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- On multivariable cumulant polynomial sequences with applications
- A new family of polynomials, called cumulant polynomial sequence, and its extension to the multivariate case is introduced relying on a purely symbolic combinatorial method. The coefficients are cumulants, but depending on what is plugged in the indeterminates, moment sequences can be recovered as well. The main tool is a formal generalization of random sums, when a not necessarily integer-valued multivariate random index is considered. Applications are given within parameter estimations, L ?evy processes and random matrices and, more generally, problems involving multivariate functions. The connection between exponential models and multivariable Sheffer polynomial sequences offers a different viewpoint in employing the method. Some open problems end the paper.
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- Algebraic geometry of Poisson regression
- Designing experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. Here we investigate local optimality. We propose to study for a given design its region of optimality in parameter space. Often these regions are semi-algebraic and feature interesting symmetries. We demonstrate this with the Rasch Poisson counts model. For any given interaction order between the explanatory variables we give a characterization of the regions of optimality of a special saturated design. This extends known results from the case of no interaction. We also give an algebraic and geometric perspective on optimality of experimental designs for the Rasch Poisson counts model using polyhedral and spectrahedral geometry.
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- A linear-algebraic tool for conditional independence inference
- In this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables.
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- Mode Poset Probability Polytopes
- A mode of a probability distribution is an elementary event that has more probability mass than each of its direct neighbors, with respect to some vicinity structure on the set of elementary events. The mode inequalities cut out a polytope from the simplex of probability distributions. Related to this is the concept of strong modes. A strong mode is an elementary event that has more probability mass than all its direct neighbors together. The set of probability distributions with a given set of strong modes is again a polytope. We study the vertices, the facets, and the volume of such polytopes depending on the sets of (strong) modes and the vicinity structures.
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- FAST AUTOMATIC BAYESIAN CUBATURE USING MATCHING KERNELS AND DESIGNS
- Automatic cubatures approximate multidimensional integrals to user-specified error tolerances. In many real-world integration problems, the analytical solution is either unavailable or difficult to compute. To overcome this, one can use numerical algorithms that approximately estimate the value of the integral. For high dimensional integrals, quasi-Monte Carlo (QMC) methods are very popular. QMC methods are equal-weight quadrature rules where the quadrature points are chosen deterministically, unlike Monte Carlo (MC) methods where the points are chosen randomly. The families of integration lattice nodes and digital nets are the most popular quadrature points used. These methods consider the integrand to be a deterministic function. An alternate approach, called Bayesian cubature, postulates the integrand to be an instance of a Gaussian stochastic process.
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- L-cumulants, L-cumulant embeddings and algebraic statistics
- Focusing on the discrete probabilistic setting we generalize the combinatorial definition of cumulants to L-cumulants. This generalization keeps all the desired properties of the classical cumulants like semi-invariance and vanishing for independent blocks of random variables. These properties make L-cumulants useful for the algebraic analysis of statistical models. We illustrate this for general Markov models and hidden Markov processes in the case when the hidden process is binary. The main motivation of this work is to understand cumulant-like coordinates in alge- braic statistics and to give a more insightful explanation why tree cumulants give such an elegant description of binary hidden tree models. Moreover, we argue that L-cumulants can be used in the analysis of certain classical algebraic varieties.
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- Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables
- We consider the lattice, L, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and supermodularity for the marginalization function, n(·), on L. We derive from the supermodularity of n(·) some generalized Fr ́echet inequalities comple- menting and extending inequalities of Dobra and Fienberg. Further, we construct new monotonic and supermodular functions from n(·), and we remark on the connection between supermodularity and some correlation inequalities for probability distributions on lattices. We also apply an inequal- ity of Ky Fan to derive a new approach to Fr ́echet inequalities for multidimensional contingency tables.
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- Maximal Length Projections in Group Algebras with Applications to Linear Rank Tests of Uniformity
- Let G be a finite group, let CG be the complex group algebra of G, and let p ∈ CG. In this paper, we show how to construct submodules S of CG of a fixed dimension with the property that the orthogonal projection of p onto S has maximal length. We then provide an example of how such submodules for the symmetric group Sn can be used to create new linear rank tests of uniformity in statistics for survey data that arises when respondents are asked to give a complete ranking of n items.
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- Connectivity for 3 x 3 x K contingency tables
- We consider an exact sequential conditional test for three-way conditional test of no interaction. At each time τ, the test uses as the conditional inference frame the set F(Hτ) of all tables with the same three two-way marginal tables as the obtained table Hτ . For 3 × 3 × K tables, we propose a method to construct F(Hτ) from F(Hτ−1). This enables us to perform efficiently the sequential exact conditional test. The subset Sτ of F (Hτ ) consisting of s + Hτ − Hτ −1 for s ∈ F(Hτ−1) contains Hτ , where the operations + and − are defined elementwise. Our argument is based on the minimal Markov basis for 3 × 3 × K contingency tables and we give a minimal subset M of some Markov basis which has the property that F (Hτ ) = {s − m | s ∈ Sτ , m ∈ M}.
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- Matrix Completion for the Independence Model
- We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex ∆mn−1. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for partial observations to come from the independence model. For each pattern of specified entries, we give equations and inequalities which are satisfied if and only if an eligible completion exists. We also describe the set of valid completions, and we optimize over this set.
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- One example of general unidentifiable tensors
- Abstract. Theidentifiabilityofparametersinaprobabilisticmodelisacrucialnotioninstatistical inference. We prove that a general tensor of rank 8 in C3 ⊗ C6 ⊗ C6 has at least 6 decompositions as sum of simple tensors, so it is not 8-identifiable. This is the highest known example of balanced tensors of dimension 3, which are not k-identifiable, when k is smaller than the generic rank.
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- Hilbert Polynomial of the Kimura 3-Parameter Model
- In [2] Buczyn ́ska and Wi ́sniewski showed that the Hilbert polynomial of the algebraic variety associated to the Jukes-Cantor binary model on a trivalent tree depends only on the number of leaves of the tree and not on its shape. We ask if this can be generalized to other group-based models. The Jukes-Cantor binary model has Z2 as the underlying group. We consider the Kimura 3-parameter model with Z2 × Z2 as the underlying group. We show that the generalization of the statement about the Hilbert polynomials to the Kimura 3-parameter model is not possible as the Hilbert polynomial depends on the shape of a trivalent tree.
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- Environmental Monitoring of University Archives and Special Collections
- This is the final report and analysis of activities conducted as part of Environmental Monitoring of University Archives and Special Collections, a project funded by a Preservation Assistance Grant from the National Endowment of the Humanities (PG-263471-19). This grant was awarded to support the first evercsystematic environmental monitoring of the UASC spaces. This report includes a summary of the collected data, analysis of the data, and potential future activities to be undertaken as a result of the grant activities and the data collected., Sponsorship: National Endowment For The Humanities, Preservation Assistance Grants for Smaller Institutions
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- Views on Ethical Issues in Research Labs: a University-Wide Survey
- Full survey used for "Views on Ethical Issues in Research Labs" published in the journal Accountability in Research: Policies and Quality Assurance in 2021. This survey was completed in 2017., Sponsorship: National Science Foundation
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- An Introduction to the Societal Roles of Ethics Codes
- In this collected volume, we are interested in the roles of ethics codes and ethical guidelines in professions in which research and innovation play an important role and where emerging technologies bring about considerable, sometimes fast-paced change.
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- Informed Consent in Digital Data Management
- This article discusses the role of informed consent, a well-known concept and standard established in the field of medicine, in ethics codes relating to digital data management. It analyzes the significance allotted to informed consent and informed consent-related principles in ethics codes, policies, and guidelines by presenting the results of a study focused on 31 ethics codes, policies, and guidelines held as part of the Ethics Codes Collection. The analysis reveals that up to now, there is a limited number of codes of ethics, policies, and guidelines on digital data management. Informed consent often is a central component in these codes and guidelines. While there undoubtedly are significant similarities between informed consent in medicine and digital data management, in ethics codes and guidelines, informed consent-related standards in some fields such as marketing are weaker and less strict. The article concludes that informed consent is an essential standard in digital data management that can help effectively shape future practices in the field. However, a more detailed reflection on the specific content and role of informed consent and informed consent-related standards in the various areas of digital data management is needed to avoid the weakening and dilution of standards in contexts where there are no clear legal regulations.
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- Interview with Todd Friedman: photos
- We conducted an interview with Todd Friedman, a game competitor who holds over 100 game world records, on Sep 25, 2015 at his home in Gurnee, IL. Todd Friedman is a game competitor and competition organizer. His personal game collections consist of 2,840 games and he has been playing video games since he was five years old. His world records are recorded on the Twin Galaxies Score Database website. For the Wii DJ Hero alone he has three pages filled with records of him placing 1st, 2nd, 3rd and 4th with songs ranging from Foo Fighters to Jackson Five. However, Todd has never worked as a full-time game competitor. Instead, he is an EDI (Electronic data interchange) analyst at HubGroup, a truck company. Generally, he arrives home from work at 4:30pm and plays games or works out with his children. Todd has his own philosophy for life and gaming. He holds world records but has never thought of earning money from playing games or having it as a “real” job. Rather, he loves the competition itself. In his view, playing games is more like something that brings people fun and happiness, instead of a tool to make money. He also enjoys being a spectator and watching others play games. This is one of the reasons why he loves not only to participate but also to organize game competitions. How does Todd balance his daily life with his gaming life? If you ask Todd they are one and the same. In fact, a quote of his is “Working and being father is my typical day.” He works his full time job, spends time with his family and ensures that he also spends time on his professional gaming activities. He has twins, a boy and a girl aged 9 years old that he does the normal after school activities with like, soccer, cheerleading, etc. He also loves video gaming especially with his family! One controversial view is that coin-operated video gaming has been a target of negative perceptions. However, Todd completely discredits this argument -- that gaming is a negative influence. He credits video gaming for keeping him on a good path, away from drugs and alcohol, fueling his interest in technology, and obtaining friendships from an array of different cultures all due to being able to meet, talk and play video games with people from around the nation and around the world. Are e-sports according to Todd a real sport? The short answer is “yes.” Todd has two favorite sports, Bowling and video gaming. He compared video game competition to bowling to how some people do not believe it is a sport by discussing hand and eye coordination, mental focus, and talent. You have to beat the other person and practice to get better at it, which is exactly like bowling or golf. According to Todd, a professional gamer, a sport consists of using your mind, practicing, and playing against someone to win. And e-sports falls within his definition. Through the interview, we found that Todd was not in agreement with a lot of the negative stereotypes that people have about gaming, such as, video games are bad for young kids, it wastes their time, money and may have a negative effect on their behaviors and social skills. Instead, he is an average guy who has been playing games since 7 years old and it has helped to evolve him socially and as a positive role model. He credits video games to keeping him away from drugs and alcohol and is also a mechanism that helps to relieve stress. It also positively affects his relationships. He is a better friend, father, husband and co-worker because of his involvement with games.