Search

Summary: High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.

Summary: This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.

Asymptotic normality of the posterior distribution of a parameter in a stochastic process is shown to hold under conditions which do little more than ensure consistency of a maximum likelihood estimator. Much more stringent conditions are required to ensure asymptotic normality of the MLE. This contrast, which has implications of considerable significance, does not emerge in the classical context of independent and identically distributed observations. [ABSTRACT FROM AUTHOR]

Genetic programming is used to automatically construct stochastic processes written in the stochastic Π-calculus. Grammar-guided genetic programming constrains search to useful process algebra structures. The time-series behaviour of a target process is denoted with a suitable selection of statistical feature tests. Feature tests can permit complex process behaviours to be effectively evaluated. However, they must be selected with care, in order to accurately characterize the desired process behaviour. Multi-objective evaluation is shown to be appropriate for this application, since it permits heterogeneous statistical feature tests to reside as independent objectives. Multiple undominated solutions can be saved and evaluated after a run, for determination of those that are most appropriate. Since there can be a vast number of candidate solutions, however, strategies for filtering and analyzing this set are required. [ABSTRACT FROM AUTHOR]

The rule with which automated computerised auctions are closed play an important role in determining bidder strategies and auction outcomes. In this paper we examine two such rules: auctions with randomised closing times and fixed deadlines. To this end, stochastic models of auctions with discrete state-space representing the prices attained are developed and analysed. The models allow us to determine the stationary probabilistic outcomes of the auctions, which are used to examine the bidder performance, measured as the savings it makes with respect to the maximum payable or its payoff. For this purpose, one bidder is singled out as the ˵special bidder″ (SB) and its performance is studied as a function of the speed with which it raises the price, or its bid rate. The results show that with random closures, the SB has incentives to place bids promptly to obtain high savings; on the other hand, with fixed deadline auctions, the SB should choose its bid rate with respect to the other system parameters in order to maximise payoffs. [ABSTRACT FROM AUTHOR]

Following the pricing approach proposed by Zhu & Lian [19], we present an exact solution for pricing variance swaps with the realized variance in the payoff function being a logarithmic return of the underlying asset at some pre-specified discrete sampling points. Our newly-found pricing formula is based on the Heston's [8] two-factor stochastic volatility model. The discovery of this exact and closed-form solution has significantly improved the computational efficiency involved in computing the value of variance swaps with discrete sampling points. [ABSTRACT FROM AUTHOR]

This paper investigates the finite time ruin probability in non-homogeneous Poisson risk model, conditional Poisson risk models and renewal risk model with stochastic returns. Under the assumption that the claimsize is subexponentially distributed, a simple asymptotic relation is established when the initial capital tends to infinity. The results obtained extend the corresponding results of constant interest force. Key Words: [ABSTRACT FROM AUTHOR]

An important challenge to any image pixels classification system is to correctly assign each pixel to its proper class without blurring edges delimiting neighboring regions. In this paper, we present an aerial image mapping approach that advantageously combines unsupervised segmentation with a supervised Markov model based recognition. The originality of the proposed system carries on three concepts: the introduction of an auto-adaptive circular-like window size while applying our stochastic classification to preserve region edges, the extension of the Dependency Tree -HMM to permit the computation of likelihood probability on windows of different shapes and sizes and a mechanism that checks the coherence of the indexing by integrating both segmentations results: from unsupervised over segmentation, regions are assigned to the predominating class with a focus on inner region pixels. To validate our approach, we achieved experiments on real world high resolution aerial images. The obtained results outperform those obtained by supervised classification alone. [ABSTRACT FROM AUTHOR]

Since Hjort's seminal work in the early twentieth century, researchers studying the early life stages of fish have attempted to understand and clarify the roles of growth and loss to help predict patterns of recruitment variability. Estimating the abundance of eggs and larvae has provided a fishery-independent measure of stock spawning potential. We also have significant skills in predicting the drift and dispersal of fish eggs and larvae, and consequently the role of wind-driven circulation on potential losses. However, there are few instances where the role of trophic dynamics on growth, starvation or mortality has been demonstrated without ambiguity. Here, I discuss what research needs to be carried out to establish a predictive capacity about the roles of food availability and predator abundance in determining development, growth and mortality of fish eggs and larvae. Revisiting laboratory approaches to determine feeding capacity and growth potential, as well as the application of advanced sampling methods and analytical approaches needed to develop an understanding of how larvae are affected by prey and predator, are just two issues that represent key challenges that we must address in order to develop rigorous frameworks within which we can make and test predictions about early life-history dynamics. Each year-class represents the outcome of a series of stochastic processes involving many factors. Although the objective of forecasting year-to-year fluctuations in recruitment is unrealistic, the development of a biophysical stochastic framework can serve to forecast probabilities of reproductive success in response to physical forcing and food web structure. [ABSTRACT FROM AUTHOR]

Chapter 61 of the book "HANDBOOK OF DEVELOPMENT ECONOMICS," VOLUME 4, edited by T. Paul Schultz and John Strauss is presented. It highlights the use of randomization as a solution to selection bias and a partial solution to publication biases. Discussions of various ways in introducing randomization in field settings, design issues, analyzing data and drawing general conclusions from randomized evaluations are presented.

This paper presents an important outcome of a research programme which focuses on the development of a method for synthesizing, under controlled conditions in the laboratory, the non-stationary random vibrations generated by road transport vehicles. It addresses an important limitation of current methods used for synthesising random vehicle vibrations which assume that vibrations produced by wheeled vehicles can be approximated by a zero-mean, normally-distributed (Gaussian) random process and, therefore, fails to accurately reproduce the fluctuations in vibration levels that occur naturally during road transportation realizations [1]. The paper builds upon the observation that non-stationary random vehicle vibrations are composed of a sequence of zero-mean random Gaussian processes of varying standard deviations [2]. It discusses the important parameters that need to be addressed when dealing with the synthesis of random sequences. The paper presents the development of a change-point detection algorithm that was used to determine the length of stationary segments within a large number of typical non-stationary random vibration records. These include measured vibration records as well as numerically-generated records based on measured pavement profiles. The algorithm, based on the cum-sum / bootstrapping techniques, was developed and applied to the instantaneous magnitude of sample vibration records. The statistical distribution of segment lengths for each vibration record was computed with the aim of identifying similarities and trends for the development of an overall statistical model for segment lengths to be used for synthesis purposes. One outcome of note was that the shape of the segment length distributions computed from a wide range of vibration records are generally comparable and exhibit an asymptotic-like decrease in probability of occurrence as the segment length increases. This behaviour was found to be adequately modelled with a hyperbolic trigonometric function which was found to be useful for characterising the general statistical behaviour of segment length for non-stationary random vibrations produced by road vehicles. Finally, the significance and relevance of this outcome with respect to the synthesis of non-stationary vibrations for package evaluation and validation purposes is highlighted. [ABSTRACT FROM AUTHOR]

The problem of estimating the intensity process of a doubly stochastic Poisson process is analyzed. Using covariance information, a recursive linear minimum mean-square error estimate is designed. Moreover, an efficient procedure for the computation of its associated error covariance is shown. The proposed solution becomes an alternative approach to the Kalman filter which is applicable under the only structural assumption that the intensity process to be estimated has a finite-dimensional covariance function. [ABSTRACT FROM AUTHOR]

In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker-Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves. [ABSTRACT FROM AUTHOR]

One of main issues in point matching is the choice of the mapping function and the computation of its optimal hyperparameters. In this paper, we propose an attractive approach to determine the mapping function based on Gaussian processes (GPs) model. The mapping function is assumed to belong to a GPs model specified by a mean and a covariance function. Meanwhile, hyperparameters optimization of mapping function is replaced by adaptation of GP model. Experiments show that the algorithm has efficient mapping capability and practical implementation in both synthetic and real cases. [ABSTRACT FROM AUTHOR]

In this paper, we present an interesting filtering algorithm to perform accurate estimation in jump Markov nonlinear systems, in case of multi-target tracking. With this paper, we aim to contribute in solving the problem of model based body motion estimation by using data coming from visual sensors. The Interacting Multiple Model (IMM) algorithm is specially designed to track accurately targets whose state and/or measurement (assumed to be linear) models changes during motion transition. However, when these models are nonlinear, the IMM algorithm must be modified in order to guarantee an accurate track. In order to deal with this problem, the IMM algorithm was combined with the Unscented Kalman Filter (UKF) [6]. Even if the later algorithm proved its efficacy in nonlinear model case; it presents a serious drawback in case of non Gaussian noise. To deal with this problem we propose to substitute the UKF with the Particle Filter (PF). To overcome the problem of data association, we propose the use of the JPDA approach, [12]. To reduce the computational burden of the latter technique, we choose firstly the most likely feasible events by applying a Genetic Algorithm; finally the derived algorithm from the combination of the IMM-PF algorithm and the GA-JPDA approach is noted GA-JPDA-IMM-PF. [ABSTRACT FROM AUTHOR]

According to foundational data of protective equipments in management information system, Markov model of protective equipments reliability analysis is developed and optimum routine test interval of protective equipments based on reliability analysis is achieved through proposed method in this paper. Three new terms, self-test index, maintenance index and repair index, are introduced and defined in this paper, which weigh heavily to reliability of protective equipment. Also, the impact of self-test index and maintenance index on protective equipments reliability index is discussed. Protective equipments reliability can be dynamically evaluated through the adapter to protective equipments Management Information System, which is of great theoretical significance and practical value and improves the function and management of protective equipments. [ABSTRACT FROM AUTHOR]

High-availability is one of the goals survivable storage systems pursuing. There are few methods for evaluating the availability of survivable storage system on secret-sharing scheme. Traditional evaluation methods usually evaluate the availability of a file (or an object) instead of the one of the system. A Markov-chained evaluation method for availability (MEMA) is proposed, whose description and calculation models are established on system level. MEMA is implemented in survivable storage system on secret-sharing scheme, and then the results are analyzed and the application scope is discussed in details. Analysis shows that our evaluation method can evaluate the availability of survivable storage system on secret-sharing scheme and find the factors affecting the availability. It is helpful to design a high-availability survivable storage system. [ABSTRACT FROM AUTHOR]

We study the use of auction algorithm in allocating a wireless fading channel among a set of non-cooperating users in both downlink and uplink communication scenarios. For the downlink case, we develop a novel auction-based algorithm to allow users to fairly compete for a wireless fading channel. We use the all-pay auction mechanism whereby user bid for the channel, during each time-slot, based on the fade state of the channel, and the user that makes the higher bid wins use of the channel. Under the assumption that each user has a limited budget for bidding, we show the existence of a unique Nash equilibrium strategy. We show that the strategy achieves a throughput allocation for each user that is proportional to the user΄s budget and establish that the aggregate throughput received by the users using the Nash equilibrium strategy is at least 3/4 of what can be obtained using an optimal centralized allocation scheme that does not take fairness into account. For the uplink case, we present a game-theoretical model of a wireless communication system with multiple competing users sharing a multiaccess fading channel. With a specified capture rule and a limited amount of energy available, a user opportunistically adjusts its transmission power based on its own channel state to maximize the user΄s own individual throughput. We derive an explicit form of the Nash equilibrium power allocation strategy. Furthermore, this Nash equilibrium power allocation strategy is unique under certain capture rule. We also quantify the loss of efficiency in throughput due to user΄s selfish behavior. Moreover, as the number of users in the system increases, the total system throughput obtained by using a Nash equilibrium strategy approaches the maximum attainable throughput. [ABSTRACT FROM AUTHOR]

Spectral analysis is a particularly valuable method for seeking dependences expressed as lags between different magnitudes. Its use in this article was first determined by the search for maximum objectivity in the observation of time series. The possibility of applying it to a large number of series was then examined. This twin requirement resulted from a desire to avoid the criticism generally levelled at statistical studies concerning cyclical movements of the economy. Spectral analysis is based on the theory of stochastic processes. It starts with the core hypothesis that a given time series consists of a large number of sinusoidal components with different frequencies (univariate spectral analysis). It makes it possible to divide a particular category of records into a set of oscillations of different frequencies and then to show the links between the components with the same frequency in the various series examined (cross-spectral or bivariate spectral analysis). It has had limited applications in cliometrics to date. It is used here to determine the frequency of GDP series of several OECD countries. A reminder of the method (I) is followed by successive examination of the various series chosen, the treatment of these series and the results of spectral analysis (II). It is then possible as a conclusion to show the prospects of this type of approach and to synthesise a completely new major result for understanding economic dynamics in the nineteenth and twentieth centuries, that is to say the existence of a single intermediate cycle with 15 to 20-year frequency that calls into question or even partially contradicts previous work on economic cycles. [ABSTRACT FROM AUTHOR]

We describe a quantitative modelling and analysis approach for signal transduction networks. We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK + 03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable. [ABSTRACT FROM AUTHOR]

Introduction Over the past fifty years or so we have seen a veritable fragmentation of economic theory. Research has ramified in different directions and its very foundations – methods and techniques of analysis, crucial concepts and simplifying assumptions, central problems – have undergone broad diversification. This has led to a division of labour among substantially autonomous groups of economists who often ignore, or in any case do not take into account in their own research, what happens in other areas of research. This trend has been reinforced by the high level of technicality that, together with diversification in the techniques of analysis, makes the studies required for any given field of research increasingly specific and time-consuming. For instance, the new evolutionary theories of the firm have no relation to research on the microeconomic foundations of macroeconomics; it would be quite difficult to find some common ground between research on the institutional evolution of financial markets and the so-called ‘new growth theory’ which seeks to make technical progress endogenous to the theory itself. Economists become ever more specialised and increasingly limit their readings and their professional contacts to researchers active in the same field and pursuing a similar research orientation; increasing numbers of specialised journals and professional societies are created; the very processes of academic selection favour the fragmentation of economists into separate corporations. It is thus quite difficult, in this situation, to provide a reasonably balanced and complete illustration of the different streams of economic research. [ABSTRACT FROM AUTHOR]

This paper studies the determinants of growth rate volatility, focusing on the effect of level of GDP, structural change and the size of economy. First we provide a graphical analysis based on nonparametric techniques, then a quantitative analysis which follows the distribution dynamics approach. Growth volatility appears to (i) decrease with per capita GDP, (ii) increase with the share of the agricultural sector on GDP and, (iii) decrease with the size of the economy, measured by a combination of total GDP and trade openness. However, we show that the explanatory power of per capita GDP tends to vanish when we control for the size of the economy. [ABSTRACT FROM AUTHOR]

This chapter presents weak convergence theory applied to approximate the risk process by Brownian motion and α-stable Lévy motion. The two different approximations are investigated. The first one assumes that the distribution of claim sizes belongs to the domain of attraction of the normal law. In second model, the claim sizes belonging to the domain of attraction of the α-stable law is considered. Weak convergence of stochastic processes does not imply the convergence of ruin probabilities in general. To take the advantage of the Brownian motion approximations it is necessary to show that the ruin probability in finite and infinite time horizons of risk processes converges to the ruin probabilities of Brownian motion.

This chapter focuses on Heston's stochastic volatility model. The properties of the model including marginal distributions and tail behavior are discussed. The original work of Heston (1993) is adapted to a foreign exchange setting because the model is particularly useful in explaining the volatility smile found in foreign exchange markets. In equity markets the typical volatility structure is an asymmetric skew also called a smirk or grimace. Calibrating Heston's model to such a structure leads to very high, unrealistic values of the correlation coefficient. The smile of vanilla options can be reproduced by suitably calibrating the model parameters.

The Introduction, Chap. 1, suggested that there is a resemblance of financial price histories to a random walk. It is therefore more than a simple curiosity that the first successful theory of the random walk was motivated by the description of financial time series. The present chapter will therefore describe the random walk hypothesis [28], as formulated by Bachelier for financial time series, in Sect. 3.2 and the physics of random walks [29], in Sect. 3.3. The mathematical description of random walks can be found in many books [30]. A classical account of the random walk hypothesis in finance has been published by Cootner [7]. [ABSTRACT FROM AUTHOR]

We now turn to the determination of the prices of derivative securities such as forwards, futures, or options in the presence of fluctuations in the price of the underlying. Such investments for speculative purposes are risky. Bachelier’s work on futures already shows that for relative prices, even the deterministic movements of the derivative are much stronger than those of the bond, and it seems clear that an investment into a derivative is then associated with a much higher risk (see also Bachelier’s evaluation of success rates) than in the underlying security, although the opportunities for profit would also be higher. Derivative prices depend on certain properties of the stochastic process followed by the price of the underlying security. Remember from Chap. 2 that options are some kind of insurance: the price of an insurance certainly depends on the frequency of occurrence of the event to be insured. We therefore introduce the standard model of stock prices, as used in textbooks of quantitative finance [10], [12]–[16] and place this model in a more general context of stochastic processes. [ABSTRACT FROM AUTHOR]

Modeling speech signals in the short-time Fourier transform (STFT) domain is a fundamental problem in designing speech enhancement systems. This chapter introduces a novel modeling approach, which is based on generalized autoregressive conditional heteroscedasticity (GARCH). GARCH is widely-used for volatility modeling of financial time-series such as exchange rates and stock returns. GARCH models take into account the heavy tailed distribution and volatility clustering characteristics of financial time-series. Spectral analysis shows that speech signals in the STFT domain are also characterized by heavy tailed distributions and volatility clustering. We demonstrate the application of GARCH modeling to speech enhancement, and show its advantage compared to using the conventional decision-directed method. [ABSTRACT FROM AUTHOR]

This paper presents an extension to our work on estimating the probability distribution by using a Markov Random Field (MRF) model in an Estimation of Distribution Algorithm (EDA) [1]. We propose a method that directly samples a MRF model to generate new population. We also present a new EDA, called the Distribution Estimation Using MRF with direct sampling (DEUMd), that uses this method, and iteratively refines the probability distribution to generate better solutions. Our experiments show that the direct sampling of a MRF model as estimation of distribution provides a significant advantage over other techniques on problems where a univariate EDA is typically used. [ABSTRACT FROM AUTHOR]

A major research focus in economics and econophysics is on the distribution of wealth in societies at different stages of development. Wealth includes money, material goods and assets of different kinds. Knowledge of the monetary equivalent of the latter two components is required in order to quantify wealth. A related and easier to measure distribution is that of income. The major motivation of theoretical models is to provide insight on the microscopic origins of income/wealth distributions. Such distributions are expected to provide good fits to the empirical data. In the context of incomes, Champernowne [2] has commented "The forces determining the distribution of incomes in any community are so varied and complex and interact and fluctuate so continuously, that any theoretical model must either be unrealistically simplified or hopelessly complicated." The statement highlights the desirability of finding a middle ground between the unrealistically simple and the hopelessly complicated. [ABSTRACT FROM AUTHOR]

We develop a stochastic model where the poorer end of the society engage in two-party trading while the richer end perform trade with gross entities. Using our model we are able to capture some of the essential features of wealth distribution in societies: the Boltzmann-Gibbs distribution at the lower end and the Pareto-like power law tails at the richer end. A reasonable scenario to connect the two ends of the wealth spectrum is presented. Also, we show analytically how different power law exponents can be obtained. Furthermore, a link with the models in macroeconomics is also attempted. [ABSTRACT FROM AUTHOR]

The Lagrange principle L = f + λg → maximum! is used to maximize a function f(x) under a constraint g(x). Economists regard f(x) = U as a rational production function, which has to be maximized under the constraint of prices g(x). In physics f(x) = lnP is regarded as entropy of a stochastic system, which has to be maximized under constraint of energy g(x). In the discussion of wealth distribution it may be demonstrated that both aspects will apply. The stochastic aspect of physics leads to a Boltzmann distribution of wealth, which applies to the majority of the less affluent population. The rational approach of economics leads to a Pareto distribution, which applies to the minority of the super rich. The boundary corresponds to an economic phase transition similar to the liquid - gas transition in physical systems. [ABSTRACT FROM AUTHOR]

Influence diagrams are now a well established tool for modeling in decision analysis. Recently, dynamic influence diagrams have been applied to help structure stochastic processes. This chapter discusses dynamic influence diagrams for structuring continuous-time Markov chains, with particular focus on medical decision modeling. We describe our freely available Excel-based software package StoTree, in which dynamic influence diagram models may be readily formulated and solved. We present medical applications as examples, including a previously published cost-effectiveness analysis for total hip replacement. [ABSTRACT FROM AUTHOR]

Medical treatment decisions are often sequential and uncertain. Markov decision processes (MDPs) are an appropriate technique for modeling and solving such stochastic and dynamic decisions. This chapter gives an overview of MDP models and solution techniques. We describe MDP modeling in the context of medical treatment and discuss when MDPs are an appropriate technique. We review selected successful applications of MDPs to treatment decisions in the literature. We conclude with a discussion of the challenges and opportunities for applying MDPs to medical treatment decisions. [ABSTRACT FROM AUTHOR]

Chapter 5 is dedicated to the processing of stochastic processes using discrete transforms and model-based approaches. It explains the Karhunen-Loeve transform and the whitening transform, gives an introduction to linear estimation theory and optimal filtering, addresses Wiener filters, linear predictors, the Yule-Walker equation, and discusses methods of estimating autocorrelation sequences and power spectra. [ABSTRACT FROM PUBLISHER]

Chapter 7 of the book "Markov Processes From K. Ito's Perspective" by Daniel W. Stroock is presented. It presents the extension of theory of K. Ito which was first accomplished by Kunita and Watanabe, although J. L. Doob was the first to acknowledge that it is the only ingredient that is essential to the theory. Meanwhile, it cites Doob-Meyer decomposition theorem for continuous martingales.

Chapter 4 of the book "Markov Processes From K. Ito's Perspective" by Daniel W. Stroock is presented. It points out important properties with which the method of K. Ito endues stochastic processes by starting with the Markov processes. It shows Corolary that the method of Ito produces a process which is the Markov under the condition that Kolmogorov's background equation can be solved.

The article describes the interference modeling in wireless communication. In wireless communication networks, signal reception is often corrupted by interference from other sources that share the same propagation medium. Knowledge of the statistics of interference is important in achieving optimum signal detection and estimation. Construction of most receivers is based on the assumption that the interference is independent, identically distributed Gaussian. The Gaussianity assumption is based on the central-limit theory.

This article focuses on maximum-likelihood estimation algorithms. The expectation-maximization algorithm, popularly known as the EM algorithm, is an iterative algorithm for computing maximum-likelihood estimates when dealing with data that have a latent structure and/or are incomplete. Moreover, computation of the maximum likelihood estimate is often greatly facilitated by formulating it as an incomplete data problem, which is invoked because the EM algorithm is able to exploit the reduced complexity of the maximum-likelihood estimate, given the complete data. In principle, the method of maximum likelihood may be applied to any estimation problem, with the provision that one should formulate the joint probability density function of the available set of observed data.

The article reports that a hidden Markov model is a doubly stochastic process with an underlying stochastic process that is not readily observable but can only be observed through another set of stochastic processes that produce the sequence of observations. By combining two levels of stochastic processes in a hierarchy, one is able to address the shorter term or instantaneous randomness in the observed event via one set of probabilistic measures while coping with the longer term, characteristic variation with another stochastic process, namely, the Markov chain. This formalism underwent rigorous theoretical developments in the 1960s and 1970s and reached some important milestones in the 1980s. Today, it has found widespread applications in stock market prediction, ecological modeling, cryptanalysis, computer vision, and most notably, automatic speech recognition.

This article discusses the digital optical correlation for fiber optic communication systems. As bit rates continue to rise in the optical core of telecommunication networks, the potential inability of electronic signal processors to handle this increase is a force driving research in optical signal processing. The term "correlator" is typically used to describe a hardware implementation of a matched filter. Although there exist strict definitions for matched filters versus correlators, most hardware implementations that produce the same output as a matched filter, sampled at the peak autocorrelation value, are referred to as "correlators."

In Chapter 10 the author considers the problem of estimating target parameters. Initially, he considers the problem of estimating the range and velocity of a single target when the interference is additive white Gaussian noise. Starting with the likelihood function, he develops the structure of the optimum receiver. He then investigates the performance of the receiver and sees how the signal characteristics affect the estimation accuracy. The author finds that the signal enters into the analysis through a function called the ambiguity function; he therefore develops various properties of the ambiguity function and discusses how to design signals with desirable ambiguity functions. The final topic is the detection of a target in the presence of other interfering targets (the discrete resolution problem). [ABSTRACT FROM PUBLISHER]

In this chapter detection and parameter estimation for range-spread targets are studied. In Section 12.1 the author develops a quantitative model for range-spread targets and channels and shows how this type of target causes frequency-selective fading. In Section 12.2, he discusses optimum receiver configurations briefly. In Section 12.3, he develop the concept of time-frequency duality. This development enables one to translate all range-spread channels into equivalent Doppler-spread channels. One can then use all of the results in Chapter 11 directly. The author also discusses a number of applications in Section 12.3. Finally, in Section 12.4, he summarizes the results. [ABSTRACT FROM PUBLISHER]

In Chapter 9 the author discusses the problem of detecting a slowly fluctuating point target at a particular range and velocity. First, he assumes that the only interference is additive white Gaussian noise and develops the optimum receiver and evaluates its performance. He then considers nonwhite Gaussian noise and finds the optimum receiver and its performance. He uses complex state-variable theory to obtain complete solutions for the nonwhite noise case. The final topic in the chapter is a brief discussion of signal design. [ABSTRACT FROM PUBLISHER]

The mapping from the parameter to the signal is random. In this chapter and the next, the author develops techniques for solving this type of problem. In Chapter 6 he develops the basic results. The quantitative model of the problem is given in Section 6.1. In Section 6.2 the likelihood function, the maximum likelihood equations, and the maximum aposteriori probability equations are derived. In Section 6.3 the author develops procedures for analyzing the performance. [ABSTRACT FROM PUBLISHER]

In this appendix the author develops complex representations for narrow-band signals, systems, and random processes. In Section A.1, he considers bandpass deterministic signals. In Section A.2, he considers bandpass linear systems. In Section A.3, bandpass random processes are studied. In Section A.4, the author summarizes the major results. Section A.5 contains some problems to demonstrate the application of the ideas discussed. [ABSTRACT FROM PUBLISHER]