define a function $f(x)$ that ...
- 2,121