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From: John Maddock (john_at_[hidden])
Date: 2008-08-13 13:15:38

Jesse Perla wrote:
> A couple of other questions on this beautiful distributions library -
> which
> I see as a great starting point for a lot of operations treating them
> as measures:
> * Is there any planned or existing support in the library for
> multi-dimensional distributions? In particular, bivariate norms with
> a covariance matrix passed in? Will the library design and notation
> support these sorts of extensions without too many problems?

Good question, it's something we've been asked for before so we're not
alone, but I haven't had a chance to implement anything.

Interface wise, we can define the distribution constructor to accept a
covariance matrix - provided as any type that looks like a matrix. The main
decision is how to store the covariance matrix internally, because that
largely determines the interface for the accessors that return the matrix.

For the pdf/cdf functions we could either accept multiple x values in a

double p = cdf(my_bivariate_distribution, x1, x2);

or in a vector:

double p = cdf(my_bivariate_distribution, my_vector);

where my_vector is basically any subscriptable type.

I haven't thought about cdf-complements, and quantiles I assume are

> * Is there any way in the current library to pass in a user created
> discrete valued probability measure and have it as a "distribution"
> here? If not, I think I may write it, but as I am not a very good
> library programmer I would love to exploit any other work out there.
> I would need this to work for at least 1 and 2 dimension measures.

Not yet, but again this is something (along with interpolation between
points) that has been asked for before. Throw in numeric
integration/differentiation and you have a rather powerful tool.

> * If we were to use a function to bundle a discrete valued function,
> is
> there a nice class/pattern out there that already combines the
> x-values and y-values into a single class? (I also want this later
> for implementing different interpolation algorithms returning
> functors after passing in a discrete function in the constructor).

I'm not sure what you're asking for there? If you mean storage for the 2-D
matrix of values, then you could either use a pair of std::vectors, a
boost::multi_array, or one of the uBLAS matrixes.

> * Then I would write a specialization of this (2nd and higher
> dimension) for
> a markov measure.
> * Then, I want to write a general operator for unconditional
> expectation passing in a function object, and over a generic
> distribution as a measure
> from this library (though I will use it for the discrete measures to
> begin with). Specializing for different types of distributions, this
> could use
> exact analytical calculations, quadrature, or use monte-carlo methods.
> * Last, I want to write a conditional expectation operator that takes
> in a function object mapping reals^2 to reals, a distribution (would
> have to be 2 dimensional), the conditional (which would be a real for
> now, but could be generic), and what dimension the condition applies
> to. * Eventually, we may be able to tie together this operator with
> boost::lambda and boost::bind and we could up with a very elegant way
> to
> write out functions that involve conditional expectations. It may
> not have
> the performance of hand-tweaked fortran loops, but it should be a good
> enough place to start and infinitely preferable to matlab.

Afraid you've lost me again now :-( Might just be stretching my stats
knowledge to breaking point too ;-)

Cheers, John.

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