4,993 research outputs found
Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models
A computationally simple approach to inference in state space models is
proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation
of an intractable likelihood by matching summary statistics for the observed
data with statistics computed from data simulated from the true process, based
on parameter draws from the prior. Draws that produce a 'match' between
observed and simulated summaries are retained, and used to estimate the
inaccessible posterior. With no reduction to a low-dimensional set of
sufficient statistics being possible in the state space setting, we define the
summaries as the maximum of an auxiliary likelihood function, and thereby
exploit the asymptotic sufficiency of this estimator for the auxiliary
parameter vector. We derive conditions under which this approach - including a
computationally efficient version based on the auxiliary score - achieves
Bayesian consistency. To reduce the well-documented inaccuracy of ABC in
multi-parameter settings, we propose the separate treatment of each parameter
dimension using an integrated likelihood technique. Three stochastic volatility
models for which exact Bayesian inference is either computationally
challenging, or infeasible, are used for illustration. We demonstrate that our
approach compares favorably against an extensive set of approximate and exact
comparators. An empirical illustration completes the paper.Comment: This paper is forthcoming at the Journal of Computational and
Graphical Statistics. It also supersedes the earlier arXiv paper "Approximate
Bayesian Computation in State Space Models" (arXiv:1409.8363
Asymptotic Properties of Approximate Bayesian Computation
Approximate Bayesian computation allows for statistical analysis in models
with intractable likelihoods. In this paper we consider the asymptotic
behaviour of the posterior distribution obtained by this method. We give
general results on the rate at which the posterior distribution concentrates on
sets containing the true parameter, its limiting shape, and the asymptotic
distribution of the posterior mean. These results hold under given rates for
the tolerance used within the method, mild regularity conditions on the summary
statistics, and a condition linked to identification of the true parameters.
Implications for practitioners are discussed.Comment: This 31 pages paper is a revised version of the paper, including
supplementary materia
Computing Bayes: From Then 'Til Now'
This paper takes the reader on a journey through the history of Bayesian
computation, from the 18th century to the present day. Beginning with the
one-dimensional integral first confronted by Bayes in 1763, we highlight the
key contributions of: Laplace, Metropolis (and, importantly, his co-authors!),
Hammersley and Handscomb, and Hastings, all of which set the foundations for
the computational revolution in the late 20th century -- led, primarily, by
Markov chain Monte Carlo (MCMC) algorithms. A very short outline of 21st
century computational methods -- including pseudo-marginal MCMC, Hamiltonian
Monte Carlo, sequential Monte Carlo, and the various `approximate' methods --
completes the paper.Comment: Material that appeared in an earlier paper, `Computing Bayes:
Bayesian Computation from 1763 to the 21st Century' (arXiv:2004.06425) has
been broken up into two separate papers: this historical overview of, and
timeline for, all computational developments is retained; and a secondary
paper (arXiv:2112.10342), which provides a more detailed review of 21st
centur
Continuous Wavelets on Compact Manifolds
Let be a smooth compact oriented Riemannian manifold, and let
be the Laplace-Beltrami operator on . Say 0 \neq f
\in \mathcal{S}(\RR^+), and that . For , let
denote the kernel of . We show that is
well-localized near the diagonal, in the sense that it satisfies estimates akin
to those satisfied by the kernel of the convolution operator on
\RR^n. We define continuous -wavelets on , in such a
manner that satisfies this definition, because of its localization
near the diagonal. Continuous -wavelets on are analogous to
continuous wavelets on \RR^n in \mathcal{S}(\RR^n). In particular, we are
able to characterize the Hlder continuous functions on by
the size of their continuous wavelet transforms, for
Hlder exponents strictly between 0 and 1. If is the torus
\TT^2 or the sphere , and (the ``Mexican hat''
situation), we obtain two explicit approximate formulas for , one to be
used when is large, and one to be used when is small
Recommended from our members
ROMOP: a light-weight R package for interfacing with OMOP-formatted electronic health record data.
Objectives:Electronic health record (EHR) data are increasingly used for biomedical discoveries. The nature of the data, however, requires expertise in both data science and EHR structure. The Observational Medical Out-comes Partnership (OMOP) common data model (CDM) standardizes the language and structure of EHR data to promote interoperability of EHR data for research. While the OMOP CDM is valuable and more attuned to research purposes, it still requires extensive domain knowledge to utilize effectively, potentially limiting more widespread adoption of EHR data for research and quality improvement. Materials and methods:We have created ROMOP: an R package for direct interfacing with EHR data in the OMOP CDM format. Results:ROMOP streamlines typical EHR-related data processes. Its functions include exploration of data types, extraction and summarization of patient clinical and demographic data, and patient searches using any CDM vocabulary concept. Conclusion:ROMOP is freely available under the Massachusetts Institute of Technology (MIT) license and can be obtained from GitHub (http://github.com/BenGlicksberg/ROMOP). We detail instructions for setup and use in the Supplementary Materials. Additionally, we provide a public sandbox server containing synthesized clinical data for users to explore OMOP data and ROMOP (http://romop.ucsf.edu)
Photodeposition of amorphous polydiacetylene films from monomer solutions onto transparent substrates
Polydiacetylenes are a very promising class of polymers for both photonic and electronic applications because of their highly conjugated structures. For these applications, high-quality thin polydiacetylene films are required. We have discovered a novel technique for obtaining such films of a polydiacetylene derivative of 2-methyl-4-nitroaniline using photodeposition from monomer solutions onto UV transparent substrates. This heretofore unreported process yields amorphous polydiacetylene films with thicknesses on the order of I micron that have optical quality superior to that of films grown by standard crystal growth techniques. Furthermore, these films exhibit good third-order nonlinear optical susceptibilities; degenerate four-wave mixing experiments give x(3) values on the order of 10(exp -8) - 10(exp -7) esu. We have conducted masking experiments which demonstrate that photodeposition occurs only where the substrate is directly irradiated, clearly indicating that the reaction occurs at the surface. Additionally, we have also been able to carry out photodeposition using lasers to form thin polymer circuits. In this work, we discuss the photodeposition of polydiacetylene thin films from solution, perform chemical characterization of these films, investigate the role of the substrate, speculate on the mechanism of the reaction, and make a preliminary determination of the third-order optical nonlinearity of the films. This simple, straightforward technique may ultimately make feasible the production of polydiacetylene thin films for technological applications
- …