Iterative Updating of Model Error for Bayesian Inversion

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when optimization algorithms are used to find a single estimate, or to speed up Markov chain Monte Carlo (MCMC) calculations in the Bayesian framework. The use of an approximate model introduces a discrepancy, or modeling error, that may have a detrimental effect on the solution of the ill-posed inverse problem, or it may severely distort the estimate of the posterior distribution. In the Bayesian paradigm, the modeling error can be considered as a random variable, and by using an estimate of the probability distribution of the unknown, one may estimate the probability distribution of the modeling error and incorporate it into the inversion. We introduce an algorithm which iterates this idea to update the distribution of the model error, leading to a sequence of posterior distributions that are demonstrated empirically to capture the underlying truth with increasing accuracy. Since the algorithm is not based on rejections, it requires only limited full model evaluations. We show analytically that, in the linear Gaussian case, the algorithm converges geometrically fast with respect to the number of iterations. For more general models, we introduce particle approximations of the iteratively generated sequence of distributions; we also prove that each element of the sequence converges in the large particle limit. We show numerically that, as in the linear case, rapid convergence occurs with respect to the number of iterations. Additionally, we show through computed examples that point estimates obtained from this iterative algorithm are superior to those obtained by neglecting the model error.Comment: 39 pages, 9 figure

BiblioBouts: A Scalable Online Social Game for the Development of Academic Research Skills

Researchers at the School of Information of the University of Michigan are designing, developing, and evaluating BiblioBouts, an online game that helps students learn academic research skills. Players practice using online library research tools while they work on an in-class assignment and produce a high-quality bibliography, at the same time as they are competing against each other to win the game! While librarians are experts at helping students who want to learn about academic research, most students are reluctant participants because they want just-in-time personal assistance that is tailored to their unique information needs, and faculty are reluctant to cede class time. The BiblioBouts project enlists games to teach undergraduate students information literacy skills and concepts in the classroom. Social gaming reinforces principles of good learning, including getting results by trial and error, self-discovery, following hunches and reinforcement through repetition. BiblioBouts also incorporates collaborative problem solving and participation in a community of learning. The project aims to explore how games can be utilized to achieve information literacy goals and to yield open-source game software that libraries could use immediately to enhance their information literacy programs. The LOEX presentation will incorporate a live interactive demo of the game, as well as videos demonstrating gameplay. We will discuss challenges in situating the game into the classroom and integrating it into existing course syllabi. The presentation will describe how we have adapted the game in response to feedback from students and instructors during the pilot process

BiblioBouts Project Interim Report #5

The University of Michigan’s School of Information and its partner, the Center for History and New Media at George Mason University, have undertaken the 4-year BiblioBouts Project (October 1, 2008 to September 30, 2012) to support the design, development, testing, and evaluation of the web-based BiblioBouts game to teach incoming undergraduate students information literacy skills and concepts. This fifth interim report describes the BiblioBouts Project team’s 12-month progress achieving the project’s 4 objectives: designing, developing, deploying, and evaluating the BiblioBouts game and recommending best practices for future information literacy games. This latest 12-month period was marked by extensive progress in the analysis of evaluation data from the testing of the beta 1.0 version of BiblioBouts and putting to work what was learned from this analysis in the design and development of the beta 2.0 version of BiblioBouts. Major tasks that will occupy the team for the next 12 months are demonstrating BiblioBouts’ learning goals, recruiting more instructors to incorporate BiblioBouts in their classes, seeking additional funding, and finding a future home for BiblioBouts. For additional information about game design, pedagogical goals, scoring, game play, project participants, and playing BiblioBouts in your course, consult the BiblioBouts Project web site (http://bibliobouts.si.umich.edu).Institute of Museum and Library Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/87186/1/bbInterimReportToIMLS05.pd

Hierarchical Bayesian level set inversion

The level set approach has proven widely successful in the study of inverse problems for inter- faces, since its systematic development in the 1990s. Re- cently it has been employed in the context of Bayesian inversion, allowing for the quantification of uncertainty within the reconstruction of interfaces. However the Bayesian approach is very sensitive to the length and amplitude scales in the prior probabilistic model. This paper demonstrates how the scale-sensitivity can be cir- cumvented by means of a hierarchical approach, using a single scalar parameter. Together with careful con- sideration of the development of algorithms which en- code probability measure equivalences as the hierar- chical parameter is varied, this leads to well-defined Gibbs based MCMC methods found by alternating Metropolis-Hastings updates of the level set function and the hierarchical parameter. These methods demon- strably outperform non-hierarchical Bayesian level set methods

Building the Games Students Want to Play: BiblioBouts Project Interim Report #2

The University of Michigan’s School of Information and its partner, the Center for History and New Media at George Mason University, are undertaking the 3-year BiblioBouts Project (October 1, 2008 to September 30, 2011) to support the design, development, testing, and evaluation of a computer game to teach incoming undergraduate students information literacy skills and concepts. This second interim report describes the project team’s 5-month progress achieving 2 of the project’s 4 objectives, designing the BiblioBouts game and engaging in evaluation activities. It also enumerates major tasks that will occupy the team for the next 6 months. Appendixes A and B describe the game’s design and include pedagogical goals and how the game scores players.Institute of Museum and Library Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64293/1/bbInterimReportToIMLS02.pd

BiblioBouts final performance review

A University of Michigan (U-M) research team designed, developed, deployed, and evaluated the BiblioBouts information literacy game. BiblioBouts gave students repeated opportunities to develop and practice information literacy skills while they completed a research-and-writing assignment. The evaluation enlisted a multi-methodological approach to data collection. BiblioBouts players were exposed to more online sources than non-players. Players cited more sources in their final-paper bibliographies than non-players. Players felt that they would be better at and more confident about performing various research tasks than they felt before playing the game. They rated their motivation and perseverance at playing the game at high and very high levels. They cited many game-play benefits such as getting a head start on their research, finding relevant sources from classmates’ submissions, becoming a more confident researcher, and being better prepared to write their papers as a result of using the Zotero citation management system.Institute of Museum and Library Serviceshttp://deepblue.lib.umich.edu/bitstream/2027.42/97036/1/bbFinalPerfReviewToIMLS.pd

What Can Causal Networks Tell Us about Metabolic Pathways?

Graphical models describe the linear correlation structure of data and have been used to establish causal relationships among phenotypes in genetic mapping populations. Data are typically collected at a single point in time. Biological processes on the other hand are often non-linear and display time varying dynamics. The extent to which graphical models can recapitulate the architecture of an underlying biological processes is not well understood. We consider metabolic networks with known stoichiometry to address the fundamental question: “What can causal networks tell us about metabolic pathways?”. Using data from an Arabidopsis BaySha population and simulated data from dynamic models of pathway motifs, we assess our ability to reconstruct metabolic pathways using graphical models. Our results highlight the necessity of non-genetic residual biological variation for reliable inference. Recovery of the ordering within a pathway is possible, but should not be expected. Causal inference is sensitive to subtle patterns in the correlation structure that may be driven by a variety of factors, which may not emphasize the substrate-product relationship. We illustrate the effects of metabolic pathway architecture, epistasis and stochastic variation on correlation structure and graphical model-derived networks. We conclude that graphical models should be interpreted cautiously, especially if the implied causal relationships are to be used in the design of intervention strategies

Building the Games Students Want to Play: BiblioBouts Project Interim Report #3

The University of Michigan's School of Information and its partner, the Center for History and New Media at George Mason University, are undertaking the 3-year BiblioBouts Project (October 1, 2008 to September 30, 2011) to support the design, development, testing, and evaluation of the web-based BiblioBouts game to teach incoming undergraduate students information literacy skills and concepts. This third interim report describes the BiblioBouts Project team’s 6-month progress achieving the project's 4 objectives: designing, developing, deploying, and evaluating the BiblioBouts game and recommending best practices for future information literacy games. This latest 6-month period was marked by extensive progress in the deployment and evaluation of the alpha version of BiblioBouts. Major tasks that will occupy the team for the next 6 months are applying evaluation findings to game redesign and enhancement. For general information about game design, pedagogical goals, scoring, game play, project participants, and playing BiblioBouts in your course, consult the BiblioBouts Project web site.Institute of Museum and Library Serviceshttp://deepblue.lib.umich.edu/bitstream/2027.42/69157/1/bbInterimReportToIMLS03.pd

Measurement of the inclusive isolated-photon cross section in pp collisions at √s = 13 TeV using 36 fb−1 of ATLAS data

The differential cross section for isolated-photon production in pp collisions is measured at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC using an integrated luminosity of 36.1 fb. The differential cross section is presented as a function of the photon transverse energy in different regions of photon pseudorapidity. The differential cross section as a function of the absolute value of the photon pseudorapidity is also presented in different regions of photon transverse energy. Next-to-leading-order QCD calculations from Jetphox and Sherpa as well as next-to-next-to-leading-order QCD calculations from Nnlojet are compared with the measurement, using several parameterisations of the proton parton distribution functions. The predictions provide a good description of the data within the experimental and theoretical uncertainties. [Figure not available: see fulltext.

Building the Games Students Want to Play: BiblioBouts Project Interim Report #4

The University of Michigan's School of Information and its partner, the Center for History and New Media at George Mason University, are undertaking the 3-year BiblioBouts Project (October 1, 2008 to September 30, 2011) to support the design, development, testing, and evaluation of the web-based BiblioBouts game to teach incoming undergraduate students information literacy skills and concepts. This fourth interim report describes the BiblioBouts Project team’s 5-month progress achieving the project’s 4 objectives: designing, developing, deploying, and evaluating the BiblioBouts game and recommending best practices for future information literacy games. This latest 5-month period was marked by extensive progress in the analysis of evaluation data from the testing of the alpha version of BiblioBouts and putting to work what was learned from this analysis in the design and development of the beta version of BiblioBouts. Major tasks that will occupy the team for the next 7 months are completing the development of beta BiblioBouts, pretesting BiblioBouts, testing BiblioBouts in classes at the five participating institutions, and evaluating test administrations. For general information about game design, pedagogical goals, scoring, game play, project participants, and playing BiblioBouts in your course, consult the BiblioBouts Project web site at http://bibliobouts.si.umich.edu/.Institute of Museum and Library Serviceshttp://deepblue.lib.umich.edu/bitstream/2027.42/78021/1/bbInterimReportToIMLS04.pd