| The world today is awash in data, and that data can be
massaged a great deal with fast computers. This course will help
you to deal intelligently with data and to assess the work of
others. (Why does the estimated value of the Hubble constant
wander beyond its error bars?) The course is different from most
others of this type in that it takes a two-pronged approach to data
analysis, whose parts may loosely be called "signal
processing" and "parameter estimation." The first
part is most useful in conditioning the data when you don't know exactly
what you're looking for, as well as in understanding how your instrument
has conditioned the data for you. The second part is useful for
comparing data with models.
The course begins with a thorough discussion of the practical aspects
of Fourier transforms, which have many applications to the theory of
data filtering and interpolation, and which play an important role in
probability theory. This is followed by an overview of relevant
aspects of probability and stochastic processes. The last two
sections of the course are about digital signal processing (e.g.,
filtering, power spectrum analysis, the effects of sampling, etc.) and
parameter estimation (maximum likelihood methods, linear and non-linear
least-mean-square analysis with emphasis on accurate error estimation). |
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