In this article we investigate the problem of measuring deviations from stationarity in locally stationary time series. Our approach is based on a direct estimate of the L2-distance between the spectral density of the locally stationary process and its best approximation by a spectral density of a stationary process. An explicit expression of the minimal distance is derived, which depends only on integrals of the spectral density of the locally stationary process and its square. These integrals can be estimated directly without estimating the spectral density, and as a consequence, the estimation of the measure of stationarity does not require the specification of a smoothing bandwidth. We show weak convergence of an appropriately standardized version of the statistic to a standard normal distribution. The results are used to construct confidence intervals for the measure of stationarity and to develop a new test for the hypothesis of stationarity. Finally, we investigate the finite sample properties of t...

https://www.ruhr-uni-bochum.de/imperia/md/content/mathematik3/publications/paperlokstat28072010website.pdf

A measure of stationarity in locally stationary processes with applications to testing

The Bayesian learning provides a natural way to model the nonlinear structure as the artificial neural networks due to their capability to cope with the model complexity. In this paper, an evolutionary Monte Carlo (MC) algorithm is proposed to train the Bayesian neural networks (BNNs) for the time series forecasting. This approach called as Genetic MC is based on Gaussian approximation with recursive hyperparameter. Genetic MC integrates MC simulations with the genetic algorithms and the fuzzy membership functions. In the implementations, Genetic MC is compared with the traditional neural networks and time series techniques in terms of their forecasting performances over the weekly sales of a Finance Magazine.

Nonlinear time series forecasting with Bayesian neural networks

Performance analysis of Bayesian networks and neural networks in classification of file system activities

A novel Monte Carlo algorithm is proposed to train Bayesian neural networks.This algorithm is based on the full Bayesian approach of artificial neural networks.Monte Carlo methods are integrated with GAs and fuzzy membership functions.Proposed algorithm is applied to time series and regression analysis in the context of BNNs.Proposed approach is superior to traditional training methods in terms of estimation performance. The Bayesian neural networks are useful tools to estimate the functional structure in the nonlinear systems. However, they suffer from some complicated problems such as controlling the model complexity, the training time, the efficient parameter estimation, the random walk, and the stuck in the local optima in the high-dimensional parameter cases. In this paper, to alleviate these mentioned problems, a novel hybrid Bayesian learning procedure is proposed. This approach is based on the full Bayesian learning, and integrates Markov chain Monte Carlo procedures with genetic algorithms and the fuzzy membership functions. In the application sections, to examine the performance of proposed approach, nonlinear time series and regression analysis are handled separately, and it is compared with the traditional training techniques in terms of their estimation and prediction abilities.

A novel hybrid learning algorithm for full Bayesian approach of artificial neural networks

This research aims to ascertain fi lesystem access patterns produced by different application programs, and evaluates their potential utility in improving digital forensic analyses. The access patterns produced by the proposed methodology can serve as a decision support system for determining the possible execution of certain applications in the event of computer misuse. For this purpose, we propose the use of a causal Bayesian network that summarizes the most important relationships among integral parameters relating to fi lesystem activities such as access, creation, modifi cation, fi le deletion, audit logs, registry entries and the manner in which the applications manipulate these parameters. Determining the state of a fi lesystem at a particular period of time is vital for conducting digital forensic analyses. Herein, we describe a Bayesian network-based technique to determine the state of a computer fi lesystem in terms of the program execution and fi les manipulated during some specific time period. Specifi cally, we discuss the construction of a Bayesian network from our prior knowledge of the manipulation of the fi lesystem and metadata information by a set of applications. The variations among the execution patterns of different applications indicate that the Bayesian network-based model is an appropriate tool, due to its ability to enable pattern learning and detection, even from an incomplete dataset. The focus of this paper is to highlight the merits of the Bayesian methods for learning, with regard to the techniques used for supervised learning in ordinary neural networks.

http://www.ijofcs.org/V02N1-P04%20-%20Extracting%20Evidence%20from%20Filesystem.pdf

Extracting Evidence from Filesystem Activity using Bayesian Networks

There is a growing interest in the use of neural networks in civil engineering to model complicated nonlinearity problems. A recent enhancement to the conventional back-propagation neural network algorithm is the adoption of a Bayesian inference procedure that provides good generalization and a statistical approach to deal with data uncertainty. A review of the Bayesian approach for neural network learning is presented. One distinct advantage of this method over the conventional back-propagation method is that the algorithm is able to provide assessments of the confidence associated with the  network’s predictions. Two examples are presented to demonstrate the capabilities of this algorithm. A third example considers the practical application of the Bayesian neural network approach for analyzing the ultimate shear strength of deep beams.

A. T. C. Goh

Papers

Nonlinear modeling with confidence estimation using Bayesian neural networks