Alternative sampling for variational quantum Monte Carlo

Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous publication it has been shown that for the simplest, most commonly applied strategy in continuum Quantum Monte Carlo, the random error in the resulting estimates is not well controlled. At best the Central Limit theorem is valid in its weakest form, and at worst it is invalid and replaced by an alternative Generalised Central Limit theorem and non-Normal random error. In both cases the random error is not controlled. Here we consider a new `residual sampling strategy' that reintroduces the Central Limit Theorem in its strongest form, and provides full control of the random error in estimates. Estimates of the total energy and the variance of the local energy within Variational Monte Carlo are considered in detail, and the approach presented may be generalised to expectation values of other operators, and to other variants of the Quantum Monte Carlo method.Comment: 14 pages, 9 figure

Developments in Statistical Graphics 1960-1980

1 online resource (PDF, 32 pages

Docketology, District Courts, and Doctrine

Empirical legal scholars have traditionally modeled trial court judicial opinion writing by assuming that judges act rationally, seeking to maximize their influence by writing opinions in politically important cases. To test such views, we collected data from a thousand cases in four different jurisdictions. We recorded information about every judicial action over each case’s life, ranging from the demographic characteristics, workload, and experience of the writing judge; to information about the case, including its jurisdictional basis, complexity, attorney characteristics, and motivating legal theory; to information about the individual orders themselves, including the relevant procedural posture and the winning party. Our data reveal opinions to be rare events in the litigation process: only 3% of all orders, and only 17% of orders applying facts to law, are fully reasoned. Using a hierarchical linear model, we conclude that judges do not write opinions to curry favor with the public or with powerful audiences, nor do they write more when they are less experienced, seeking to advance their careers, or in more interesting case types. Instead, opinion writing is significantly affected by procedure: we predict that judges are three times more likely to write an opinion on a summary judgment motion than a discovery motion, all else held equal. Judges similarly write more in cases that are later appealed, and in commercial cases, while writing less in tort and prisoner cases. Finally, jurisdictional culture is very important. These findings challenge the conventional wisdom and suggest the need for further research on the behavioral aspects of opinion writing

Assessing Dimensionality in Multivariate Regression

1 online resource (PDF, 37 pages

Reduced rank ridge regression and its kernel extensions

In multivariate linear regression, it is often assumed that the response matrix is intrinsically of lower rank. This could be because of the correlation structure among the prediction variables or the coefficient matrix being lower rank. To accommodate both, we propose a reduced rank ridge regression for multivariate linear regression. Specifically, we combine the ridge penalty with the reduced rank constraint on the coefficient matrix to come up with a computationally straightforward algorithm. Numerical studies indicate that the proposed method consistently outperforms relevant competitors. A novel extension of the proposed method to the reproducing kernel Hilbert space (RKHS) set‐up is also developed. © 2011 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 4: 612–622, 2011Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/88011/1/10138_ftp.pd

Does segmentation always improve model performance in credit scoring?

Credit scoring allows for the credit risk assessment of bank customers. A single scoring model (scorecard) can be developed for the entire customer population, e.g. using logistic regression. However, it is often expected that segmentation, i.e. dividing the population into several groups and building separate scorecards for them, will improve the model performance. The most common statistical methods for segmentation are the two-step approaches, where logistic regression follows Classification and Regression Trees (CART) or Chi-squared Automatic Interaction Detection (CHAID) trees etc. In this research, the two-step approaches are applied as well as a new, simultaneous method, in which both segmentation and scorecards are optimised at the same time: Logistic Trees with Unbiased Selection (LOTUS). For reference purposes, a single-scorecard model is used. The above-mentioned methods are applied to the data provided by two of the major UK banks and one of the European credit bureaus. The model performance measures are then compared to examine whether there is improvement due to the segmentation methods used. It is found that segmentation does not always improve model performance in credit scoring: for none of the analysed real-world datasets, the multi-scorecard models perform considerably better than the single-scorecard ones. Moreover, in this application, there is no difference in performance between the two-step and simultaneous approache

Invariance Properties of Schoenberg's Tone Row System

1 online resource (PDF, 24 pages

Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness

In this paper we suggest that, under suitable conditions, supervised learning can provide the basis to formulate at the microscopic level quantitative questions on the phenotype structure of multicellular organisms. The problem of explaining the robustness of the phenotype structure is rephrased as a real geometrical problem on a fixed domain. We further suggest a generalization of path integrals that reduces the problem of deciding whether a given molecular network can generate specific phenotypes to a numerical property of a robustness function with complex output, for which we give heuristic justification. Finally, we use our formalism to interpret a pointedly quantitative developmental biology problem on the allowed number of pairs of legs in centipedes

Electrochemical sensor-based devices for assessing bioactive compounds in olive oils: a brief review

Electrochemical bioinspired sensor devices combined with chemometric tools have experienced great advances in the last years, being extensively used for food qualitative and quantitative evaluation, namely for olive oil analysis. Olive oil plays a key role in the Mediterranean diet, possessing unique and recognized nutritional and health properties as well as highly appreciated organoleptic characteristics. These positive attributes are mainly due to olive oil richness in bioactive compounds such as phenolic compounds. In addition, these compounds enhance their overall sensory quality, being mainly responsible for the usual olive oil pungency and bitterness. This review aims to compile and discuss the main research advances reported in the literature regarding the use of electrochemical sensor based-devices for assessing bioactive compounds in olive oil. The main advantages and limitations of these fast, accurate, bioinspired voltammetric, potentiometric and/or amperometric sensor green-approaches will be addressed, aiming to establish the future challenges for becoming a practical quality analytical tool for industrial and commercial applications.This research was funded by Project POCI-01–0145-FEDER-006984–Associate Laboratory LSRE-LCM, Project UID/BIO/04469/2013–CEB, Project UID/QUI/50006/2013–REQUIMTE-LAQV and strategic project PEst-OE/AGR/UI0690/2014–CIMO all funded by European Regional Development Fund (ERDF) through COMPETE2020–Programa Operacional Competitividade e Internacionalização (POCI)–and by national funds through FCT–Fundação para a Ciência e a Tecnologia I.P. Ítala G. Marx also acknowledges the research grant provided by Project UID/EQU/50020/2013 and POCI-01-0145-FEDER-006984. The APC was kindly waived by MDPI.info:eu-repo/semantics/publishedVersio