International Conference on Monte Carlo techniques
Closing conference of thematic cycle
Paris July 5-8th 2016
Campus les Cordeliers
Slides of Richard Everitt's presentation
International Conference on Monte Carlo techniques
Closing conference of thematic cycle
Paris July 5-8th 2016
Campus les cordeliers
Jere Koskela's slides
Rao-Blackwellisation schemes for accelerating Metropolis-Hastings algorithmsChristian Robert
Aggregate of three different papers on Rao-Blackwellisation, from Casella & Robert (1996), to Douc & Robert (2010), to Banterle et al. (2015), presented during an OxWaSP workshop on MCMC methods, Warwick, Nov 20, 2015
International Conference on Monte Carlo techniques
Closing conference of thematic cycle
Paris July 5-8th 2016
Campus les Cordeliers
Slides of Richard Everitt's presentation
International Conference on Monte Carlo techniques
Closing conference of thematic cycle
Paris July 5-8th 2016
Campus les cordeliers
Jere Koskela's slides
Rao-Blackwellisation schemes for accelerating Metropolis-Hastings algorithmsChristian Robert
Aggregate of three different papers on Rao-Blackwellisation, from Casella & Robert (1996), to Douc & Robert (2010), to Banterle et al. (2015), presented during an OxWaSP workshop on MCMC methods, Warwick, Nov 20, 2015
Sequential quasi-Monte Carlo (SQMC) is a quasi-Monte Carlo (QMC) version of sequential Monte Carlo (or particle filtering), a popular class of Monte Carlo techniques used to carry out inference in state space models. In this talk I will first review the SQMC methodology as well as some theoretical results. Although SQMC converges faster than the usual Monte Carlo error rate its performance deteriorates quickly as the dimension of the hidden variable increases. However, I will show with an example that SQMC may perform well for some "high" dimensional problems. I will conclude this talk with some open problems and potential applications of SQMC in complicated settings.
Sequential quasi-Monte Carlo (SQMC) is a quasi-Monte Carlo (QMC) version of sequential Monte Carlo (or particle filtering), a popular class of Monte Carlo techniques used to carry out inference in state space models. In this talk I will first review the SQMC methodology as well as some theoretical results. Although SQMC converges faster than the usual Monte Carlo error rate its performance deteriorates quickly as the dimension of the hidden variable increases. However, I will show with an example that SQMC may perform well for some "high" dimensional problems. I will conclude this talk with some open problems and potential applications of SQMC in complicated settings.
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1. Where distributions comes from?
2. Interpret and compare distributions.
3. Why normal, chi-square, t and F distributions?
4. Distributions for survivals.
Building Compatible Bases on Graphs, Images, and ManifoldsDavide Eynard
Spectral methods are used in computer graphics, machine learning, and computer vision, where many important problems boil down to constructing a Laplacian operator and finding its eigenvalues and eigenfunctions. We show how to generalize spectral geometry to multiple data spaces. Our construction is based on the idea of simultaneous diagonalization of Laplacian operators. We describe this problem and discuss numerical methods for its solution. We provide several synthetic and real examples of manifold learning, object classification, and clustering, showing that the joint spectral geometry better captures the inherent structure of multi-modal data.
Talk at SIAM-IS 2014 (http://www.math.hkbu.edu.hk/SIAM-IS14/). A big thanks to Michael Bronstein for providing a great set of slides this presentation is a mere extension of.
I am Ben R. I am a Statistics Assignment Expert at statisticshomeworkhelper.com. I hold a Ph.D. in Statistics, from University of Denver, USA. I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
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You can also call on +1 678 648 4277 for any assistance with Statistics Assignment.
Image sciences, image processing, image restoration, photo manipulation. Image and videos representation. Digital versus analog imagery. Quantization and sampling. Sources and models of noises in digital CCD imagery: photon, thermal and readout noises. Sources and models of blurs. Convolutions and point spread functions. Overview of other standard models, problems and tasks: salt-and-pepper and impulse noises, half toning, inpainting, super-resolution, compressed sensing, high dynamic range imagery, demosaicing. Short introduction to other types of imagery: SAR, Sonar, ultrasound, CT and MRI. Linear and ill-posed restoration problems.
In this talk, I address two new ideas in sampling geometric objects. The first is a new take on adaptive sampling with respect to the local feature size, i.e., the distance to the medial axis. We recently proved that such samples acn be viewed as uniform samples with respect to an alternative metric on the Euclidean space. The second is a generalization of Voronoi refinement sampling. There, one also achieves an adaptive sample while simultaneously "discovering" the underlying sizing function. We show how to construct such samples that are spaced uniformly with respect to the $k$th nearest neighbor distance function.
Here we give an overview of the causes of pinning in multiphase lattice Boltzmann models and propose a stochastic sharpening approach to overcome this spurious phenomenon.
RSS discussion of Girolami and Calderhead, October 13, 2010
1. About discretising Hamiltonians
Christian P. Robert
Universit´ Paris-Dauphine and CREST
e
http://xianblog.wordpress.com
Royal Statistical Society, October 13, 2010
Christian P. Robert About discretising Hamiltonians
2. Hamiltonian dynamics
Dynamic on the level sets of
1 1
H (θ, p) = −L(θ) + log{(2π)D |G(θ)|} + pT G(θ)−1 p ,
2 2
where p is an auxiliary vector of dimension D, is associated with
Hamilton’s pde’s
∂H ˙ ∂H (θ, p)
˙
p= (θ, p) , θ=
∂p ∂θ
which preserve the potential H (θ, p) and hence the target
distribution at all times t
Christian P. Robert About discretising Hamiltonians
3. Discretised Hamiltonian
Girolami and Calderhead reproduce Hamiltonian equations within
the simulation domain by discretisation via the generalised leapfrog
(!) generator,
[Subliminal French bashing?!]
Christian P. Robert About discretising Hamiltonians
4. Discretised Hamiltonian
Girolami and Calderhead reproduce Hamiltonian equations within
the simulation domain by discretisation via the generalised leapfrog
(!) generator,
but...
Christian P. Robert About discretising Hamiltonians
5. Discretised Hamiltonian
Girolami and Calderhead reproduce Hamiltonian equations within
the simulation domain by discretisation via the generalised leapfrog
(!) generator,
but...
invariance and stability properties of the [background] continuous
time process the method do not carry to the discretised version of
the process [e.g., Langevin]
Christian P. Robert About discretising Hamiltonians
6. Discretised Hamiltonian (2)
Is it useful to so painstakingly reproduce the continuous
behaviour?
Approximations (see R&R’s Langevin) can be corrected by a
Metropolis-Hastings step, so why bother with a second level
of approximation?
Discretisation induces a calibration problem: how long is long
enough?
Convergence issues (for the MCMC algorithm) should not be
impacted by inexact renderings of the continuous time process
in discrete time: loss of efficiency?
Christian P. Robert About discretising Hamiltonians
7. An illustration
Comparison of the fits of discretised Langevin diffusion sequences
to the target f (x) ∝ exp(−x4 ) when using a discretisation step
σ 2 = .1 and σ 2 = .0001, after the same number T = 107 of steps.
0.6
0.5
0.4
Density
0.3
0.2
0.1
0.0
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
Christian P. Robert About discretising Hamiltonians
8. An illustration
Comparison of the fits of discretised Langevin diffusion sequences
to the target f (x) ∝ exp(−x4 ) when using a discretisation step
σ 2 = .1 and σ 2 = .0001, after the same number T = 107 of steps.
0.8
0.6
Density
0.4
0.2
0.0
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
Christian P. Robert About discretising Hamiltonians
9. An illustration
Comparison of the fits of discretised Langevin diffusion sequences
to the target f (x) ∝ exp(−x4 ) when using a discretisation step
σ 2 = .1 and σ 2 = .0001, after the same number T = 107 of steps.
1e+05
8e+04
6e+04
time
4e+04
2e+04
0e+00
−2 −1 0 1 2
Christian P. Robert About discretising Hamiltonians
10. Back on Langevin
For the Langevin diffusion, the corresponding Langevin
(discretised) algorithm could as well use another scale η for the
gradient, rather than the one τ used for the noise
Christian P. Robert About discretising Hamiltonians
11. Back on Langevin
For the Langevin diffusion, the corresponding Langevin
(discretised) algorithm could as well use another scale η for the
gradient, rather than the one τ used for the noise
y = xt + η∇π(x) + τ ǫt
rather than a strict Euler discretisation
y = xt + τ 2 ∇π(x)/2 + τ ǫt
Christian P. Robert About discretising Hamiltonians
12. Back on Langevin
For the Langevin diffusion, the corresponding Langevin
(discretised) algorithm could as well use another scale η for the
gradient, rather than the one τ used for the noise
y = xt + η∇π(x) + τ ǫt
rather than a strict Euler discretisation
y = xt + τ 2 ∇π(x)/2 + τ ǫt
A few experiments run in Robert and Casella (1999, Chap. 6, §6.5)
hinted that using a scale η = τ 2 /2 could actually lead to
improvements
Christian P. Robert About discretising Hamiltonians
13. Back on Langevin
For the Langevin diffusion, the corresponding Langevin
(discretised) algorithm could as well use another scale η for the
gradient, rather than the one τ used for the noise
y = xt + η∇π(x) + τ ǫt
rather than a strict Euler discretisation
y = xt + τ 2 ∇π(x)/2 + τ ǫt
A few experiments run in Robert and Casella (1999, Chap. 6, §6.5)
hinted that using a scale η = τ 2 /2 could actually lead to
improvements
Which [independent] framework should we adopt for
assessing discretised diffusions?
Christian P. Robert About discretising Hamiltonians