Uncertainty Quantification for NASA's Orbiting Carbon Observatory-2 Mission
DateFriday, March 15, 2019 - 3:00pm
AbstractSpace-borne remote sensing instruments measure high-dimensional vectors of radiances for each ground footprint over which they observe. These observations are converted into estimates of geophysical quantities through complex processing algorithms called retrievals. Many instruments use \optimal estimation" (OE) methods based on Bayes' Rule to obtain the posterior distribution of the state given the radiances, and report the estimated posterior mean and variance as a shorthand description of this distribution. However, numerous computational compromises and imperfect knowledge about other required inputs including the prior distribution, create uncertainties. Here we present a post-hoc methodology for assessing the biases and variances of individual estimates produced by OE. The method is based on simulations that characterize the performance of OE, under different geophysical conditions, as functions of measured radiances. The simulation results are used to t a nonlinear regression model that predicts bias and variance as a function of (dimension-reduced) radiance. We describe the methodology and its rationale, and illustrate using examples from NASA's Orbiting Carbon Observatory 2 (OCO-2) instrument.
Partial Sample Average Approximation Method for Chance Constrained Programs
DateFriday, March 22, 2019 - 3:00pm
AbstractIn this talk, we present a new scheme of a sampling-based method, named Partial Sample Average Approximation (PSAA) method, to solve chance constrained programs. In contrast to Sample Average Approximation (SAA) which samples all of the random variables, PSAA only samples a portion of random variables by making use of the independence of some of the random variables for stepwise evaluation of the expectation. The main advantage of the proposed approach is that the PSAA approximation problem contains only continuous auxiliary variables, whilst the SAA reformulation contains binary ones. Moreover, we prove that the proposed approach has the same convergence properties as SAA. At the end, a numerical study on different applications shows the strengths of the proposed approach, in comparison with other popular approaches, such as SAA and scenario approach.
Dimensionality in biological networks
DateFriday, March 29, 2019 - 3:00pm
AbstractThere is an avalanche of new data on the brain’s activity, revealing the collective dynamics of vast numbers of neurons. In principle, these collective dynamics can be of almost arbitrarily high dimension, with many independent degrees of freedom — and this may reflect powerful capacities for general computing or information. In practice, neural datasets reveal a range of outcomes, including collective dynamics of much lower dimension — and this may reflect other desiderata for neural codes. For what networks does each case occur? Our contribution to the answer is a new graphical framework, based on "motif cumulants," that links tractable statistical properties of network connectivity with the dimension of the activity that they produce. In tandem, we study how features of connectivity and dynamics that impact dimension arise as networks learn to perform basic tasks. I’ll describe where we have succeeded, where we have failed, and the many avenues that remain.