Probability density function

About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.

Reconstructing random media. II. Three-dimensional media from two-dimensional cuts

Abstract: We report on an investigation concerning the utilization of morphological information obtained from a two-dimensional (2D) slice (thin section) of a random medium to reconstruct the full three-dimensional (3D) medium. We apply a procedure that we developed in an earlier paper that incorporates any set of statistical correlation functions to reconstruct a Fontainebleau sandstone in three dimensions. Since we have available the experimentally determined 3D representation of the sandstone, we can probe the extent to which intrinsically 3D information (such as connectedness) is captured in the reconstruction. We considered reconstructing the sandstone using the two-point probability function and lineal-path function as obtained from 2D cuts (cross sections) of the sample. The reconstructions are able to reproduce accurately certain 3D properties of the pore space, such as the pore-size distribution, the mean survival time of a Brownian particle, and the fluid permeability. The degree of connectedness of the pore space also compares remarkably well with the actual sandstone. However, not surprisingly, visualization of the 3D pore structures reveals that the reconstructions are not perfect. A more refined reconstruction can be produced by incorporating higher-order information at the expense of greater computational cost. Finally, we remark that our reconstruction study sheds lightmore » on the nature of information contained in the employed correlation functions. thinsp {copyright} {ital 1998} {ital The American Physical Society}« less

On the First Passage Time Probability Problem

Abstract: We have derived an exact solution for the first passage time probability of a stationary one-dimensional Markoffian random function from an integral equation. A recursion formula for the moments is given for the case that the conditional probability density describing the random function satisfies a Fokker-Planck equation. Various known solutions for special applications (noise, Brownian motion) are shown to be special cases of our solution. The Wiener-Rice series for the recurrence time probability density is derived from a generalization of Schr\"odinger's integral equation, for the case of a two-dimensional Markoffian random function.

Inference and computation with population codes

Abstract: In the vertebrate nervous system, sensory stimuli are typically encoded through the concerted activity of large populations of neurons. Classically, these patterns of activity have been treated as encoding the value of the stimulus (e.g., the orientation of a contour), and computation has been formalized in terms of function approximation. More recently, there have been several suggestions that neural computation is akin to a Bayesian inference process, with population activity patterns representing uncertainty about stimuli in the form of probability distributions (e.g., the probability density function over the orientation of a contour). This paper reviews both approaches, with a particular emphasis on the latter, which we see as a very promising framework for future modeling and experimental work.

Optimized computation of the voigt and complex probability functions

Abstract: Methods for computing the complex probability function w(z) = e−z2 erfc (−iz), which is related to the Voigt spectrum line profiles, are developed. The basic method is a rational approximation, minimizing the relative error of the imaginary part on the real axis. It is complemented by other methods in order to increase efficiency and to overcome the inevitable failure of any rational approximation near the real axis. The procedures enable one to evaluate both real and imaginary parts of w(z) with high relative accuracy. The methods are simple, as demonstrated by a sample FORTRAN program.