Wavelets in Lisp-Stat.
Robert A. Stine
Department of Statistics, / The Wharton School / The University of Pennsylvania /
Philadelphia, PA 19104-6302.
The wavelet transform is a recent development in mathematics with broad
applications in statistics. In nonparametric regression, wavelets
provide a basis for adaptive smoothing. In time series analysis,
wavelets give localized estimates of the spectral density which can be
used to study nonstationary processes. In either setting, the
calculations of wavelets are quite fast, faster than the familiar fast
Fourier transform (FFT).
This talk will describe a package of Lisp-Stat objects and methods that
compute wavelets in either context. The software is partially written in
C and makes use of methods (which are also described) for dynamically
loading external functions. Several examples will illustrate the
software and, along the way, draw comparisons to lowess smoothers and the
FFT.
Interactive Kernel Density Estimation with Lisp-Stat
Frederic Udina
Universitat Pompeu Fabra /
Barcelona, SPAIN.
Kernel Density Estimation is one of the most commonly used methods for
density estimation. Two issues play a role in its use: the high
computational cost of the involved algorithms and the amount of
user-discretion present in the choice of the parameters and the
general set-up.
We present a highly interactive package for Kernel Density Estimation
(KDE) in Lisp-Stat. Using a standard graphical interface the user can
select the kernel function to use and adjust the smoothing parameter
while seeing the effect of the changes dynamically. Graphical
facilities include comparison of several estimations, histograms and
other data summaries, drawing a normal density function fitted to data
or user defined normal mixture densities, visualization of the kernel
function, output to postscript files via GNUplot, etc. Fast
computational such as binned FFT and binned updating methods along
with currently preferred methods for automatic bandwidth selection are
also provided. A new and general Lisp-Stat object allows the user to
control parameters and define the transformation graph by moving the
knots of a spline-generated curve. We conclude with some remarks on
future extensions that include hazard function estimation, kernel
regression and histogram exploration and multivariate density
estimation.
Graphical user interfaces for statistical applications in Quail
R. W. Oldford
Department of Statistics and Actuarial Science /
University of Waterloo.
Quail extends the Common Lisp language to provide a programming
environment for quantitative analysis.
Among these extensions are capabilities for a general graphical user
interface and for the specification and fitting of generalized
linear models (including such specializations as the Gaussian linear
model).
In this presentation the use of Quail to build graphical user
interfaces for statistical analysis applications will be described.
By demonstrating the construction of
display-oriented tools for regression analysis,
many of the design decisions for both graphics and statistical
modelling will be illustrated.
The general principles on which these facilities are based are
then described.
Should time permit, a general overview of the entire Quail environment
and design philosophy will be given.
This project represents joint work with C.B. Hurley, D.G. Anglin, M.E.
Lewis, N.G. Bennett, and others that have been associated with the Quail
project over many years now.
Exploratory Analysis of Geographical Data
Chris Brunsdon
Dept. Of Town and Country Planning /
University of Newcastle Upon Tyne.
In recent years, there has been much interest in Geographical
Information Systems (GIS). These are essentially database packages
capable of handling spatially referenced information. The growth
of these packages has led to an interest in computer-based mapping,
and to the visual exploration of geographical data. However, most
GIS packages lack the degree of interaction, and flexibility of
graphical techniques required by many techniques for exploratory data
analysis. In this presentation, it is intended to demonstrate that
the Lisp language (and in particular
Lisp-Stat) is itself an
extremely good tool for handling geographical data, and that by
adding cartographic visualisation tools to existing Lisp-Stat
graphical objects, a powerful exploratory spatial data analysis
system can be achieved.
The working system will be demonstrated using 1991 British Census
data, and also with data relating to the locations of household
burglaries.
Robert Stine on
Wavelets in Lisp-Stat
.