Characteristics of queueing systems observed at events and the connection between stochastic intensity and palm probability

This article explores the link between the concepts of stochastic intensity and Palm probability and gives a new proof and useful extensions to the so-called PASTA property of queueing theory.     

Multiple ground-based observations at Zhongshan Station during the April/May 1998 solar events

Simultaneous observations at Zhongshan Station, Antarctica, during May 1-7, 1998 are presented to show the responses of the polar ionosphere to the April/May 1998 solar events. One of the main geo-effects of the solar events resulted in the major magnetic storm on May 4. At the storm onset on May 2 the ionosphere F2 layer abruptly increased in altitude, the geomagnetic H-component started negative deviation and the spectral amplitude of the ULF wave intensified. Both large isolated riometer absorption and large negative deviation of the geomagnetic H-component occurred at about 0639UT. There was a time lag of about one hour and ten minutes between the storm onset and the IMF southward turning, as measured by the WIND satellite. The polar ionosphere was highly disturbed, as shown by frequent large deviations of the geomagnetic H-component, large riometer absorption events and strong ULF waves in all the courses of the storm. The absorption increased greatly causing the digisonde to be blackout most of the time. However, the data still showed a substantial decrease in the F2 electron density and oscillation of the F2 layer peak height with an amplitude exceeding 200 km.     

Resistive plate chambers for muon detection at LHC

One resistive plate chamber made of Chinese materials and one Italian resistive plate chamber have been tested in the Gamma Irradiation Facility (GIF) at CERN on a high intensity muon beam together with a¹³⁷Cs source to give a uniform photon background, and simulating conditions close to those expected for an LHC muon detector. The results are analyzed. Good space and time resolutions are obtained which satisfy the future CMS experiment requirements. The detection efficiency is different between two RPCs against a high irradiation background. The reason is discussed.     

Control of partially observed diffusions

The optimal control of a partially observed diffusion is discussed when the control parameter is present in both the drift and diffusion coefficients. Using a differentiation result of Blagovescenskii and Freidlin, and adapting techniques of Bensoussan, we obtain a stochastic minimum principle.This research was partially supported by NSERC Grant A7964, by the US Air Force Office of Scientific Research Contract AFOSR-86-0332, and by the US Army Research Office Contract DAAL03-87-K-0102.     

Optimization-based heuristics for underground mine scheduling

Underground mine production scheduling possesses mathematical structure similar to and yields many of the same challenges as general scheduling problems. That is, binary variables represent the time at which various activities are scheduled. Typical objectives seek to minimize costs or some measure of production time, or to maximize net present value; two principal types of constraints exist: (i) resource constraints and (ii) precedence constraints. In our setting, we maximize “discounted metal production” for the remaining life of an underground lead and zinc mine that uses three different underground methods to extract the ore. Resource constraints limit the grade, tonnage, and backfill paste (used for structural stability) in each time period, while precedence constraints enforce the sequence in which extraction (and backfill) is performed in accordance with the underground mining methods used. We tailor exact and heuristic approaches to reduce model size, and develop an optimization-based decomposition heuristic; both of these methods transform a computationally intractable problem to one for which we obtain solutions in seconds, or, at most, hours for problem instances based on data sets from the Lisheen mine near Thurles, Ireland.     

Primary cosmic ray nucleon spectrum from sea-level muon spectrum and scaling hypothesis parameters

Based on the measured sea-level muon energy spectrum and the fitted parameters of Feynman’s scaling hypothesis that describe high energy collisions, we have deduced the primary cosmic ray nucleon spectrum in the energy range 50 GeV < E < 5000 GeV. It is shown that the statistical errors in the resulting nucleon spectrum are among the lowest that exist now and any residual systematic uncertainties in the evaluated flux can be reduced further by using accurate high energy collision data of nucleons and pions in light nuclei at current accelerator energies.     

Effective dimensions of partially observed polytrees

Model complexity is an important factor to consider when selecting among Bayesian network models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e., the number of linearly independent network parameters. When latent variables are present, however, standard dimension is no longer appropriate and effective dimension should be used instead [Proc. 12th Conf. Uncertainty Artificial Intell. (1996) 283]. Effective dimensions of Bayesian networks are difficult to compute in general. Work has begun to develop efficient methods for calculating the effective dimensions of special networks. One such method has been developed for partially observed trees [J. Artificial Intell. Res. 21 (2004) 1]. In this paper, we develop a similar method for partially observed polytrees.     

Independent fuzzy events

An algorithm for the reconstruction of a symmetric matrix from the spectral data is given. All cases in which the number of solutions is finite are determined. These results are applied to a certain inverse eigenvalue problem which arises in molecular spectroscopy.     

State estimation for partially observed Markov chains

Recursive equations are derived for the conditional distribution of the state of a Markov chain, given observations of a function of the state. Mainly continuous time chains are considered. The equations for the conditional distribution are given in matrix form and in differential equation form. The conditional distribution itself forms a Markov process. Special cases considered are doubly stochastic Poisson processes with a Markovian intensity, Markov chains with a random time, and Markovian approximations of semi-Markov processes. Further the results are used to compute the Radon-Nikodym derivative for two probability measures for a Markov chain, when a function of the state is observed.     

Structural results for partially observed control models

A general partially observed control model with discrete time parameter is investigated. Our main interest concerns monotonicity results and bounds for the value functions and for optimal policies. In particular, we show how the value functions depend on the observation kernels and we present conditions for a lower bound of an optimal policy. Our approach is based on two multivariate stochastic orderings: theTP ₂ ordering and the Blackwell ordering.Dedicated to Prof. Dr. K. Hinderer on the occassion of his 60^th birthday     

Quasi-likelihood analysis for nonsynchronously observed diffusion processes

We consider nonsynchronous sampling of parameterized stochastic regression models, which contain stochastic differential equations. Constructing a quasi-likelihood function, we prove that the quasi-maximum likelihood estimator and the Bayes type estimator are consistent and asymptotically mixed normal when the sampling frequency of the nonsynchronous data becomes large.     

State estimation for partially observed jump processes

In this paper partially observed jump processes are considered and optimal filtering equations are given for the conditional expectation of a functional on the past of the process.Rudemo [6] derived filtering equations for a partially observed jump Markov process. Snyder [3] gives equations for the conditional characteristic function of a jump process. Segall et al. [2] discuss filtering for processes with counting observations. Their work carries over to processes with counting observations the martingale methods that Fujisaki et al. [1] had used to derive nonlinear filtering equations for processes governed by Ito equations. Many further references to filtering for processes with discrete state measurements are given in the references cited.The objective of this paper is to show that by making use of the concept of a representation of a functional the idea of Rudemo's proof of [6, pp. 595–599] can be carried over to jump processes. The author feels that this is a very interesting proof because of its simplicity. It involves only calculations with conditional expectations and the rule for differentiation of a quotient.     

Optimal observation network in geostatistics and underground hydrology

Mathematical models and algorithms for the optimal design of data collection for regionalized variables are presented. The topics considered subsume as a special case optimal drilling strategies in hydrology, the mining industries and other geostatistical applications. In these disciplines an optimal design is a critical consideration since data, can only be obtained through an expensive drilling process.The methods given here are based on the theory of regionalized variables and of kriging. The basis of the methods for locating a single additional data point, and for locating multiple points, is the theory of minimizing uncertainty in parameter estimation. That is, the possible locations of additional points must be determined on the basis of surface analysis with respect to the projected costs of obtaining this data.After a summary of basic kriging techniques, four models are discussed. The first deals with the optimal location problem for a single experimental point, and the second, third and fourth models pertain to the case of multiple additional points. (Unfortunately the repeated application of the single-point model leads only to approximations of the global optima, since the global optima are usually unobtainable as a simple sum of the partial optima.) In the second model, an optimal regular observation network is to be designed to minimize the uncertainty of the estimation process subject to either the given number of additional data, or an upper bound for the cost of the additional data. In the fourth model, the number or cost of additional points is minimized subject to bounded uncertainty conditions. Finally, a numerical example will be used to illustrate the models and algorithms.     

Economically relevant preferences for all observed epsilon

The common investment decision rules, Markowitz’s Mean-Variance (MV) rule and the non-parametric Stochastic Dominance (SD) rules, suffer from one severe drawback: there are pairs of prospects where experimentally 100% of the subjects choose one prospect, yet these rules are unable to rank the two prospects—a paradoxical result. Thus, the set of all preferences corresponding to these decision rules is too large, because it contains theoretical preferences that are not encountered in practice. Based on 400 subjects’ choices we define the economically relevant set of preference and the corresponding new decision rules, which avoid the paradoxical results. The results are very robust and are almost unaffected by the magnitude of the outcomes and the structure of the prospects under consideration.     

Inventory management with partially observed nonstationary demand

We consider a continuous-time model for inventory management with Markov modulated non-stationary demands. We introduce active learning by assuming that the state of the world is unobserved and must be inferred by the manager. We also assume that demands are observed only when they are completely met. We first derive the explicit filtering equations and pass to an equivalent fully observed impulse control problem in terms of the sufficient statistics, the a posteriori probability process and the current inventory level. We then solve this equivalent formulation and directly characterize an optimal inventory policy. We also describe a computational procedure to calculate the value function and the optimal policy and present two numerical illustrations.     

Local Lyapunov exponents computed from observed data

Summary We develop methods for determining local Lyapunov exponents from observations of a scalar data set. Using average mutual information and the method of false neighbors, we reconstruct a multivariate time series, and then use local polynomial neighborhood-to-neighborhood maps to determine the phase space partial derivatives required to compute Lyapunov exponents. In several examples we demonstrate that the methods allow one to accurately reproduce results determined when the dynamics is known beforehand. We present a new recursive QR decomposition method for finding the eigenvalues of products of matrices when that product is severely ill conditioned, and we give an argument to show that local Lyapunov exponents are ambiguous up to order 1/L in the number of steps due to the choice of coordinate system. Local Lyapunov exponents are the critical element in determining the practical predictability of a chaotic system, so the results here will be of some general use.     

Parametric inference for discretely observed subordinate diffusions

Statistical Inference for Stochastic Processes - Subordinate diffusions are constructed by time changing diffusion processes with an independent Lévy subordinator. This is a rich family of...     

Controlled partially observed diffusions with correlated noise

This work is concerned with separated control problems for optimal stochastic controls under partial observations. Continuity properties of the unnormalized conditional distribution measure are found, and the Nisio nonlinear semigroup is formed in the case when a functionh(X _t ,Y _t ,U _t ) of stateX _t observationY _t , and controlU _t plus correlated additive white noise is observed.