4,942 research outputs found
MCMC methods for functions modifying old algorithms to make\ud them faster
Many problems arising in applications result in the need\ud
to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods which ensures that their speed of convergence is robust under mesh refinement. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modeling strategy. The algorithmic approach that we describe is applicable whenever the desired probability measure has density with respect to a Gaussian process or Gaussian random field prior, and to some useful non-Gaussian priors constructed through random truncation. Applications are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration. The key design principle is to formulate the MCMC method for functions. This leads to algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems
Implementation of the Combined--Nonlinear Condensation Transformation
We discuss several applications of the recently proposed combined
nonlinear-condensation transformation (CNCT) for the evaluation of slowly
convergent, nonalternating series. These include certain statistical
distributions which are of importance in linguistics, statistical-mechanics
theory, and biophysics (statistical analysis of DNA sequences). We also discuss
applications of the transformation in experimental mathematics, and we briefly
expand on further applications in theoretical physics. Finally, we discuss a
related Mathematica program for the computation of Lerch's transcendent.Comment: 23 pages, 1 table, 1 figure (Comput. Phys. Commun., in press
Nonlinear spectral analysis: A local Gaussian approach
The spectral distribution of a stationary time series
can be used to investigate whether or not periodic
structures are present in , but has some
limitations due to its dependence on the autocovariances . For
example, can not distinguish white i.i.d. noise from GARCH-type
models (whose terms are dependent, but uncorrelated), which implies that
can be an inadequate tool when contains
asymmetries and nonlinear dependencies.
Asymmetries between the upper and lower tails of a time series can be
investigated by means of the local Gaussian autocorrelations introduced in
Tj{\o}stheim and Hufthammer (2013), and these local measures of dependence can
be used to construct the local Gaussian spectral density presented in this
paper. A key feature of the new local spectral density is that it coincides
with for Gaussian time series, which implies that it can be used to
detect non-Gaussian traits in the time series under investigation. In
particular, if is flat, then peaks and troughs of the new local
spectral density can indicate nonlinear traits, which potentially might
discover local periodic phenomena that remain undetected in an ordinary
spectral analysis.Comment: Version 4: Major revision from version 3, with new theory/figures.
135 pages (main part 32 + appendices 103), 11 + 16 figure
- …