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Recent documents in Worksen-usThu, 22 Feb 2024 01:39:19 PST3600An Exploration Of Parameter Duality In Statistical Inference
https://works.swarthmore.edu/fac-math-stat/311
https://works.swarthmore.edu/fac-math-stat/311Mon, 12 Feb 2024 12:37:54 PST
Well-known debates among statistical inferential paradigms emerge from conflicting views on the notion of probability. One dominant view understands probability as a representation of sampling variability; another prominent view understands probability as a measure of belief. The former generally describes model parameters as fixed values, in contrast to the latter. We propose that there are actually two versions of a parameter within both paradigms: a fixed unknown value that generated the data and a random version to describe the uncertainty in estimating the unknown value. An inferential approach based on CDs deciphers seemingly conflicting perspectives on parameters and probabilities.
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Suzanne Thornton et al.On The Third Moment Of <em>L</em>(½, <em>χ<sub>d</sub></em>) {II}: The Number Field Case
https://works.swarthmore.edu/fac-math-stat/312
https://works.swarthmore.edu/fac-math-stat/312Mon, 12 Feb 2024 12:37:54 PST
We establish a smoothed asymptotic formula for the third moment of quadratic Dirichlet L-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size x^{¾}. The error term in the asymptotic formula is on the order of O(x^{⅔+δ}) for every δ > 0.
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A. Diaconu et al.Bridging Bayesian, Frequentist And Fiducial Inferences Using Confidence Distributions
https://works.swarthmore.edu/fac-math-stat/310
https://works.swarthmore.edu/fac-math-stat/310Mon, 12 Feb 2024 12:37:53 PST
Bayesian, frequentist, and fiducial (BFF) inferences are much more congruous than have been perceived historically in the scientific community (e.g., Reid and Cox (2015); Kass (2011); Efron (1998)). Most practitioners are probably more familiar with the two dominant statistical inferential paradigms, Bayesian inference and frequentist inference. The third, lesser known fiducial inference paradigm was pioneered by R.A. Fisher in an attempt to define an inversion procedure for inference as an alternative to Bayes’ theorem. Although each paradigm has its own strengths and limitations subject to their different philosophical underpinnings, this chapter intends to bridge these different inferential methodologies by calling upon confidence distribution theory and Monte-Carlo simulation procedures, thereby increasing the range of possible techniques available to both statistical theorists and practitioners across all fields.
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Suzanne Thornton et al.Statistics Education And Reconsidering The Status Quo
https://works.swarthmore.edu/fac-math-stat/308
https://works.swarthmore.edu/fac-math-stat/308Mon, 12 Feb 2024 12:37:52 PSTSuzanne ThorntonStatistics For Equity: Capturing, Not Masking, Intersectional Dynamics In Data
https://works.swarthmore.edu/fac-math-stat/309
https://works.swarthmore.edu/fac-math-stat/309Mon, 12 Feb 2024 12:37:52 PSTS. H. Cook et al.Towards Statistical Best Practices For Gender And Sex Data
https://works.swarthmore.edu/fac-math-stat/307
https://works.swarthmore.edu/fac-math-stat/307Mon, 12 Feb 2024 12:37:51 PST
Suzanne Thornton, Dooti Roy, Stephen Parry, Donna LaLonde, Wendy Martinez, Renee Ellis and David Corliss call for a more inclusive – and informative – approach to collecting data on human gender and sex.
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Suzanne Thornton et al.Approximate Confidence Distribution Computing
https://works.swarthmore.edu/fac-math-stat/306
https://works.swarthmore.edu/fac-math-stat/306Mon, 12 Feb 2024 12:37:50 PST
Approximate confidence distribution computing (ACDC) offers a new take on the rapidly developing field of likelihood-free inference from within a frequentist framework. The appeal of this computational method for statistical inference hinges upon the concept of a confidence distribution, a special type of estimator which is defined with respect to the repeated sampling principle. An ACDC method provides frequentist validation for computational inference in problems with unknown or intractable likelihoods. The main theoretical contribution of this work is the identification of a matching condition necessary for frequentist validity of inference from this method. In addition to providing an example of how a modern understanding of confidence distribution theory can be used to connect Bayesian and frequentist inferential paradigms, we present a case to expand the current scope of so-called approximate Bayesian inference to include non-Bayesian inference by targeting a confidence distribution rather than a posterior. The main practical contribution of this work is the development of a data-driven approach to drive ACDC in both Bayesian or frequentist contexts. The ACDC algorithm is data-driven by the selection of a data-dependent proposal function, the structure of which is quite general and adaptable to many settings. We explore three numerical examples that both verify the theoretical arguments in the development of ACDC and suggest instances in which ACDC outperform approximate Bayesian computing methods computationally.
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Suzanne Thornton et al.A Global Ecological Signal Of Extinction Risk In Terrestrial Vertebrates
https://works.swarthmore.edu/fac-math-stat/305
https://works.swarthmore.edu/fac-math-stat/305Mon, 12 Feb 2024 12:37:50 PST
To determine the distribution and causes of extinction threat across functional groups of terrestrial vertebrates, we assembled an ecological trait data set for 18,016 species of terrestrial vertebrates and utilized phylogenetic comparative methods to test which categories of habitat association, mode of locomotion, and feeding mode best predicted extinction risk. We also examined the individual categories of the International Union for Conservation of Nature Red List extinction drivers (e.g., agriculture and logging) threatening each species and determined the greatest threats for each of the four terrestrial vertebrate groups. We then quantified the sum of extinction drivers threatening each species to provide a multistressor perspective on threat. Cave dwelling amphibians (p < 0.01), arboreal quadrupedal mammals (all of which are primates) (p < 0.01), aerial and scavenging birds (p < 0.01), and pedal (i.e., walking) squamates (p < 0.01) were all disproportionately threatened with extinction in comparison with the other assessed ecological traits. Across all threatened vertebrate species in the study, the most common risk factors were agriculture, threatening 4491 species, followed by logging, threatening 3187 species, and then invasive species and disease, threatening 2053 species. Species at higher risk of extinction were simultaneously at risk from a greater number of threat types. If left unabated, the disproportionate loss of species with certain functional traits and increasing anthropogenic pressures are likely to disrupt ecosystem functions globally. A shift in focus from species- to trait-centric conservation practices will allow for protection of at-risk functional diversity from regional to global scales.
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M. J. Munstermann et al.On Fossil Recovery Potential In The <em>Australopithecus anamensis–Australopithecus afarensis</em> Lineage: A Reply To Žliobaitė (2020)
https://works.swarthmore.edu/fac-math-stat/304
https://works.swarthmore.edu/fac-math-stat/304Mon, 12 Feb 2024 12:37:49 PST
We thank Žliobaitė (2020) for the interest in our article (Du et al., 2020) and the resulting dialogue. In this response, we briefly summarize Du and colleagues' analysis and Žliobaitė's commentary, respond to the points raised by Žliobaitė, and conclude with some thoughts on why the distribution of Australopithecus anamensis–Australopithecus afarensis fossil horizons does not conform to a wax–wane pattern.
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A. Du et al.Generalized Sasakian Structures From A Poisson Geometry Viewpoint
https://works.swarthmore.edu/fac-math-stat/303
https://works.swarthmore.edu/fac-math-stat/303Mon, 12 Feb 2024 12:37:48 PST
In this paper we define a canonical Poisson structure on a normal generalized contact metric space and use this structure to define a generalized Sasakian structure. We show also that this canonical Poisson structure enables us to distinguish generalized Sasakian structures from generalized coKähler structures.
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Janet TalvacchiaOn Best Practices For The Recruitment, Retention, And Flourishing Of LGBTQ+ Mathematicians
https://works.swarthmore.edu/fac-math-stat/301
https://works.swarthmore.edu/fac-math-stat/301Mon, 12 Feb 2024 12:37:47 PSTR. Buckmire et al.Spectra Of Variants Of Distance Matrices Of Graphs And Digraphs: A Survey
https://works.swarthmore.edu/fac-math-stat/302
https://works.swarthmore.edu/fac-math-stat/302Mon, 12 Feb 2024 12:37:47 PST
Distance matrices of graphs were introduced by Graham and Pollack in 1971 to study a problem in communications. Since then, there has been extensive research on the distance matrices of graphs—a 2014 survey by Aouchiche and Hansen on spectra of distance matrices of graphs lists more than 150 references. In the last 10 years, variants such as the distance Laplacian, the distance signless Laplacian, and the normalized distance Laplacian matrix of a graph have been studied. After a brief description of the early history of the distance matrix and its motivating problem, this survey focuses on comparing and contrasting techniques and results for the four types of distance matrices. Digraphs are treated separately after the discussion of graphs, including discussion of similarities and differences between graphs and digraphs. New results are presented that complement existing results, including results for some the matrices on unimodality of characteristic polynomials for graphs, preservation of parameters by cospectrality for graphs, and bounds on spectral radii for digraphs.
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L. Hogben et al.Recent Activities And Progress By Spectra And The LGBTQ+ Mathematics Community
https://works.swarthmore.edu/fac-math-stat/300
https://works.swarthmore.edu/fac-math-stat/300Mon, 12 Feb 2024 12:37:46 PSTJoseph NakaoStrongly Invertible Knots, Equivariant Slice Genera, And An Equivariant Algebraic Concordance Group
https://works.swarthmore.edu/fac-math-stat/299
https://works.swarthmore.edu/fac-math-stat/299Mon, 12 Feb 2024 07:33:39 PST
We use the Blanchfield form to obtain a lower bound on the equivariant slice genus of a strongly invertible knot. For our main application, let K be a strongly invertible genus one slice knot with nontrivial Alexander polynomial. We show that the equivariant slice genus of an equivariant connected sum #^{nK is at least n/4. We also formulate an equivariant algebraic concordance group, and show that the kernel of the forgetful map to the classical algebraic concordance group is infinite rank.}
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Allison N. Miller et al.Branched Covers Bounding Rational Homology Balls
https://works.swarthmore.edu/fac-math-stat/298
https://works.swarthmore.edu/fac-math-stat/298Mon, 12 Feb 2024 07:33:38 PST
Prime power–fold cyclic branched covers along smoothly slice knots all bound rational homology balls. This phenomenon, however, does not characterize slice knots. We give a new construction of nonslice knots that have the above property. The sliceness obstruction comes from computing twisted Alexander polynomials, and we introduce new techniques to simplify their calculation.
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P. Aceto et al.Embedding Spheres In Knot Traces
https://works.swarthmore.edu/fac-math-stat/297
https://works.swarthmore.edu/fac-math-stat/297Mon, 12 Feb 2024 07:33:37 PST
The trace of the n-framed surgery on a knot in S³ is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded 2-sphere whose complement has abelian fundamental group. Our characterisation is in terms of classical and computable 3-dimensional knot invariants. For each n, this provides conditions that imply a knot is topologically n-shake slice, directly analogous to the result of Freedman and Quinn that a knot with trivial Alexander polynomial is topologically slice.
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P. Feller et al.Amphichiral Knots With Large 4-Genus
https://works.swarthmore.edu/fac-math-stat/295
https://works.swarthmore.edu/fac-math-stat/295Mon, 12 Feb 2024 07:33:36 PST
For each we give g > 0 infinitely many knots that are strongly negative amphichiral, hence rationally slice and representing 2-torsion in the smooth concordance group, yet which do not bound any locally flatly embedded surface in the 4-ball with genus less than or equal to g. Our examples also allow us to answer a question about the four-dimensional clasp number of knots.
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Allison N. MillerThe Topological Slice Genus Of Satellite Knots
https://works.swarthmore.edu/fac-math-stat/296
https://works.swarthmore.edu/fac-math-stat/296Mon, 12 Feb 2024 07:33:36 PST
We present evidence supporting the conjecture that, in the topological category, the slice genus of a satellite knot P(K) is bounded above by the sum of the slice genera of K and P(U). Our main result establishes this conjecture for a variant of the topological slice genus, the ℤ–slice genus. Notably, the conjectured upper bound does not involve the algebraic winding number of the pattern P. This stands in stark contrast with the smooth category, where, for example, there are many genus 1 knots whose (n,1)–cables have arbitrarily large smooth 4–genera. As an application, we show that the (n,1)–cable of any knot of 3–genus 1 (eg the figure-eight or trefoil knot) has topological slice genus at most 1, regardless of the value of n∈N. Further, we show that the lower bounds on the slice genus coming from the Tristram–Levine and Casson–Gordon signatures cannot be used to disprove the conjecture.
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P. Feller et al.A Note on the Concordance ℤ-Genus
https://works.swarthmore.edu/fac-math-stat/294
https://works.swarthmore.edu/fac-math-stat/294Mon, 12 Feb 2024 07:33:35 PST
We show that the difference between the topological 4-genus of a knot and the minimal genus of a surface bounded by that knot that can be decomposed into a smooth concordance followed by an algebraically simple locally flat surface can be arbitrarily large. This extends work of Hedden, Livingston, and Ruberman showing that there are topologically slice knots which are not smoothly concordant to any knot with trivial Alexander polynomial.
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Allison N. Miller et al.Homomorphism Obstructions For Satellite Maps
https://works.swarthmore.edu/fac-math-stat/293
https://works.swarthmore.edu/fac-math-stat/293Mon, 12 Feb 2024 07:33:34 PST
A knot in a solid torus defines a map on the set of (smooth or topological) concordance classes of knots in S³. This set admits a group structure, but a conjecture of Hedden suggests that satellite maps never induce interesting homomorphisms: we give new evidence for this conjecture in both categories. First, we use Casson-Gordon signatures to give the first obstruction to a slice pattern inducing a homomorphism on the topological concordance group, constructing examples with every winding number besides ± 1. We then provide subtle examples of satellite maps which map arbitrarily deep into the n-solvable filtration of Cochran, Orr, and Teichner [Ann. of Math. (2) 157 (2003), pp. 433–519], act like homomorphisms on arbitrary finite sets of knots, and yet which still do not induce homomorphisms. Finally, we verify Hedden’s conjecture in the smooth category for all small crossing number satellite operators but one.
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Allison N. Miller