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Nonlinear applications of Markov Chain Monte Carlo


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Lee, G 2010 , 'Nonlinear applications of Markov Chain Monte Carlo', PhD thesis, University of Tasmania.

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In the early 20th century data analysis was constrained by computability. Calculations
were performed by hand, providing real practical limits on the types of
problems which were tractable. Salsburg (2002) provides a calculation showing that
at least 8 months of 12-hour days would have been required for R. A. Fisher to have
produced the tables in his \Studies in Crop Variation I" (Fisher, 1921) with the
mechanical means at his disposal. It is hardly surprising that the emphasis during
this period remained on linear models { problems soluble by ordinary least squares,
with the tools at hand.
It was not until the 1960s that nonlinear regression began to appear regularly in the
literature, and no accident that this eventuates concurrently with the appearance
of machines to automate iterative calculations. The heavier computational burden
had previously been insurmountable. But even after the advent of early computers,
great emphasis was placed on the development of algorithms which could make e�-
cient use of limited hardware resources { processors were slow and memory limited.
Research into algorithms became synonymous with e�ciency, and the attendant
O-notation. The Fast Fourier Transform of Cooley and Tukey (1965) provides the
archetypal example of the era. The explicit reference to speed in the title underscores
the imperative.

Item Type: Thesis - PhD
Authors/Creators:Lee, G
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© 2010 the author

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