May 2, 2024Open Access

Statistical algorithms for low-frequency diffusion data: A PDE approach

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Authors

MGMatteo GiordanoUniversity of Turin SWSven WangRush University Medical Center

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Implication

Theoretical analysis demonstrates efficient likelihood evaluation in multidimensional diffusion models, highlighting substantial computational speed-ups.

Key Points

Numerical evaluation of likelihoods and gradients for diffusion models reduces directly to standard elliptic eigenvalue problems, enabling efficient statistical inference.
Rapid convergence towards stationary points was observed in simulation studies, and optimization schemes achieved satisfactory diffusivity recovery under Gaussian process priors.
Simulation studies coupled with parabolic PDE theory characterise transition densities via the Fokker-Planck equation, enabling finite element methods to solve the system.
May enable significant computational speed-ups for maximum-a-posteriori estimation and posterior sampling, replacing expensive simulation-based diffusion methods.

Cite This Study

Giordano et al. (2024) studied this question.

synapsesocial.com/papers/68e6beabb6db64358763edbd https://doi.org/10.48550/arxiv.2405.01372

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Implication

Theoretical analysis demonstrates efficient likelihood evaluation in multidimensional diffusion models, highlighting substantial computational speed-ups.

Statistical algorithms for low-frequency diffusion data: A PDE approach

Discussion

Member takes

Implication

Key Points

Cite This Study

Statistical algorithms for low-frequency diffusion data: A PDE approach

Discussion

Member takes

Implication

Key Points

Cite This Study

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