Interdisciplinary teams are of increasing importance and mathematicians can be valuable contributors to them. Mathematicians can be leaders, not just reactive problem solvers in these teams. PhD training for mathematicians should be augmented so that graduates are best able to contribute in this environment. The nature of some new PhD programs is described together with detail of the program of the Industry Doctoral Training Centre of the Australian Technology Network of Universities.

International Statistical ReviewVolume 65, Issue 3 p. 277-280 Discussion: Current Influences of Computing on Statistics Murray Cameron, Murray Cameron CSIRO, Mathematical & Information Sciences, Sydney, AustraliaSearch for more papers by this author Murray Cameron, Murray Cameron CSIRO, Mathematical & Information Sciences, Sydney, AustraliaSearch for more papers by this author First published: 21 May 2007 https://doi.org/10.1111/j.1751-5823.1997.tb00306.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat References Abel, D.J. (1997). Spatial internet marketplaces: a grand challenge? In Proc. 5th Intl. Symp Large Spatial Databases. Ed. M. Scholl. Google Scholar Chambers, J.M. (1993). Greater or lesser statistics: a choice for future research. Statistics and Computing, 3, 182–184. 10.1007/BF00141776 Web of Science®Google Scholar J.M. Chambers & T. J. Hastie (eds.) (1991). Statistical Models in S. Pacific Grove: Wadsworth & Brooks Cole. Google Scholar Donoho, A. W., Donoho, D.L. & Gasko, M. (1986). MACSPIN: Graphical data analysis software, In Computer Science and Statistics: Proceedings of the 18th symposium on the interface, Ed. J. Boardman. Thomas American Statistical Association, Alexandria , VA . Web of Science®Google Scholar Krzanowski, W.J. (1997). Recent trends and developments in computational multivariate analysis. Statistics and Computing, 7, 87–99. 10.1023/A:1018565514339 Web of Science®Google Scholar Nelder, J.A. & Wedderburn, R.W.M. (1972). Generalized linear models. J. R. Statist. Soc. A, 135, 370–384. 10.2307/2344614 Web of Science®Google Scholar Ripley, B.D. (1996). Pattern recognition and neural networks. Cambridge University Press. 10.1017/CBO9780511812651 Google Scholar Tierney, L. (1990). Lisp-Stat: an object-oriented environment for statistical computing and dynamic graphics. New York: John Wiley. Google Scholar Tukey, J.W. (1962). The Future of Data Analysis. Ann. Math. Statist. 33, 1–67. 10.1214/aoms/1177704711 Web of Science®Google Scholar Velleman, P.F. (1997). ActivStats Data Description Inc., ( Ithaca , NY ). Google Scholar Wichura, M.J., Editor (1996). Current Index to Statistics Extended Database. American Statistical Association (Alexandria, VA) and Institute of Mathematical Statistics (Hayward, CA). Google Scholar Volume65, Issue3December 1997Pages 277-280 ReferencesRelatedInformation

The transient electromagnetic (TEM) method is used extensively for mineral exploration and other applications such as geothermal soundings, oil exploration, groundwater pollution, soil salinity and geological mapping. Sferics pulses produced by lightning strokes propagating in the ionosphere‐earth waveguide cavity induce noise in a bandwidth of a few Hz to tens of kHz. The usual method of stacking and calculating the mean of a given stack cannot effectively reduce the spike‐like noise induced by high‐amplitude sferics pulses. To reduce this type of noise, a number of different ways of stacking data were investigated and compared. Noise data were stacked by using robust estimators such as the median, trimmed mean, and a range of M‐estimators. Since storage of all the samples of a given stack can take up a prohibitively large amount of microprocessor memory, recursive algorithms for the M‐estimators and their standard error were developed for the real‐time reduction of sferics pulses. The recursive algorithms have been demonstrated to work effectively on windowed data, and thus the memory normally required to obtain the mean is sufficient for calculation of the M‐estimate. In the recursive calculation of the robust estimate of the transient response, the spread of the background noise distribution (known as the scale of the data) needs to be known or calculated. In the algorithm that has been developed, the scale of the data is derived from a noise run carried out before pulsing the transmitter loop with current. It has been assumed that the presence of a signal does not change the scale of the data. This value of the scale of the data has been used to obtain a robust estimate of the transient response itself. To allow for possible changes in the background noise level during a given survey, the estimate of the scale of the data is updated throughout the survey. Many tests of the performance of the recursive algorithms have been carried out with both simulated noise data and sferics data that have been recorded previously on magnetic tape. The results show that for sferics activity as high as that observed in northern latitudes of Australia in summer, a noise reduction by a factor of about 5 (when compared with simple stacking) should be obtained. In areas where sferics noise predominates over geological background signal, such a reduction should lead to an increase in target detection depth by approximately 50%.

When faced with high-dimensional data, one often uses principal component analysis (PCA) for dimension reduction. Classical PCA constructs a set of uncorrelated variables, which correspond to eigenvectors of the sample covariance matrix. However, it is well-known that this covariance matrix is strongly affected by anomalous observations. It is therefore necessary to apply robust methods that are resistant to possible outliers.Li and Chen [J. Am. Stat. Assoc. 80 (1985) 759] proposed a solution based on projection pursuit (PP). The idea is to search for the direction in which the projected observations have the largest robust scale. In subsequent steps, each new direction is constrained to be orthogonal to all previous directions. This method is very well suited for high-dimensional data, even when the number of variables p is higher than the number of observations n. However, the algorithm of Li and Chen has a high computational cost. In the references [C. Croux, A. Ruiz-Gazen, in COMPSTAT: Proceedings in Computational Statistics 1996, Physica-Verlag, Heidelberg, 1996, pp. 211–217; C. Croux and A. Ruiz-Gazen, High Breakdown Estimators for Principal Components: the Projection-Pursuit Approach Revisited, 2000, submitted for publication.], a computationally much more attractive method is presented, but in high dimensions (large p) it has a numerical accuracy problem and still consumes much computation time.In this paper, we construct a faster two-step algorithm that is more stable numerically. The new algorithm is illustrated on a data set with four dimensions and on two chemometrical data sets with 1200 and 600 dimensions.

The problem of classifying ventricular arrhythmias from intracardial electrograms is considered, Standard statistical discrimination procedures are applied using a simple parametric model for the shape of the pulse near its peak. This approach makes simultaneous use of the model parameters, has well known statistical properties, and involves computations that can be carried out efficiently. Preliminary analyses of real data sets, using both linear and quadratic discrimination functions, yield promising results.

It is shown that a recursive estimator with the same asymptotic properties as the median has convergence properties in finite samples which depend heavily on the scale of the data. A simple modification which adjusts for the scale is suggested and its application illustrated on simulated data. The modified estimator has much improved properties which are similar to those of the sample (non-recursive) median. Keywords: robust estimationstochastic approximationmean deviationrecursive estimation Additional informationNotes on contributorsMurray A. Cameron

On montre que les calculs pour l'estimation des parametres dans le domaine des frequences, dans plusieurs modeles de series temporelles sont essentiellement ceux des moindres carres reponderes iterativement et donc peuvent etre realises par la majorite des programmes-produits statistiques

Abstract. An estimator of the spectral density of a stationary process is obtained by approximating it with a step function. The positions of the level changes are determined using partitioning algorithms. The algorithms are stopped by using criteria such as AIC. In examples, the resulting estimates are shown to be good representations of the true spectra in most circumstances, even when the series are fairly short. In particular the estimates highlight spikes in the spectral density that are caused by periodicities.

In some experiments an ‘observation' is a time series and the ‘treatments' are stimuli which elicit changes in the nature of the time series for only a short period. One approach to analysing data from such experiments is presented here. Tests are given for detecting responses in such experiments, and for comparing responses elicited under different treatment regimes. The tests are based on frequency-domain estimates of the prediction variance for stationary time series. If several stimuli are applied within each observed time series at regular intervals, then the method of analysis may be designed so that the estimates of the different responses are orthogonal and most of the calculations can be performed using standard analysis of variance programs.

Microlithotype composition of a coal sample is often summarized by examining a large number (~500) of subsamples of a grain mount and estimating proportions of vitrite, intermediates, and inertite, where, for samples we have investigated, the proportion of intermediates is generally less than 0.4. This suggests that most subsamples are either greater than 95% vitrinite or greater than 95% inertinite, so that the statistical distribution of vitrinite has most of its weight in its tails. Two distributions which may have this shape are the beta and the logistic normal, and these have been fitted to the microlithotype distribution of some coal samples. Parameters of these fitted distributions are related to the proportion of vitrinite in the sample and thickness of microscopic bands in the coal. For coals in the Sydney Basin, at least, it was found that the parameter relating to band thickness is approximately constant over a coal seam; therefore, fitting one or other of these distributions to such data leads to directly interpretable parameters.

SummaryIn this paper, a new test of the hypothesis that all the correlations between a set of variables are zero is proposed. It is based on the asymptotic behaviour of the largest of the observed correlation coefficients. Here “asymptotic” refers to the size of the correlation matrix considered. Simulations show that the critical levels, calculated using the asymptotic theory, are conservative but quite accurate, even for small correlation matrices.

Attempts have been made to optimize the determination of Pb isotope ratios in over 700 analyses of standards and natural samples on an Isomass 54E in fully automatic operation. Amounts of Pb analysed for the N.B.S. standards 981 (common Pb) and 983 (radiogenic Pb) were initially about 100 ng Pb, but these have been increased to about 300 ng to conform with the usual amounts for natural samples.

Rb-Sr isotopic data for large, relatively homogeneous, whole-rock samples of Uivak 1 gneiss from the Saglek-Hebron area of northern Labrador exhibit a scatter which exceeds that predicted by experimental error. Isotopic analyses of adjacent compositionally-different layers of Uivak gneiss, 1–2 cm in width, define secondary isochrons, with slopes corresponding to an age of ca. 1800 Ma. As field evidence combined with previous isotopic dating demonstrates that the compositional layering did not form at this time, the secondary isochrons are interpreted as resulting from localized Sr-isotopic homogenization along 87Sr abundance gradients generated by ageing in the previously-layered gneisses. The geological scatter in the larger gneiss specimens is therefore attributed to the same phenomenon on a reduced scale, viz. Sr isotopic equilibration at 1800 Ma between adjacent volumes of gneiss. However regional differences in mean 87Sr86Sr and mean 87Rb86Sr are assumed to be unchanged.

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A review is presented of methods for estimating the dispersion law of a plane wave which is observed over time at a set of recorders located in an irregularly spaced array. The wave is represented by a signal, which may be either deterministic or random, plus noise which is represented by a stationary random process. The combination of several sets of observations for the one array and the estimation procedure when more than one signal is present are also discussed. A procedure which may give improved estimates for transient signals is introduced. An application of this procedure to some data and the results of some simulations are presented.