Sequential Sensing with Model Mismatch

We characterize the performance of sequential information guided sensing, Info-Greedy Sensing, when there is a mismatch between the true signal model and the assumed model, which may be a sample estimate. In particular, we consider a setup where the signal is low-rank Gaussian and the measurements are taken in the directions of eigenvectors of the covariance matrix in a decreasing order of eigenvalues. We establish a set of performance bounds when a mismatched covariance matrix is used, in terms of the gap of signal posterior entropy, as well as the additional amount of power required to achieve the same signal recovery precision. Based on this, we further study how to choose an initialization for Info-Greedy Sensing using the sample covariance matrix, or using an efficient covariance sketching scheme.Comment: Submitted to IEEE for publicatio

Resonance-Induced Effects in Photonic Crystals

For the case of a simple face-centered-cubic photonic crystal of homogeneous dielectric spheres, we examine to what extent single-sphere Mie resonance frequencies are related to band gaps and whether the width of a gap can be enlarged due to nearby resonances. Contrary to some suggestions, no spectacular effects may be expected. When the dielectric constant of the spheres $\epsilon_s$ is greater than the dielectric constant $\epsilon_b$ of the background medium, then for any filling fraction $f$ there exists a critical $\epsilon_c$ above which the lowest lying Mie resonance frequency falls inside the lowest stop gap in the (111) crystal direction, close to its midgap frequency. If $\epsilon_s <\epsilon_b$, the correspondence between Mie resonances and both the (111) stop gap and a full gap does not follow such a regular pattern. If the Mie resonance frequency is close to a gap edge, one can observe a resonance-induced widening of a relative gap width by $\approx 5$.Comment: 14 pages, 3 figs., RevTex. For more info look at http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm

Robust detection of exotic infectious diseases in animal herds: A comparative study of three decision methodologies under severe uncertainty

When animals are transported and pass through customs, some of them may have dangerous infectious diseases. Typically, due to the cost of testing, not all animals are tested: a reasonable selection must be made. How to test effectively whilst avoiding costly disease outbreaks? First, we extend a model proposed in the literature for the detection of invasive species to suit our purpose. Secondly, we explore and compare three decision methodologies on the problem at hand, namely, Bayesian statistics, info-gap theory and imprecise probability theory, all of which are designed to handle severe uncertainty. We show that, under rather general conditions, every info-gap solution is maximal with respect to a suitably chosen imprecise probability model, and that therefore, perhaps surprisingly, the set of maximal options can be inferred at least partly---and sometimes entirely---from an info-gap analysis

Managing uncertainty through robust-satisficing monetary policy

We employ information-gap decision theory to derive a robust monetary policy response to Knightian parameter uncertainty. This approach provides a quantitative answer to the question: For a specified policy, how much can our models and data err or vary, without rendering the outcome of that policy unacceptable to a policymaker? For a given acceptable level of performance, the policymaker selects the policy that delivers acceptable performance under the greatest range of uncertainty. We show that such information-gap robustness is a proxy for probability of policy success. Hence, policies that are likely to succeed can be identified without knowing the probability distribution. We adopt this approach to investigate empirically the robust monetary policy response to a supply shock with an uncertain degree of persistence.Knightian uncertainty, Monetary policy, Info-gap decision theory.

Photonic crystals of coated metallic spheres

It is shown that simple face-centered-cubic (fcc) structures of both metallic and coated metallic spheres are ideal candidates to achieve a tunable complete photonic bandgap (CPBG) for optical wavelengths using currently available experimental techniques. For coated microspheres with the coating width to plasma wavelength ratio $l_c/\lambda_p \leq 10$ and the coating and host refractive indices $n_c$ and $n_h$, respectively, between 1 and 1.47, one can always find a sphere radius $r_s$ such that the relative gap width $g_w$ (gap width to the midgap frequency ratio) is larger than 5% and, in some cases, $g_w$ can exceed 9%. Using different coatings and supporting liquids, the width and midgap frequency of a CPBG can be tuned considerably.Comment: 14 pages, plain latex, 3 ps figures, to appear in Europhys. Lett. For more info on this subject see http://www.amolf.nl/research/photonic_materials_theory/moroz/moroz.htm

Home bias in financial markets: robust satisficing with info gaps

The observed patterns of equity portfolio allocation around the world are at odds with predictions from a capital asset pricing model (CAPM). What has come to be called the “home-bias” phenomenon is that investors tend to hold a disproportionately large share of their equity portfolio in home country stocks as compared with predictions of the CAPM. This paper provides an explanation of the home-bias phenomenon based on information-gap decision theory. The decision concept that is used here is that profit is satisficed and robustness to uncertainty is maximized rather than expected profit being maximized. Furthermore, uncertainty is modeled nonprobabilistically with info-gap models of uncertainty, which can be viewed as a possible quantification of Knightian uncertainty.