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The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation developed to help illustrate the Central Limit Theorem. Students use the computer mouse to hand draw a population of arbitrary shape and then watch as the sampling distribution grows with each sample selected. A simple assessment tool is also given to check students' understanding of this crucial concept.

In this article, we introduce the Bayesian change point and variable selection algorithm that uses dynamic programming recursions to draw direct samples from a very high-dimensional space in a computationally efficient manner, and apply this algorithm to a geoscience problem that concerns the Earth's history of glaciation. Strong evidence exists for at least two changes in the behavior of the Earth's glaciers over the last five million years. Around 2.7 Ma, the extent of glacial cover on the Earth increased, but the frequency of glacial melting events remained constant at 41 kyr. A more dramatic change occurred around 1 Ma. For over three decades, the “Mid-Pleistocene Transition” has been described in the geoscience literature not only by a further increase in the magnitude of glacial cover, but also as the dividing point between the 41 kyr and the 100 kyr glacial worlds. Given such striking changes in the glacial record, it is clear that a model whose parameters can change through time is essential for the analysis of these data. The Bayesian change point algorithm provides a probabilistic solution to a data segmentation problem, while the exact Bayesian inference in regression procedure performs variable selection within each regime delineated by the change points. Together, they can model a time series in which the predictor variables as well as the parameters of the model are allowed to change with time. Our algorithm allows one to simultaneously perform variable selection and change point analysis in a computationally efficient manner. Supplementary materials including MATLAB code for the Bayesian change point and variable selection algorithm and the datasets described in this article are available online or by contacting the first author. [ABSTRACT FROM AUTHOR]

Given distinct climatic periods in the various facets of the Earth's climate system, many attempts have been made to determine the exact timing of 'change points' or regime boundaries. However, identification of change points is not always a simple task. A time series containing N data points has approximately N k distinct placements of k change points, rendering brute force enumeration futile as the length of the time series increases. Moreover, how certain are we that any one placement of change points is superior to the rest? This paper introduces a Bayesian Change Point algorithm which provides uncertainty estimates both in the number and location of change points through an efficient probabilistic solution to the multiple change point problem. To illustrate its versatility, the Bayesian Change Point algorithm is used to analyse both the NOAA/NCDC annual global surface temperature anomalies time series and the much longer δ18O record of the Plio-Pleistocene. Copyright © 2012 Royal Meteorological Society [ABSTRACT FROM AUTHOR]

Structural changes, or changepoints, coinciding in multiple ice core records over the Greenland Ice Sheet (GrIS) may reflect a widespread response of the GrIS to atmospheric forcing. Thus, to better understand how atmospheric circulation may regulate sudden changes in δ18O of Greenland precipitation, we seek synchronous changepoints occurring in ice core-derived δ18O time series across the GrIS and in the North Atlantic Oscillation (NAO) over the past millennium. By utilizing a Bayesian changepoint detection method, four changepoint horizons were revealed: at the beginning of the 20th century, in the late-15th century, and around the turn of the 11th and 10th centuries. Although the changepoints in ice core δ18O records exhibited distinctive spatial arrangements in each horizon, all corresponded to changepoints in the NAO, indicative of a consistent atmospheric influence on GrIS surface changes over the past millennium. [ABSTRACT FROM AUTHOR]