A literature review on the use of expert opinion in probabilistic risk analysis

Risk assessment is part of the decision making process in many fields of discipline, such as engineering, public health, environment, program management, regulatory policy, and finance. There has been considerable debate over the philosophical and methodological treatment of risk in the past few decades, ranging from its definition and classification to methods of its assessment. Probabilistic risk analysis (PRA) specifically deals with events represented by low probabilities of occurring with high levels of unfavorable consequences. Expert judgment is often a critical source of information in PRA, since empirical data on the variables of interest are rarely available. The author reviews the literature on the use of expert opinion in PRA, in particular on the approaches to eliciting and aggregating experts'assessments. The literature suggests that the methods by which expert opinions are collected and combined have a significant effect on the resulting estimates. The author discusses two types of approaches to eliciting and aggregating expert judgments-behavioral and mathematical approaches, with the emphasis on the latter. It is generally agreed that mathematical approaches tend to yield more accurate estimates than behavioral approaches. After a short description of behavioral approaches, the author discusses mathematical approaches in detail, presenting three aggregation models: non-Bayesian axiomatic models, Bayesian models, andpsychological scaling models. She also discusses issues of stochastic dependence.Health Monitoring&Evaluation,ICT Policy and Strategies,Public Health Promotion,Enterprise Development&Reform,Statistical&Mathematical Sciences,ICT Policy and Strategies,Health Monitoring&Evaluation,Statistical&Mathematical Sciences,Science Education,Scientific Research&Science Parks

Derived factorization categories of non-Thom--Sebastiani-type sums of potentials

We first prove semi-orthogonal decompositions of derived factorization categories arising from sums of potentials of gauged Landau-Ginzburg models, where the sums are not necessarily Thom--Sebastiani type. We then apply the result to the category \HMF^{L_f}(f) of maximally graded matrix factorizations of an invertible polynomial $f$ of chain type, and explicitly construct a full strong exceptional collection E_1,\hdots,E_{\mu} in \HMF^{L_f}(f) whose length $\mu$ is the Milnor number of the Berglund--H\"ubsch transpose $\widetilde{f}$ of $f$. This proves a conjecture, which postulates that for an invertible polynomial $f$ the category \HMF^{L_f}(f) admits a tilting object, in the case when $f$ is a chain polynomial. Moreover, by careful analysis of morphisms between the exceptional objects $E_i$, we explicitly determine the quiver with relations $(Q,I)$ which represents the endomorphism ring of the associated tilting object $\oplus_{i=1}^{\mu}E_i$ in \HMF^{L_f}(f), and in particular we obtain an equivalence \HMF^{L_f}(f)\cong \Db(\fmod kQ/I).Comment: Major improvements. The proof of the existence of a tilting object is added, and we compute the associated quiver with relations. 48 page

A Method for Measuring the Bias of High-Redshift Galaxies from Cosmic Variance

As deeper observations discover increasingly distant galaxies, characterizing the properties of high-redshift galaxy populations will become increasingly challenging and paramount. We present a method for measuring the clustering bias of high-redshift galaxies from the field-to-field scatter in their number densities induced by cosmic variance. Multiple widely-separated fields are observed to provide a large number of statistically-independent samples of the high-redshift galaxy population. The expected Poisson uncertainty is removed from the measured dispersion in the distribution of galaxy number counts observed across these many fields, leaving, on average, only the contribution to the scatter expected from cosmic variance. With knowledge of the Lambda Cold Dark Matter power spectrum, the galaxy bias is then calculated from the measured cosmic variance. The results of cosmological N-body simulations can then be used to estimate the halo mass associated with the measured bias. We use Monte Carlo simulations to demonstrate that Hubble Space Telescope pure parallel programs will be able to determine galaxy bias at z>~6 using this method, complementing future measurements from correlation functions.Comment: Accepted by ApJ Letter