1.
Analyzing Musical Structure and Performance---A Statistical
Approach - Beran, Jan; Mazzola, Guerino
Musical performance theory and the theory of musical structure in
general is a rapidly developing field of musicology that has wide practical
implications. Due to the complex nature of music, statistics is likely to play
an important role. In spite of this, up to the present, applications of
statistical methods to music have been rare and mostly limited to a formal
confirmation of results obtained by other methods. The present paper introduces
a statistical approach to the analysis of metric, melodic and harmonic
structures of a score and their influence on musical performance. Examples by
Schumann, Webern and Bach illustrate the proposed method of numerical encoding
and hierarchical decomposition...
2.
Gustav Elfving's contribution to the emergence of the optimal
experimental design theory - Fellman, J.
Gustav Elfving contributed to the genesis of optimal experimental
design theory with several papers mainly in the 1950s. These papers are
presented and briefly analyzed. The connections between Elfvings
results and the results of his successors are elucidated to stress the
relevance of Elfvings impact on the development of optimal design
theory.
3.
Student and small-sample theory - Lehmann, E. L.
.The paper discusses the contributions Student W. S. Gosset made to
the three stages in which small-sample methodology was established in the
period 19081933: (i) the distributions of the test-statistics under the
assumption of normality, (ii) the robustness of these distributions against
nonnormality, (iii) the optimal choice of test statistics. The conclusions are
based on a careful reading of the correspondence of Gosset with Fisher and E.
S. Pearson.
4.
Statistical Thinking an Statistical Practice: Themes Gleaned from
Professional Statisticians - Pfannkuch, Maxine; Wild, Chris J.
Advancing computer technology is allowing us to downplay instruction
in mechanical procedures and shift emphasis towards teaching the
art of statistics. This paper is based upon interviews with six
professional statisticians about statistical thinking and statistical practice.
It presents themes emerging from their professional experience, emphasizing
dimensions that were surprising to them and were not part of their statistical
training. Emerging themes included components of sta tistical thinking,
pointers to good statistical practices and the subtleties of interacting with
the thinking of others, particularly coworkers and clients. The main purpose of
the research is to uncover basic elements of applied statistical practice and
statistical thinking for the use of teachers...
5.
The spectral envelope and its applications - Stoffer, David S.; Tyler, David E.; Wendt, David A.
The concept of the spectral envelope was recently introduced as a
statistical basis for the frequency domain analysis and scaling of
qualitative-valued time series. In the process of developing the spectral
envelope methodology, many other interesting extensions became evident. In this
article we explain the basic concept and give numerous examples of the
usefulness of the technology. These examples include analyses of DNA sequences,
finding optimal transformations for the analysis of real-valued time series,
residual analysis, detecting common signals in many time series,and the
analysis of textures.
6.
Nonparametric Regressin with Correlated Errors - Opsomer, Jean; Wang, Yuedong; Yang, Yuhong
Nonparametric regression techniques are often sensitive to the
presence of correlation in the errors. The practical consequences of this
sensitivity are explained, including the breakdown of several popular
data-driven smoothing parameter selection methods. We review the existing
literature in kernel regression, smoothing splines and wavelet regression under
correlation, both for short-range and long-range dependence. Extensions to
random design, higher dimensional models and adaptive estimation are
discussed.
7.
A Geometric Interpretation of the Metropolis-Hastings
Algorithm - Billera, Louis J.; Diaconis, Persi
The MetropolisHastings algorithm transforms a given
stochastic matrix into a reversible stochastic matrix with a prescribed
stationary distribution. We show that this transformation gives the minimum
distance solution in an $L^1$ metric.
8.
Inference for Superpopulation Parameters Using Sample
Surveys - Graubardand, Barry I.; Korn, Edward L.
Sample survey inference is historically concerned with
finite-population parameters, that is, functions (like means and totals) of the
observations for the individuals in the population. In scientific applications,
however, interest usually focuses on the superpopulation
parameters associated with a stochastic mechanismhypothesized to generate the
observations in the population rather than the finite-population parameters.
Two relevant findings discussed in this paper are that (1) with stratified
sampling, it is not sufficient to drop finite-population correction factors
from standard design-based variance formulas to obtain appropriate variance
formulas for superpopulation inference, and (2) with cluster sampling, standard
design-based variance formulas can dramatically underestimate superpopulation
variability, even with a small sampling fraction of the final...
9.
Statistical methods for DNA sequence segmentation - Braun, Jerome V.; Müller, Hans-Georg
This article examines methods, issues and controversies that have
arisen over the last decade in the effort to organize sequences of DNA base
information into homogeneous segments. An array of different models and
techniques have been considered and applied. We demonstrate that most
approaches can be embedded into a suitable version of the multiple change-point
problem, and we review the various methods in this light. We also propose and
discuss a promising local segmentation method, namely, the application of split
local polynomial fitting. The genome of bacteriophage $\lambda$ serves as an
example sequence throughout the paper.
10.
A conversation with Harald Bergström - Råde, Lennart
Harald Bergström was born on April 1, 1908, in Mölltorp, situated
in the middle of Sweden. A Master of Philosophy degree was awarded in 1931 at
the University of Uppsala (in mathematics, physics and chemistry, extended to
theoretical physics in 1932). He taught in secondary schools (gymnasiums) from
1932 to 1934, and then returned to Uppsala to pursue his research in
mathematics toward a doctorate degree, which he received in 1938. He had a
permanent lectureship in mathematics at the University of Uppsala from 1938 to
1945, and at a military college in 1945. In 1946, he was asked to hold a new
established professorship in applied mathematics...
11.
A conversation with Tavia Gordon - Geller, Nancy L.
Tavia Gordon was born on December 14, 1917, in Chicago, Illinois. He
received a B.A. degree in anthropology from the University of California in
1938. He did graduate work in anthropology at the University of Chicago in
1938-1939, in mathematics at the University of Southern California in
1947-1948, and in mathematical statistics at the University of California,
Berkeley, in 1948-1950. He is a Fellow of the American Statistical
Association and the Council on Epidemiology, American Heart Association. His
tenure at NIH included the years 1954-1960 and 1966-1977, beginning as an
Analytical Statistician with the Biometrics Research Section of the National
Heart Institute. He spent the next two years at...
12.
What did Fisher mean by "inverse probability" in 1912--1922? - Edwards, A. W. F.
The method of maximum likelihood was introduced by R. A. Fisher in
1912, but not until 1922 under that name. This paper seeks to elucidate what
Fisher understood by the phrase "inverse probability," which he used
in various ways before defining "likelihood" in 1921 to clarify his
meaning.
13.
R. A. Fisher and multivariate analysis - Anderson, T. W.
This paper reviews R. A. Fisher's many fundamental contributions
to multivariate statistical analysis--from the derivation of the distribution
of the sample correlation coefficient to discriminant analysis. The emphasis
here is on the conceptual and mathematical development. All of his papers on
multivariate analysis will be included in this survey.
14.
Bootstrap confidence intervals - DiCiccio, Thomas J.; Efron, Bradley
This article surveys bootstrap methods for producing good approximate confidence intervals. The goal is to improve by an order of magnitude upon the accuracy of the standard intervals $\hat{\theta} \pm z^{(\alpha)} \hat{\sigma}$, in a way that allows routine application even to very complicated problems. Both theory and examples are used to show how this is done. The first seven sections provide a heuristic overview of four bootstrap confidence interval procedures: $BC_a$, bootstrap-t , ABC and calibration. Sections 8 and 9 describe the theory behind these methods, and their close connection with the likelihood-based confidence interval theory developed by Barndorff-Nielsen, Cox...
15.
Flexible smoothing with B-splines and penalties - Eilers, Paul H. C.; Marx, Brian D.
B-splines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots and a difference penalty on coefficients of adjacent B-splines. We show connections to the familiar spline penalty on the integral of the squared second derivative. A short overview of B-splines, of their construction and of penalized likelihood is presented. We discuss properties of penalized B-splines and propose various criteria for the choice...
16.
The Mixture Transition Distribution Model for High-Order Markov Chains and Non-Gaussian Time Series - Berchtold, André; Raftery, Adrian
The mixture transition distribution model (MTD) was introduced in 1985
by Raftery for the modeling of high-order Markov chains with a finite state
space. Since then it has been generalized and successfully applied to a range of
situations, including the analysis of wind directions, DNA sequences and social behavior.
Here we review the MTD model and the developments since 1985. We first introduce the
basic principle and then we present several extensions, including general state spaces
and spatial statistics. Following that, we review methods for estimating the model
parameters. Finally, a review of different types of applications shows the practical
interest of the MTD model.
17.
The mathematics and statistics of voting power - Gelman, Andrew; Katz, Jonathan N.; Tuerlinckx, Francis
In an election, voting power---the probability that a single
vote is decisive---is affected by the rule for aggregating votes into
a single outcome. Voting power is important for studying political
representation, fairness and strategy, and has been much discussed in
political science. Although power indexes are often considered as
mathematical definitions, they ultimately depend on statistical models
of voting. Mathematical calculations of voting power usually have
been performed under the model that votes are decided by coin flips.
This simple model has interesting implications for weighted elections,
two-stage elections (such as the U.S. Electoral College) and
coalition structures.
We discuss empirical failings of the coin-flip model
of voting and consider, first, the...
18.
Class Prediction by Nearest Shrunken Centroids, with Applications to DNA Microarrays - Tibshirani, Robert; Hastie, Trevor; Narasimhan, Balasubramanian; Chu, Gilbert
We propose a new method for class prediction in DNA microarray studies based on an enhancement of the nearest prototype classifier. Our technique uses "shrunken" centroids as prototypes for each class to identify the subsets of the genes that best characterize each class. The method is general and can be applied to the other high-dimensional classification problems. The method is illustrated on data from two gene expression studies: lymphoma and cancer cell lines.
19.
The Impact of the Bootstrap on Statistical Algorithms and Theory - Beran, Rudolf
Bootstrap ideas yield remarkably effective algorithms for realizing certain programs in statistics. These include the construction of (possibly simultaneous) confidences sets and tests in classical models for which exact or asymptotic distribution theory is intractable. Success of the bootstrap, in the sense of doing what is expected under a probability model for data, is not universal. Modifications to Efron's definition of the bootstrap are needed to make the idea work for modern procedures that are not classically regular.
20.
John W. Tukey and Data Analysis - Hoaglin, David C.
From the time that John W. Tukey started to do serious work in statistics, he was interested in problems and techniques of data analysis. Some people know him best for exploratory data analysis, which he pioneered, but he also made key contributions in analysis of variance, in regression and through a wide range of applications.This paper reviews illustrative contributions in these areas.
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