Since their inception almost fifty years ago, hidden Markov models (HMMs) have have become the predominant methodology for automatic speech recognition (ASR) systems--today, most state-of-the-art speech systems are HMM-based. There have been a number of ways to explain HMMs and to list their capabilities, each of these ways having both advantages and disadvantages. In an effort to better understand what HMMs can do, this tutorial article analyzes HMMs by exploring a definition of HMMs in terms of random variables and conditional independence assumptions. We prefer this definition as it allows us to reason more throughly about the capabilities of HMMs. In particular, it is possible to deduce that there are, in theory at least, no limitations to the class of probability distributions representable by HMMs. This paper concludes that, in search of a model to supersede the HMM (say for ASR), rather than trying to correct for HMM limitations in the general case, new models should be found based on their potential for better parsimony, computational requirements, and noise insensitivity.

A review of research, covering about 50 years, about random phenomena in nonlinear dynamical systems and the problems of modeling such phenomena using real (as contrasted to abstract, axiomatic) mathematics. Private views of the author concerning personalities and events.

Video service is slated to be a major application of emerging high-speed communications networks of the future. In particular, full-motion video is designed to take advantage of the high bandwidths that will become affordably available with the advent of B-ISDN. A salient feature of compressed video sources is that they give rise to autocorrelated traffic streams, which are difficult to model with traditional modeling techniques. In this paper, we describe a new methodology, called TES (Transform-Expand-Sample) , for modeling general autocorrelated time series, and we apply it to traffic modeling of compressed video. The main characteristic of this methodology is that it can model an arbitrary marginal distribution and approximate the autocorrelation structure of an empirical sample such as traffic measurements. Furthermore, the empirical marginal (histogram) and leading autocorrelations are captured simultaneously. Practical TES modeling is computationally intensive and is effectively carried out with software support. A computerized modeling environment, called TEStool, is briefly reviewed. TEStool supports a heuristic search approach for fitting a TES model to empirical time series. Finally, we exemplify our approach by two examples of TES video source models, constructed from empirical codec bitrate measurements: one at the frame level and the other at the group-of-block level. The examples demonstrate the efficacy of the TES modeling methodology and the TEStool modeling environment.