Inferences about means and variances under the normal model are covered in Chapter 7, beginning with the simplest variance-known situation, and ending with use of the normal-gamma as the natural conjugate when neither mean nor variance is known. Welsh 1984 The antivoter problem: random 2 2-colourings of graphs. Saks 1989 On the cover time of random walks on graphs. Alon 1986 Eigenvalues and expanders. The contents of the book, while self-contained, are presented in a terse style with practically no motivation.
Saloff-Coste 1993 Comparison theorems for reversible Markov chains. A comparative study of the results of ap- plying several different classification algorithms to the same data set could have proved useful in illustrating the ways in which different methods impose a certain amount of structure on data. Thanks for contributing an answer to Cross Validated! Stein 1981 The jackknife estimate of variance. Broder 1989 Generating random spanning trees. Many problems supplement the material in the text.
This video gives a 'real life' problem as some motivation and intuition, as well as introduces a bit of terminology. Or one can use Markov chain and Markov process synonymously, precising whether the time parameter is continuous or discrete as well as whether the state space is continuous or discrete. The serious reader is advised by both the author and the reviewer to attempt the exercises. The fundamental concepts related to the Markov property are sketched in the first chapter. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. Stroock 1987 Logarithmic Sobolev inequalitites and stochastic Ising models. The study of general chains in Chapter 3 in- cludes sections on invariant events and transient and recurrent sets, as well as the recurrence of a right random walk on locally comnpact separable groups.
Shahshahani 1986 Time to reach stationarity in the Bernouilli-Laplace diffusion model. Diaconis 1988 Group representations in probability and statistics. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail. Barlow 1998 Diffusions on fractals. Sudbury 1994 Approach to stationarity of the Bernouilli-Laplace diffusion model.
Durrett 1991 Probability: theory and examples. Theory of Computing 1989 574-586 Cited by: , , , ,. Sbihi 1992 Inequalities for random walks on trees. Starting from a consideration of errors in estimation and prediction, and types of loss functions, the authors develop the mean, median, mode, variance, and cor- relation coefficient in approximately ten pages. I'm reading conflicting information: sometimes the definition is based on whether the state space is discrete or continuous, and sometimes it is based on whether the time is discrete of continuous.
Winkler 1990 Maximum hitting time for random walks on graphs. Potential Theory for Harris Chains. Bulletin of the American Mathematical Society. In 1953 the term Markov chain was used for with discrete or continuous index set, living on a countable or finite state space, see Doob. Aldous 1983 On the time taken by random walks on finite groups to visit every state. Friedman 1991 On the second eigenvalue and random walk in random regular graphs.
Aldous 1991 Meeting times for independent Markov chains. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Hildebrand 1996 Enumeration and random random walks on finite groups. Thorisson 1992 Stationarity detection in the initial transient problem. Holt 1981 A graph which is edge-transitive but not arc-transitive.
Barlow 1991 Random walks and diffusions on fractals. Note: Extended abstract originally published in Proc. Interest in the theory of Markov chains has grown at an ever- increasing rate, beginning with the introduction of the concept by A. Where exactly in Chapter 5 is this interesting truth spelled out? Hilhorst 1991 Covering of a finite lattice by a random walk. Feige 1995 A tight upper bound on the cover time for random walks on graphs.
One can construct for any Markov kernel and any probability measure an associated Markov chain. Elton 1988 A new class of Markov processes for image encoding. Bingham 1991 Fluctuation theory for the Ehrenfest urn. Test theory also receives additional attention. Jerrum 1995 A very simple algorithm for estimating the number of k k-colorings of a low-degree graph. Meyer 1983 Probabilités et potentiel: théorie discrète du potentiel. Chung 1967 Markov chains with stationary transition probabilities.