3,053 research outputs found
Expectation Propagation for Nonlinear Inverse Problems -- with an Application to Electrical Impedance Tomography
In this paper, we study a fast approximate inference method based on
expectation propagation for exploring the posterior probability distribution
arising from the Bayesian formulation of nonlinear inverse problems. It is
capable of efficiently delivering reliable estimates of the posterior mean and
covariance, thereby providing an inverse solution together with quantified
uncertainties. Some theoretical properties of the iterative algorithm are
discussed, and the efficient implementation for an important class of problems
of projection type is described. The method is illustrated with one typical
nonlinear inverse problem, electrical impedance tomography with complete
electrode model, under sparsity constraints. Numerical results for real
experimental data are presented, and compared with that by Markov chain Monte
Carlo. The results indicate that the method is accurate and computationally
very efficient.Comment: Journal of Computational Physics, to appea
Analytical probabilistic approach to the ground state of lattice quantum systems: exact results in terms of a cumulant expansion
We present a large deviation analysis of a recently proposed probabilistic
approach to the study of the ground-state properties of lattice quantum
systems. The ground-state energy, as well as the correlation functions in the
ground state, are exactly determined as a series expansion in the cumulants of
the multiplicities of the potential and hopping energies assumed by the system
during its long-time evolution. Once these cumulants are known, even at a
finite order, our approach provides the ground state analytically as a function
of the Hamiltonian parameters. A scenario of possible applications of this
analyticity property is discussed.Comment: 26 pages, 5 figure
Likelihood-Based Inference for Discretely Observed Birth-Death-Shift Processes, with Applications to Evolution of Mobile Genetic Elements
Continuous-time birth-death-shift (BDS) processes are frequently used in
stochastic modeling, with many applications in ecology and epidemiology. In
particular, such processes can model evolutionary dynamics of transposable
elements - important genetic markers in molecular epidemiology. Estimation of
the effects of individual covariates on the birth, death, and shift rates of
the process can be accomplished by analyzing patient data, but inferring these
rates in a discretely and unevenly observed setting presents computational
challenges. We propose a mutli-type branching process approximation to BDS
processes and develop a corresponding expectation maximization (EM) algorithm,
where we use spectral techniques to reduce calculation of expected sufficient
statistics to low dimensional integration. These techniques yield an efficient
and robust optimization routine for inferring the rates of the BDS process, and
apply more broadly to multi-type branching processes where rates can depend on
many covariates. After rigorously testing our methodology in simulation
studies, we apply our method to study intrapatient time evolution of IS6110
transposable element, a frequently used element during estimation of
epidemiological clusters of Mycobacterium tuberculosis infections.Comment: 31 pages, 7 figures, 1 tabl
Diffeomorphic random sampling using optimal information transport
In this article we explore an algorithm for diffeomorphic random sampling of
nonuniform probability distributions on Riemannian manifolds. The algorithm is
based on optimal information transport (OIT)---an analogue of optimal mass
transport (OMT). Our framework uses the deep geometric connections between the
Fisher-Rao metric on the space of probability densities and the right-invariant
information metric on the group of diffeomorphisms. The resulting sampling
algorithm is a promising alternative to OMT, in particular as our formulation
is semi-explicit, free of the nonlinear Monge--Ampere equation. Compared to
Markov Chain Monte Carlo methods, we expect our algorithm to stand up well when
a large number of samples from a low dimensional nonuniform distribution is
needed.Comment: 8 pages, 3 figure
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