Mathematical Basis for Physical Inference

While the axiomatic introduction of a probability distribution over a space is common, its use for making predictions, using physical theories and prior knowledge, suffers from a lack of formalization. We propose to introduce, in the space of all probability distributions, two operations, the OR and the AND operation, that bring to the space the necessary structure for making inferences on possible values of physical parameters. While physical theories are often asumed to be analytical, we argue that consistent inference needs to replace analytical theories by probability distributions over the parameter space, and we propose a systematic way of obtaining such "theoretical correlations", using the OR operation on the results of physical experiments. Predicting the outcome of an experiment or solving "inverse problems" are then examples of the use of the AND operation. This leads to a simple and complete mathematical basis for general physical inference.Comment: 24 pages, 4 figure

Alternative causal inference methods in population health research: Evaluating tradeoffs and triangulating evidence.

Population health researchers from different fields often address similar substantive questions but rely on different study designs, reflecting their home disciplines. This is especially true in studies involving causal inference, for which semantic and substantive differences inhibit interdisciplinary dialogue and collaboration. In this paper, we group nonrandomized study designs into two categories: those that use confounder-control (such as regression adjustment or propensity score matching) and those that rely on an instrument (such as instrumental variables, regression discontinuity, or differences-in-differences approaches). Using the Shadish, Cook, and Campbell framework for evaluating threats to validity, we contrast the assumptions, strengths, and limitations of these two approaches and illustrate differences with examples from the literature on education and health. Across disciplines, all methods to test a hypothesized causal relationship involve unverifiable assumptions, and rarely is there clear justification for exclusive reliance on one method. Each method entails trade-offs between statistical power, internal validity, measurement quality, and generalizability. The choice between confounder-control and instrument-based methods should be guided by these tradeoffs and consideration of the most important limitations of previous work in the area. Our goals are to foster common understanding of the methods available for causal inference in population health research and the tradeoffs between them; to encourage researchers to objectively evaluate what can be learned from methods outside one's home discipline; and to facilitate the selection of methods that best answer the investigator's scientific questions

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Robust H∞ filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the robust H∞ filtering problem is studied for a class of uncertain nonlinear networked systems with both multiple stochastic time-varying communication delays and multiple packet dropouts. A sequence of random variables, all of which are mutually independent but obey Bernoulli distribution, are introduced to account for the randomly occurred communication delays. The packet dropout phenomenon occurs in a random way and the occurrence probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval. The discrete-time system under consideration is also subject to parameter uncertainties, state-dependent stochastic disturbances and sector-bounded nonlinearities. We aim to design a linear full-order filter such that the estimation error converges to zero exponentially in the mean square while the disturbance rejection attenuation is constrained to a give level by means of the H∞ performance index. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the exponential stability as well as prescribed H∞ performance for the overall filtering error dynamics, in the presence of random delays, random dropouts, nonlinearities, and the parameter uncertainties. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities (LMIs), and then the explicit expression is given for the desired filter parameters. Simulation results are employed to demonstrate the effectiveness of the proposed filter design technique in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the Alexander von Humboldt Foundation of Germany, National Natural Science Foundation of China under Grant 60825303, 60834003, 973 Project under Grant 2009CB320600, Fok Ying Tung Education Foundation under Grant 111064, and the Youth Science Fund of Heilongjiang Province under Grant QC2009C63