SIAM Journal on Scientific Computing, Vol. 22, No. 1, (2000), pp. 152-176.
Ömer Egecioglu and Ashok Srinivasan
Efficient Non-parametric Density Estimation on the Sphere with Applications in Fluid Mechanics
Abstract.
The application of non-parametric probability density
function estimation for the
purpose of data analysis is well established. More recently, such
methods have been applied to fluid flow calculations, since the
density of the fluid plays a crucial role in determining the flow.
Furthermore, when
the calculations involve directional or axial data, the domain of
interest falls on the surface of the sphere. Accurate and fast
estimation of probability density functions is
crucial for these calculations since the density estimation is
performed at each iteration during the computation. In particular
the values f_n(X_1), f_n(X_2),..., f_n(X_n) of the
density estimate at the sampled points X_i are needed to evolve
the system. Usual
non-parametric estimators make use of kernel
functions to construct f_n. We propose a
special sequence of weight functions for non-parametric
density estimation
that are especially suitable for such applications.
The resulting method
has a computational advantage over kernel methods in certain situations,
and also
parallelizes easily.
Conditions for
convergence turn out to be similar
to those required for kernel based methods.
We also discuss experiments on different distributions and compare the
computational efficiency of our method with kernel based
estimators.
omer@cs.ucsb.edu