Questions tagged [slice-sampler]
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8 questions
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
2 votes
1 answer
219 views
Algebra for logistic regression slice sampler
I am having some difficulties when trying to do a little bit of algebra from Example 7.11 from the book "Introducing Monte Carlo Methods with R: Robert & Casella" The example relates to ...
- 902
3 votes
1 answer
231 views
Can the elliptical slice sampler be used to infer kernel hyperparameters for GP Regression?
Context Suppose I have some sample points $X$, and responses, $\mathbf{y}$. I wish infer the mechanism by which $\mathbf{y}$ is generated from $X$ using a Gaussian Process (GP) as a prior ...
- 815
3 votes
1 answer
336 views
Using QR Factorization to improve Sliced Inverse Regression
This code implements Slice Inverse Regression (SIR) in an unusual way. I notice that, when I compare it to the standard algorithm, the modified algorithm does better. By better, I mean that the ...
- 237
2 votes
1 answer
143 views
Generate random samples from $f(x) \propto [1 + \sin^2(3 x)] [ 1+ \cos^4(5x)] e^{-x^2/2}$ using slice sampler
I am trying to understanding the Example 8.3 of Monte Carlo Statistical Methods from Robert and Casella. The example shows how to generate from the density $$f(x) \propto [1 + \sin^2(3x)] [ 1+ \cos^4(...
- 333
1 vote
3 answers
536 views
NUTS Drawing samples from slice sampler; how to keep bounds on log scale?
I'm currently working to adapt the No U-Turn Sampler from this paper for a model I'm working on. The No-U Turn sampler augments the typical hamiltonian system by incorporating a slice variable $u$ ...
2 votes
1 answer
277 views
slice sampling correctness
Theoretically, the slice sampling has equilibrium distribution as the target distribution. If we can sample exactly as follows, $y' = U(0, p^*(x))$ $x' = U\{x: p^*(x) > y' \}$ However, in the ...
- 142
3 votes
1 answer
67 views
Slice Sampling asks to draw from $f^{-1}]y,+\infty[$
Slice Sampling asks to draw uniformly from $f^{-1}]y,+\infty[$. Wikipedia page However, how can we be sure that a uniform defined over the set $f^{-1}]y,+\infty[$ is in fact proper? If I had to ...
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