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Real-world phenomena simulation models, which can be used to engage middle-school students with probability, are described. Links to R instructional material and easy-to-use code are provided to facilitate implementation in the classroom.

The increasing popularity of R is leading to an increase in its use in undergraduate courses at universities (R Development Core Team 2008). One of the strengths of R is the flexible graphics provided in its "base" package. However, students often run up against its limitations, or they find the amount of effort to create an interesting plot may be excessive. The "grid" package (Murrell 2005) has a wealth of graphical tools which are more accessible to such R users than many people may realize. The purpose of this paper is to highlight the main features of this package and to provide some examples to illustrate how students can have fun with this different form of plotting and to see that it can be used directly in the visualization of data. (Contains 22 figures.)

As the climate changes, it is important to understand the effects on the environment. Changes in wildland fire risk are an important example. A stochastic lattice-based wildland fire spread model was proposed by Boychuk et al. (2007), followed by a more realistic variant (Braun andWoolford, 2013). Fitting such a model to data from remotely sensed images could be used to provide accurate fire spread risk maps, but an intermediate step on the path to that goal is to verify the model on data collected under experimentally controlled conditions. This paper presents the analysis of data from small-scale experimental fires that were digitally video-recorded. Data extraction and processing methods and issues are discussed, along with an estimation methodology that uses differential equations for the moments of certain statistics that can be derived from a sequential set of photographs from a fire. The interaction between model variability and raster resolution is discussed and an argument for partial validation of the model is provided. Visual diagnostics show that the model is doing well at capturing the distribution of key statistics recorded during observed fires. [ABSTRACT FROM AUTHOR]

We study the problem of estimating σ from individuals' data in the presence of out-of-control and nonnormal conditions. We consider a large number of estimators for a that have been proposed in the last 20 years. Using simulation, we compute the mean squared errors for 10 of these estimators, both before and after screening for outliers with median-absolute-deviation-based control limits. We also consider the effect of contaminated data on the performance of EWMA (exponentially weighted moving average) charts. We show, by simulation, that Boyles' dynamic linear model estimator is, after screening, often the best way of estimating σ. We also show that an approach that involves robustly testing for shifts prior to final estimation of σ can be approximated by an automatic method based on smoothing the data first and estimating σ from residuals; this method is often nearly as effective as that of Boyles and is sometimes better. We also find that there are some situations where noisy data are not amenable to accurate estimation of σ, even at a moderately large sample size. In such cases, engineering considerations and careful data analysis are required to obtain more accurate estimates. [ABSTRACT FROM AUTHOR]

The geometric process has been proposed as a simple model for use in reliability. Recently, the α-series process was proposed as a complementary model which can be used in situations where the geometric process is inappropriate. In this article, we show that the increasing geometric process grows at most logarithmically in time while the decreasing geometric process is almost certain to have a time of explosion. The α-series process grows either as a polynomial in time or exponentially in time. We also show that, unlike most renewal processes, the geometric process does not satisfy a central limit theorem, while the α-series process does. [ABSTRACT FROM AUTHOR]

This study presents an exploratory analysis of Ontario lightning and fire ignition data. Our main goal is to relate forest fire ignitions to lightning stroke occurrences. However, due to the sheer volume of the lightning data. as well as accuracy and missing data issues, changes to the data are required prior to any such investigation. Planning to employ cluster-based point-process methods in future lightning-caused fire ignition models, we wish to cluster the lightning strokes in space-time, We propose a mode-seeking clustering algorithm that is based on a convergent form of 'data sharpening' methods. Data sharpening is based on local constant regression and was introduced as a bias-reduction method in kernel density estimation. Data sharpening nudges observations closer to their nearest local mode(s) at each iteration. We propose to iterate the algorithm until convergence, showing that the data will converge to either local or global modes. The usefulness of the algorithm in the lightning context is threefold: first, the lightning data can be reduced to corresponding local spatial-temporal modes; second, slight modifications result in a noise-reduction method that can be applied to estimate short-term spatial track(s) of lightning storm system(s); third, the sharpened data provide a means for a bootstrap-based simulation of spatial lightning strike patterns. Numerical examples and comments on the algorithm's appropriateness related to the lightning application appear throughout. The study concludes by noting some of the further work to be done. [ABSTRACT FROM AUTHOR]