| 1. |
- Arnaudon, Alexis, et al.
(författare)
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Diffusion Bridges for Stochastic Hamiltonian Systems and Shape Evolutions
- 2022
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Ingår i: SIAM Journal on Imaging Sciences. - 1936-4954. ; 15:1, s. 293-323
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Tidskriftsartikel (refereegranskat)abstract
- Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modeling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a natural generalization as diffusion bridges in a sto-chastic setting. Simulation of such bridges is key to solving inference and registration problems in shape analysis. We demonstrate how to apply state-of-the-art diffusion bridge simulation methods to recently introduced stochastic shape deformation models, thereby substantially expanding the appli-cability of such models. We exemplify these methods by estimating template shapes from observed shape configurations while simultaneously learning model parameters.
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| 2. |
- Bierkens, Joris, et al.
(författare)
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A piecewise deterministic Monte Carlo method for diffusion bridges
- 2021
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Ingår i: Statistics and Computing. - : Springer Science and Business Media LLC. - 0960-3174 .- 1573-1375. ; 31:3
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Tidskriftsartikel (refereegranskat)abstract
- We introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic Markov process. Similar to the Lévy–Ciesielski construction of a Brownian motion, we expand the diffusion path in a truncated Faber–Schauder basis. The coefficients within the basis are sampled using a Zig-Zag sampler. A key innovation is the use of the fully local algorithm for the Zig-Zag sampler that allows to exploit the sparsity structure implied by the dependency graph of the coefficients and by the subsampling technique to reduce the complexity of the algorithm. We illustrate the performance of the proposed methods in a number of examples.
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| 3. |
- Bierkens, Joris, et al.
(författare)
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Simulation of elliptic and hypo-elliptic conditional diffusions
- 2020
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Ingår i: Advances in Applied Probability. - : Cambridge University Press (CUP). - 0001-8678 .- 1475-6064. ; 52:1, s. 173-212
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Tidskriftsartikel (refereegranskat)abstract
- Suppose X is a multidimensional diffusion process. Assume that at time zero the state of X is fully observed, but at time 0$ ]]> only linear combinations of its components are observed. That is, one only observes the vector for a given matrix L. In this paper we show how samples from the conditioned process can be generated. The main contribution of this paper is to prove that guided proposals, introduced in [35], can be used in a unified way for both uniformly elliptic and hypo-elliptic diffusions, even when L is not the identity matrix. This is illustrated by excellent performance in two challenging cases: a partially observed twice-integrated diffusion with multiple wells and the partially observed FitzHugh-Nagumo model.
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| 4. |
- Bierkens, Joris, et al.
(författare)
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Sticky PDMP samplers for sparse and local inference problems
- 2023
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Ingår i: Statistics and Computing. - : Springer Science and Business Media LLC. - 0960-3174 .- 1573-1375. ; 33
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Tidskriftsartikel (refereegranskat)abstract
- We construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge that many coordinates are likely to be exactly 0. This is achieved with the fairly simple idea of endowing existing PDMP samplers with “sticky” coordinate axes, coordinate planes etc. Upon hitting those subspaces, an event is triggered during which the process sticks to the subspace, this way spending some time in a sub-model. This results in non-reversible jumps between different (sub-)models. While we show that PDMP samplers in general can be made sticky, we mainly focus on the Zig-Zag sampler. Compared to the Gibbs sampler for variable selection, we heuristically derive favourable dependence of the Sticky Zig-Zag sampler on dimension and data size. The computational efficiency of the Sticky Zig-Zag sampler is further established through numerical experiments where both the sample size and the dimension of the parameter space are large.
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| 5. |
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| 6. |
- Fahlgren, Anna, et al.
(författare)
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The effects of PTH, loading and surgical insult on cancellous bone at the bone-implant interface in the rabbit
- 2013
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Ingår i: Bone. - : Elsevier. - 8756-3282 .- 1873-2763. ; 52:2, s. 718-724
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Tidskriftsartikel (refereegranskat)abstract
- Enhancing the quantity and quality of cancellous bone with anabolic pharmacologic agents may lead to more successful outcomes of non-cemented joint replacements. Using a novel rabbit model of cancellous bone loading, we examined two specific questions regarding bone formation at the bone-implant interface: (1) does the administration of intermittent PTH, a potent anabolic agent, and mechanical loading individually and combined enhance the pen-implant cancellous bone volume fraction; and, (2) does surgical trauma enhance the anabolic effect of PTH on pen-implant bone volume fraction. In this model, PTH enhanced pen-implant bone volume fraction by 30% in loaded bone, while mechanical loading alone increased bone volume fraction modestly (+10%). Combined mechanical loading and PTH treatment had no synergistic effect on any cancellous parameters. However, a strong combined effect was found in bone volume fraction with combined surgery and PTH treatment (+34%) compared to intact control limbs. Adaptive changes in the cancellous bone tissue included increased ultimate stress and enhanced remodeling activity. The number of proliferative osteoblasts increased as did their expression of pro-collagen 1 and PTH receptor 1, and the number of TRAP positive osteoclasts also increased. In summary, both loading and intermittent PTH treatment enhanced pen-implant bone volume, and surgery and PTH treatment had a strong combined effect This finding is of clinical importance since enhancing early osseointegration in the post-surgical period has numerous potential benefits.
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| 7. |
- Gugushvili, Shota, et al.
(författare)
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Nonparametric Bayesian estimation of a Hölder continuous diffusion coefficient
- 2020
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Ingår i: Brazilian Journal of Probability and Statistics. - 0103-0752. ; 34:3, s. 537-579
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Tidskriftsartikel (refereegranskat)abstract
- We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a histogram-type prior with piecewise constant realisations on bins forming a partition of the time interval. Specifically, these constants are realizations of independent inverse Gamma distributed randoma variables. We justify our approach by deriving the rate at which the corresponding posterior distribution asymptotically concentrates around the data-generating diffusion coefficient. This posterior contraction rate turns out to be optimal for estimation of a Hölder-continuous diffusion coefficient with smoothness parameter 0<λ≤1. Our approach is straightforward to implement, as the posterior distributions turn out to be inverse Gamma again, and leads to good practical results in a wide range of simulation examples. Finally, we apply our method on exchange rate data sets.
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| 8. |
- Gugushvili, Shota, et al.
(författare)
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Nonparametric Bayesian volatility estimation
- 2019
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Ingår i: 2017 MATRIX Annals. - Cham : Springer International Publishing. - 9783030041601 ; , s. 279-302
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 9. |
- Mider, Marcin, et al.
(författare)
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Continuous-discrete smoothing of diffusions
- 2021
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Ingår i: Electronic Journal of Statistics. - 1935-7524. ; 15:2, s. 4295-4342
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Tidskriftsartikel (refereegranskat)abstract
- Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the process, consistent with the observations. We derive a novel Markov Chain Monte Carlo algorithm to sample from the exact smoothing distribution. The resulting algorithm is called the Backward Filtering Forward Guiding (BFFG) algorithm. We extend the algorithm to include parameter estimation. The proposed method relies on guided proposals introduced in [53]. We illustrate its efficiency in a number of challenging problems.
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