On Bayesian Consistency for Flows Observed Through a Passive Scalar

Details

• Personal Author:
  Borggaard J ; Glatt-Holtz N ; Krometis J
• Description:
  We consider the statistical inverse problem of estimating a background fluid flow field v from the partial, noisy observations of the concentration theta of a substance passively advected by the fluid, so that theta is governed by the partial differential equation d/dt theta(t, x) = -v(x) · deltheta(t, x) + kdeltatheta(t, x), theta(0, x) = theta0(x) for t is an element of [0, T], T > 0 and x is an element of T2 = [0, 1]2. The initial condition theta0 and diffusion coefficient k are assumed to be known and the data consist of point observations of the scalar field theta corrupted by additive, i.i.d. Gaussian noise. We adopt a Bayesian approach to this estimation problem and establish that the inference is consistent, that is, that the posterior measure identifies the true background flow as the number of scalar observations grows large. Since the inverse map is ill-defined for some classes of problems even for perfect, infinite measurements of theta, multiple experiments (initial conditions) are required to resolve the true fluid flow. Under this assumption, suitable conditions on the observation points, and given support and tail conditions on the prior measure, we show that the posterior measure converges to a Dirac measure centered on the true flow as the number of observations goes to infinity. [Description provided by NIOSH]
• Subjects:
  Occupational Health Safety
• Keywords:
  Author Keywords: Bayesian Statistical Inversion Bayesian Consistency Mathematical Models Passive Scalars Quantitative Analysis Statistical Analysis Statistical Quality Control
• ISSN:
  1050-5164
• Document Type:
  Text
• Funding:
  Contract
• Genre:
  Journal Article
• Place as Subject:
  Louisiana ; OSHA Region 3 ; OSHA Region 6 ; Virginia
• CIO:
  National Institute for Occupational Safety and Health (NIOSH)
• Topic:
  Workplace Safety & Health
• Location:
  North America
• Volume:
  30
• Issue:
  4
• NIOSHTIC Number:
  nn:20068301
• Citation:
  Ann Appl Probab 2020 Aug; 30(4):1762-1783
• Contact Point Address:
  Jef Borggaard, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061
• Email:
  jborggaard@vt.edu
• Federal Fiscal Year:
  2020
• Performing Organization:
  Virginia Polytechnic Institute & State University
• Peer Reviewed:
  True
• Start Date:
  20140901
• Source Full Name:
  Annals of Applied Probability
• End Date:
  20190831
• Collection(s):
  National Institute for Occupational Safety and Health
• Main Document Checksum:
  urn:sha-512:d513226752ac7f58e95a856c64b4f3f16455c2768fcd1738863f33be91c3d33920182f8537c1eb1d856551736fc4225681db5e917cf43f5866f86b44483a8e6d
• Download URL:
  https://stacks.cdc.gov/view/cdc/230477/cdc_230477_DS1.pdf
• File Type:
  [PDF - 296.80 KB ]