Multi-stage decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future uncertain values on which the decision will depend on. The quality of the scenario model severely affects the quality of the solution of the optimization model. Various approaches towards an optimal generation of discrete-state approxi...

Probabilistic sampling methods have become very popular to solve single-shot path planning problems. Rapidlyexploring Random Trees (RRTs) in particular have been shown to be efficient in solving high dimensional problems. Even though several RRT variants have been proposed for dynamic replanning, these methods only perform well in environments with infrequent changes. This paper addresses the d...

The Möbius function is utilised to propose a class of multi-channel, multi-sampling rate theorems. Our construction facilitates a parallel decomposition of the Fourier transform into an array of general integral transform operators. A practical example is discussed which employs a complex square wave biorthonormal basis.

For importance sampling (IS), multiple proposals can be combined to address different aspects of a target distribution. There are various methods for IS with multiple proposals, including Hesterberg’s stratified IS estimator, Owen and Zhou’s regression estimator, and Tan’s maximum likelihood estimator. For the problem of efficiently allocating samples to different proposals, it is natural to us...

Many health and other surveys aim to produce statistics on small subpopulations, such as specific ethnic groups or the indigenous population of a country. In most countries, there is no reliable sampling frame of the subpopulations of interest, hence it is necessary to sample from the general population, which can be very expensive. A range of issues and strategies for sampling rare subpopulati...

The first-order sampling of multi-band bandpass signals with arbitrary band positions is considered in this paper. Gaps between the spectral sub-bands are utilized to achieve lower sampling rates than the Nyquist. The lowest possible sampling rate along with other permissible sampling rates is identified via a unique partition of the frequency axis. With the complete identification of all the p...

The first-order sampling of multi-band bandpass signals with arbitrary band positions is considered in this paper. Gaps between the spectral sub-bands are utilized to achieve lower sampling rates than the Nyquist. The lowest possible sampling rate along with other permissible sampling rates is identified via a unique partition of the frequency axis. With the complete identification of all the p...

The optimal allocation of available resources is the concern of every investigator in choosing a study design. The recent development of statistical methods for the analysis of two-stage data makes these study designs attractive for their economy and efficiency. However, little work has been done on deriving two-stage designs that are optimal under the kinds of constraints encountered in practi...

Decimator is an important sampling device used for multi-rate signal processing in wireless communication systems. Multirate systems have traditionally played the important role in compression for contemporary communication application.In this paper it demonstrated that a multistage implementation of sampling rate conversion often provides for a more efficient realization, especially when filte...