Tag Archives: Other Statistics

A Conceptual Introduction to Markov Chain Monte Carlo Methods [CL]

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http://arxiv.org/abs/1909.12313


Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random samples. This article provides a basic introduction to MCMC methods by establishing a strong conceptual understanding of what problems MCMC methods are trying to solve, why we want to use them, and how they work in theory and in practice. To develop these concepts, I outline the foundations of Bayesian inference, discuss how posterior distributions are used in practice, explore basic approaches to estimate posterior-based quantities, and derive their link to Monte Carlo sampling and MCMC. Using a simple toy problem, I then demonstrate how these concepts can be used to understand the benefits and drawbacks of various MCMC approaches. Exercises designed to highlight various concepts are also included throughout the article.

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J. Speagle
Mon, 30 Sep 19
45/55

Comments: 54 pages, 15 figures, submitted to the Journal of Statistics Education. All comments and feedback greatly appreciated

Robust Registration of Astronomy Catalogs with Applications to the Hubble Space Telescope [IMA]

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http://arxiv.org/abs/1908.10971


Astrometric calibration of images with a small field of view is often inferior to the internal accuracy of the source detections due to the small number of accessible guide stars. One important experiment with such challenges is the Hubble Space Telescope (HST). A possible solution is to cross-calibrate overlapping fields instead of just relying on standard stars. Following the approach of \citet{2012ApJ…761..188B}, we use infinitesimal 3D rotations for fine-tuning the calibration but devise a better objective that is robust to a large number of false candidates in the initial set of associations. Using Bayesian statistics, we accommodate bad data by explicitly modeling the quality, which yields a formalism essentially identical to an $M$-estimation in robust statistics. Our results on simulated and real catalogs show great potentials for improving the HST calibration, and those with similar challenges.

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F. Tian, T. Budavári, A. Basu, et. al.
Fri, 30 Aug 19
27/58

Comments: N/A

Introducing Bayesian Analysis with $\text{m&m's}^\circledR$: an active-learning exercise for undergraduates [CL]

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http://arxiv.org/abs/1904.11006


We present an active-learning strategy for undergraduates that applies Bayesian analysis to candy-covered chocolate $\text{m&m’s}^\circledR$. The exercise is best suited for small class sizes and tutorial settings, after students have been introduced to the concepts of Bayesian statistics. The exercise takes advantage of the non-uniform distribution of $\text{m&m’s}^\circledR~$ colours, and the difference in distributions made at two different factories. In this paper, we provide the intended learning outcomes, lesson plan and step-by-step guide for instruction, and open-source teaching materials. We also suggest an extension to the exercise for the graduate-level, which incorporates hierarchical Bayesian analysis.

Read this paper on arXiv…

G. Eadie, D. Huppenkothen, A. Springford, et. al.
Fri, 26 Apr 19
2/69

Comments: Accepted to the Journal of Statistics Education (in press); 15 pages, 7 figures