Statistics 248 D.R. Brillinger

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Statistics 248 D.R. Brillinger
Process data indexed values Y(?), ? time,
space, set, function
curves, surfaces, shapes, measure, images,
sequences, scatter, spirals, trajectories,
mosaics - and they may be moving
Random process data
Put process data in an urn and pick one,
Y(??), ? a random variable
time series, point process, marked point process,
spatial process, spatial-temporal process,
categorical-valued, hybrids, ...
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Time series data.
t time (but could be space) 0 ? t ? T
(continuous) t 0,...,T-1 (discrete) t
?1 ,..., ?N
(unique) value Y(t) Y in R
0,1 Rp N, category,
0, 2?)
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Tufte (1983). 10th or 11th century movement of
planets and sun
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Symbol graph. Good for long term behavior
cannot appreciate middle and high frequency
behavior irregular sampling can be
unclear plot(type"p",...) seals T 940
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Connected. Good for smooth series individual
data points not unambiguously displayed
irregular sampling can be unclear plot(type"l",
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Both. Points and line segments plot(type"b",
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Both. Points on top of connected plot(type"o",
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plot(type"n" points(pch""
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plot(type"n" lines(type3
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plot(type"h" Good when need to see individual
values when series long about
centralvalue (next) Not good when strong trend
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plot(type"h",...) Amazon T 32875 Good
about central value
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Vector ts case matplot(type"l" use
several line types
colors use to force comparison
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Useful when there is special period P tnPp,
p0,...,P-1 Yn(p)Y(nPp)
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14.2 Computer software
R CRAN
Ross Ihaka is one the originators of R, a
software package for statistical computing that
has had phenomenal uptake internationally. It can
be downloaded free and easily customised for a
very wide variety of applications. The package
and the paper introducing it have been cited over
1700 times, by far the highest for publications
in the mathematical sciences over the last ten
years, worldwide. It is now disseminated from
over 75 internet sites in 30 countries.
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The package is used both for teaching and
research by hundreds of universities around the
world, including Stanford, Oxford, Cambridge and
Berkeley. There are over 40 books written about,
or featuring, the use of R.
http//www.nytimes.com/2009/01/07/technology/busin
ess-computing/07program.html?scp2sqihakastcse