Connecting GRBs and galaxies: the probability of chance coincidence

Studies of GRB host galaxies are crucial to understanding GRBs. However, since they are identified by the superposition in the plane of the sky of a GRB afterglow and a galaxy there is always a possibility that an association represents a chance alignment, rather than a physical connection. We examine a uniform sample of 72 GRB fields to explore the probability of chance superpositions. There is typically a ~1% chance that an optical afterglow will coincide with a galaxy by chance. While spurious host galaxy detections will, therefore, be rare, the possibility must be considered when examining individual GRB/host galaxy examples. It is also tempting to use the large and uniform collection of X-ray afterglow positions to search for GRB-associated galaxies. However, we find that approximately half of the 14 superpositions in our sample are likely to occur by chance, so in the case of GRBs localized only by an X-ray afterglow, even statistical studies are suspect.Comment: edited, accepted by Ap

A Project Based Approach to Statistics and Data Science

In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathematics faculty to teach statistics courses. This paper presents a model that a mathematician asked to teach statistics can follow. This model entails connecting with faculty from numerous departments on campus to develop a list of topics, building a repository of real-world datasets from these faculty, and creating projects where students interface with these datasets to write lab reports aimed at consumers of statistics in other disciplines. The end result is students who are well prepared for interdisciplinary research, who are accustomed to coping with the idiosyncrasies of real data, and who have sharpened their technical writing and speaking skills

Voters punish politicians for misinformation that portrays them in a favourable light, but not for inaccurate information that attacks their opponents.

What impact does inaccurate information have on political campaigning? Outlining the results of three studies on the role of misinformation in politics, Michael D. Cobb finds that voters react to positive and negative information in very different ways. While negative misinformation, such as using false figures to attack a political opponent, tends to linger in the minds of voters even after it is retracted; there is no such effect when positive information about a politician is debunked. Indeed, voters appear to actively punish politicians in the aftermath of positive misinformation

Nature's Starships II: Simulating the Synthesis of Amino Acids in Meteorite Parent Bodies

Carbonaceous chondrite meteorites are known for having high water and organic material contents, including amino acids. Here we address the origin of amino acids in the warm interiors of their parent bodies (planetesimals) within a few million years of their formation, and connect this with the astrochemistry of their natal protostellar disks. We compute both the total amino acid abundance pattern as well as the relative frequencies of amino acids within the CM2 (e.g. Murchison) and CR2 chondrite subclasses based on Strecker reactions within these bodies. We match the relative frequencies to well within an order of magnitude among both CM2 and CR2 meteorites for parent body temperatures $<$ 200$^{\circ}$C. These temperatures agree with 3D models of young planetesimal interiors. We find theoretical abundances of approximately 7x10$^5$ parts-per-billion (ppb), which is in agreement with the average observed abundance in CR2 meteorites of 4$\pm$7x10$^5$, but an order of magnitude higher than the average observed abundance in CM2 meteorites of 2$\pm$2x10$^4$. We find that the production of hydroxy acids could be favoured over the production of amino acids within certain meteorite parent bodies (e.g. CI1, CM2) but not others (e.g. CR2). This could be due to the relatively lower NH$_3$ abundances within CI1 and CM2 meteorite parent bodies, which leads to less amino acid synthesis. We also find that the water content in planetesimals is likely to be the main cause of variance between carbonaceous chondrites of the same subclass. We propose that amino acid abundances are primarily dependent on the ammonia and water content of planetesimals that are formed in chemically distinct regions within their natal protostellar disks.Comment: 19 pages, 11 figures, Accepted for publication in Ap

Wavelet Ensemble Kalman Filters

We present a new type of the EnKF for data assimilation in spatial models that uses diagonal approximation of the state covariance in the wavelet space to achieve adaptive localization. The efficiency of the new method is demonstrated on an example.Comment: 4 pages, 4 figure

Marginal likelihoods in phylogenetics: a review of methods and applications

By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to increase in complexity to better capture micro and macroevolutionary processes. In a Bayesian framework, the marginal likelihood is how data update our prior beliefs about models, which gives us an intuitive measure of comparing model fit that is grounded in probability theory. Given the rapid increase in the number and complexity of phylogenetic models, methods for approximating marginal likelihoods are increasingly important. Here we try to provide an intuitive description of marginal likelihoods and why they are important in Bayesian model testing. We also categorize and review methods for estimating marginal likelihoods of phylogenetic models, highlighting several recent methods that provide well-behaved estimates. Furthermore, we review some empirical studies that demonstrate how marginal likelihoods can be used to learn about models of evolution from biological data. We discuss promising alternatives that can complement marginal likelihoods for Bayesian model choice, including posterior-predictive methods. Using simulations, we find one alternative method based on approximate-Bayesian computation (ABC) to be biased. We conclude by discussing the challenges of Bayesian model choice and future directions that promise to improve the approximation of marginal likelihoods and Bayesian phylogenetics as a whole.Comment: 33 pages, 3 figure

Are Young People's Educational Outcomes Linked to their Sense of Control?

This paper analyzes the link between young people's sense (locus) of control over their lives and their investments in education. We find that young people with a more internal locus of control have a higher probability of finishing secondary school and, conditional on completion, meeting the requirements to obtain a university entrance rank. Moreover, those with an internal locus of control who obtain a university entrance rank achieve somewhat higher rankings than do their peers who have a more external locus of control. Not surprisingly, there is a negative relationship between growing up in disadvantage and educational outcomes. However, this effect does not appear to operate indirectly by increasing the likelihood of having a more external locus of control. In particular, we find no significant relationship between family welfare history and young people's locus of control.locus of control, parental socio-economic background, education

Astronomy : a themantic unit : an honors thesis (HONRS 499)

Education occurs constantly, and not always in a classroom. I want my students to realize that learning does not end when they leave my classroom. I wrote lesson plans with the common theme of astronomy to show my students that astronomy is not limited to science. Not all lessons were specifically about astronomy, but they contained symbols or visual references which remind students of the integration of astronomy into every aspect of the curriculum. I want my students to realize that any area of interest they have should not be compartmentalized or limited. I want them to see that all aspects of life are interrelated with many commonalities and that they can use their knowledge to draw correlations and relationships between things.I wrote my lesson plans for different ages in elementary school so that they can be adapted or expanded to fit any age group. These lessons can easily be adapted for special education classes or for students with special needs so that they do not miss out on anything. I tried to make as many hands on lessons as possible to get children to be active learning participants. I also included extensions to lessons or activities children could do alone, both to increase learning opportunities and to allow the teacher flexibility in planning.Honors CollegeThesis (B.?.