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CONFIRMED
Ka Lok Chu & George P. H. Styan
Some illustrated comments on Anderson graphs and
Greek mythology tables for classic magic squares
Amali Dassanayake
Local Orthogonal Polynomial Expansions For Density Estimations.
Sami Helle
Error Bound for Metamodel Extreme Value Approximation
of BlackBox Computer Experiments
Joonas Kauppinen
Decomposing selfsimilarity matrices to infer structure
in music

AWAITING CONFIRMATION
Suresh Kumar Sharma
Efficiency of Various Smoothers in Generalized
Additive Models
 WITHDRAWN
 Afarin Habibi Rad, Mobina
Nemooneh Highschool,
Interval and point estimators for the parameters
of Lognormal Distribution based on unified hybrid
censored data
 Danielle Richer, McMaster
University
Learning from Ecology: The PresenceAbsence
Matrix applied to Network MetaAnalysis

Ka Lok Chu & George P. H. Styan
Some illustrated comments on Anderson graphs and Greek mythology
tables for classic magic squares
We present several new classifications for the 880 classic
order4 magic squares first enumerated by the French mathematician
Bernard Fr\'enicle de Bessy (c.~16051675). We identify 382
distinct Anderson graphs (Bragdon's ``magic lines'' diagrams,
Moran's ``sequence designs'') and study their symmetry and path
lengths, building on results by BrigadierGeneral Sir Francis
James Anderson (18601920), architect Claude Fayette Bragdon
(18661946), mathematical puzzle aficionado Henry Ernest Dudeney
(18571930), and publicist James Sterling ``Jim'' Moran (19081999),
who in his 1980 book {\it The Wonders of Magic Squares,} identified
a Greek deity for each Dudeney Type. Our ``Anderson graph''
is the graph produced by the lines joining the consecutive numbers
in sequence. We also consider matrix factorizations due to the
mathematicians Leonhard Euler (17071783) and Friedrich Fitting
(18621945). We illustrate our findings as much as possible
and whenever feasible with images of postage stamps or other
philatelic items. This is joint research wth Reijo Sund (Helsinki)
and Walter Trump (N\"urnberg). With this talk we are pleased
to celebrate the International Year of Statistics 2013 and the
special year for Mathematics of Planet Earth 2013.

Amali Dassanayake
Local Orthogonal Polynomial Expansions For Density Estimations.
We propose a new method to estimate the density function of
a univariate continuous random variable. This new method, local
orthogonal polynomial expansions (LOrPE), draws similarities
with kernel density estimation (KDE), orthogonal series density
estimation (OSDE) and local likelihood density estimation (LLDE).
It is most similar to LLDE in that it is a local method where
the approximation is obtained at each point of the support.
It is connected to the OSDE in that it is constructed by using
an orthogonal polynomial series expansion at each point of the
support. The order of the series (M) used is one of the method’s
tuning parameters, a localized version of OSDE. Finally, LOrPE
utilizes a bandwidth (h), the second tuning parameter, in order
to construct the orthogonal polynomials over a localized window,
and in this respect it is similar to KDE. Also, we show that
under certain conditions, LOrPE is equivalent to KDE with a
high order kernel. Comparisons of LOrPE with KDE are performed
under a variety of conditions. We find that in terms of MISE,
LOrPEperforms better than KDE when estimating densities with
sharp boundaries and both LOrPE and KDE results remain same
when estimating densities which decay slowly to zero at infinity.

Sami Helle, Tampere University of
Technology and University of Tampere
Error Bound for Metamodel Extreme Value Approximation of BlackBox
Computer Experiments
One important field of statistical design of experiments
is design of computationally expensive computer experiments
(see, for example Chen et al. 2003, Fang et al. 1994,
2003, 2006, Cioppa and Lucas 2007, Koehler and Owen
1989, Lin 2003, Niederreiter 1992, Sacks et al. 1989).
Theoretically computer models are deterministic and
model is completely known. With stochastic simulations,
like reliability or risk simulations, this is true
in some sense but the simulation does include quasirandom
components and it's difficult to treat it as deterministic
model. Also computer model could be completely unknown
"blackbox" or it is too complicated. In
many cases computationally inexpensive metamodel is
fitted to simulation output data for approximating
unknown model and metamodel is used for analyzing
properties of a computer simulation (see, for example
Chen et al. 2003, Fang et al. 2000, 2002, 2003, 2006,
Lin 2003, Muller et al. 2010, 2012, 2013).
In this paper we analyze error bound of metamodel
extreme value approximation of blackbox computer
experiments in deterministic and stochastic event
simulation cases. Results show that error bound will
be minimized by minimizing the uniformity measure
of the point set if the model is unknown in deterministic
case. In the stochastic event simulation case error
is unbounded if random variables are unbounded. However,
functions of simulation output parameter estimates
could be used for estimating extreme values. The result
will show that the expected value of the error bound
of function of simulation output parameters estimates
will be minimized by minimizing the uniformity measure
of the point set in stochastic event simulation case
under some assumptions.
References:
Chen, V. C. P., Tsui, K.L., Barton, R. R. and Allen,
J. K. (2003), A Review of Design and Modeling in Computer
Experiments, Handbook of Statistics Vol 22, Ed. Khattree,
R. and Rao, C. R., Elsevier, Amsterdam, 231262.
Cioppa, T. M. and Lucas, T. W. (2007), Efficient
Nearly Orthogonal and SpaceFilling Latin Hypercubes,
Technometrics, 49 (1), 4555.
Fang, K.T. and Wang Y. (1994), Numbertheoretic
Methods in Statistics, Chapman & Hall, London.
Fang, K.T. Lin, D.K.J., Winker, P. and Zhang, Y.
(2000), Uniform Design: Theory and Applications, Technometrics,
42, 237248.
Fang, K.T. (2002), Theory, Method and Applications
of the Uniform Design, International Journal of Reliability,
Quality and Safety Engineering, 9 (4), 305315.
Fang K.T. and Lin, D. K. J. (2003), Uniform Experimental
Design and Their Applications in Industry, Handbook
of Statistics Vol 22, Ed. Khattree, R. and Rao, C.
R., Elsevier, Amsterdam, 131170.
Fang, K.T. , Li, R. and Sudjianto, A. (2006), Design
and Modeling for Computer Experiments, Chapman &
Hall, New York.
Koehler, J. R. and Owen, A. B., (1996), Computer
Experiments, Handbook of Statistics Vol 13, Ed. Ghosh,
S. and Rao, C. R., Elsevier, Amsterdam, 261308.
Lin, D. K. J. (2003), Industrial Experimentation
for Screening, Handbook of Statistics Vol 22, Ed.
Khattree, R. and Rao, C. R., Elsevier, Amsterdam,
3374.
 Muller, J. and Piche, R. (2011), Mixture surrogate
models based on DempsterShafer theory for global
optimization problems, Journal of Global Optimization,
51, 79–104.
Muller, J. (2012), Surrogate Model Algorithms for
Computationally Expensive BlackBox Optimization Problems,
Tampere University of Technology publication 1092,
Juvenes Print TTY, Tampere.
Muller, J, Shoemaker, C. A. and Piche, R. (2013),
SOMI: A surrogate model algorithm for computationally
expensive nonlinear mixedinteger blackbox global
optimization problems, Computers & Operations
Research, 40(5), 1383–1400.
 Niederreiter, H., (1992), Random Number Generation
and QuasiMonte Carlo Methods, Society for Industrial
and Applied Mathematics (SIAM), Philadelphia.
 Sacks J., Welch, W. J. , Mitchell, T. J. and Wynn,
H. P. (1989), Design and Analysis of Computer Experiments,
Statistical Science, 4, 409423.
Joonas Kauppinen, University
of Tampere
Decomposing selfsimilarity matrices to infer structure
in music
Coauthors: Anssi Klapuri and Tuomas Virtanen (Department
of Signal Processing, Tampere University of Technology)
In the emerging field of music information retrieval,
the goal of structure analysis is to discover the
sectional form of musical works. This corresponds
to locating segment boundaries and clustering the
obtained segments to consistent parts, such as verse
and chorus in popular music. The information on sectional
form is useful for several applications, including
cover song identification, music summarization, and
music playback interfaces that allow jumping between
the sections. An efficient approach to visualizing
and analyzing the sectional form is to construct a
symmetric selfsimilarity matrix (SSM) from a time
series of acoustic feature vectors representing a
song. Provided that we have used appropriate features,
we can often discern two prominent structures in SSMs:
rectangular blocks of high similarity and diagonal
stripes off and parallel to the main diagonal. We
explore some classic methods for inferring musical
structure from SSMs. Furthermore, we illustrate novel
methods to model the block and stripelike structures
in SSMs simultaneously. The common theme to the methods
is that they are all based on the use of matrix decompositions,
namely the singular value decomposition or nonnegative
matrix factorization.

Danielle Richer, McMaster
University
Learning from Ecology: The PresenceAbsence Matrix
applied to Network MetaAnalysis
Coauthors: Joseph Beyene
Metaanalysis is a statistical practice that has
been welldeveloped to combine results from trials
comparing the same interventions. In an effort to
address broader questions of comparative effectiveness,
concepts used in traditional metaanalysis have been
extended to create the field of network metaanalysis.
A connected network of studies between multiple treatments
can be represented geometrically with treatments as
nodes and edges as studies. Several methods, both
Bayesian and frequentist, have been proposed for network
metaanalysis. Researchers are beginning to investigate
the role that a network’s geometry might play
in statistical inference. Recent simulations have
determined that the shape of a network and number
of studies per edge may affect the appropriateness
of different models. Salanti (2008) proposes that
the networks of treatments can be described using
terms from ecology – diversity and cooccurrence.
In particular, the presenceabsence matrix used to
measure cooccurrence of species in ecology can be
used to identify possible biases in treatment networks.
This poster highlights the concept of cooccurrence
in ecology, the related cscore measurement with which
it is quantified, its application to network metaanalysis,
and its limitations.

Suresh Kumar Sharma, Panjab
University
Efficiency of Various Smoothers in Generalized Additive
Models
Department of Statistics, Panjab University, Chandigarh,
India
Coauthors: Kanchan Jain and Rashmi Aggarwal
A trend in the past few years has been to move away
from linear functions and model the dependence of
Y on X1,…,Xk in a nonparametric fashion. Generalized
additive models try to expose the functional dependence
without imposing rigid parametric assumptions about
that dependence. Here, the data shows us the appropriate
functional form and that is idea behind a scatter
plot smoother. In Generalized additive models, smoother
is a tool for summarizing the trend of a response
measurement Y as a function of one or more predictor
measurements X1,…,Xk. In literature, various
smoothers, viz running mean, running line, bin, Kernel
etc. are available. In this paper, our basic aim is
to compare the efficiency of various smoothers in
terms of Average Mean Squared Error (AMSE) for distributions
including Binomial, Poisson, Normal and Exponential.
For theoretical considerations, Biasvariance trades
off for scatter plot smoothers and moment generating
functions are also discussed.
Key Words: running mean, running lines, span, average
mean squared error, biasvariance tradeoff
References:
[1] Friedman, J.H. and Stuetzle, W.(1981): “Projection
Pursuit Regression,” Journal of the American
Statistical Association, 76, 817–823.
[2] Hastie, T. J. and Tibshirani, R. J. (1990): Generalized
Additive Models, Chapman & Hall/CRC
