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PHASE-TYPE QUEUES

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0005
Subject:
Mathematics, Numerical Analysis

In this chapter a series of processes with a variety of transition structures are considered and their analysis is presented in a unifying manner. These processes are grouped under the generic name ... More


Markov Processes

M. Vidyasagar

in Hidden Markov Processes: Theory and Applications to Biology

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691133157
eISBN:
9781400850518
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691133157.003.0004
Subject:
Mathematics, Probability / Statistics

This chapter deals with Markov processes. It first defines the “Markov property” and shows that all the relevant information about a Markov process assuming values in a finite set of cardinality n ... More


Profit scoring and dynamic models

Lyn C. Thomas

in Consumer Credit Models: Pricing, Profit and Portfolios

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199232130
eISBN:
9780191715914
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232130.003.0004
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

This chapter begins by reviewing the role of behavioural scoring and risk/reward matrices in the way a lender manages borrowers. It points out that current methods do not allow for the future changes ... More


A SURVEY ON THE USE OF MARKOV CHAINS TO RANDOMLY SAMPLE COLOURINGS

Alan Frieze and Eric Vigoda

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0004
Subject:
Mathematics, Probability / Statistics

In recent years, considerable progress has been made on the analysis of Markov chains for generating a random colouring of an input graph. These improvements have come in conjunction with refinements ... More


Markov Chain Models of Ion Channels and Calcium Release Sites

Jeffrey R. Groff, Hilary DeRemigio, and Gregory D. Smith

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0002
Subject:
Mathematics, Biostatistics

This chapter is an introduction to modelling stochastically gating ion channels using continuous-time discrete-state Markov chains. Analytical and numerical methods are presented for determining ... More


Hidden Markov Processes: Basic Properties

M. Vidyasagar

in Hidden Markov Processes: Theory and Applications to Biology

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691133157
eISBN:
9781400850518
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691133157.003.0006
Subject:
Mathematics, Probability / Statistics

This chapter considers the basic properties of hidden Markov processes (HMPs) or hidden Markov models (HMMs), a special type of stochastic process. It begins with a discussion of three distinct types ... More


LOGARITHMIC REDUCTION AND CYCLIC REDUCTION

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0007
Subject:
Mathematics, Numerical Analysis

This chapter is concerned with quadratically convergent algorithms for solving nonlinear matrix equations encountered in M/G/1, G/M/1, and QBD processes. The algorithm of logarithmic reduction for ... More


Introduction to Large Deviation Theory

M. Vidyasagar

in Hidden Markov Processes: Theory and Applications to Biology

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691133157
eISBN:
9781400850518
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691133157.003.0005
Subject:
Mathematics, Probability / Statistics

This chapter provides an introduction to large deviation theory. It begins with an overview of the motivatio n for the problem under study, focusing on probability distributions and how to construct ... More


SPECIALIZED STRUCTURES

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0009
Subject:
Mathematics, Numerical Analysis

Some specialized structures are investigated in this chapter and some of the algorithms in previous chapters are adapted to the specific cases. Markov chains with limited displacement (non-skip-free ... More


Markov Chain Monte Carlo

N. Thompson Hobbs and Mevin B. Hooten

in Bayesian Models: A Statistical Primer for Ecologists

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691159287
eISBN:
9781400866557
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159287.003.0007
Subject:
Biology, Ecology

This chapter explains how to implement Bayesian analyses using the Markov chain Monte Carlo (MCMC) algorithm, a set of methods for Bayesian analysis made popular by the seminal paper of Gelfand and ... More


Carnapian Inductive Logic for Markov Chains

Brian Skyrms

in From Zeno to Arbitrage: Essays on Quantity, Coherence, and Induction

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199652808
eISBN:
9780191745829
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652808.003.0014
Subject:
Philosophy, Philosophy of Science, Metaphysics/Epistemology

In his Nachlass, Carnap listed outstanding problems for the development of inductive logic. One was the treatment of what he called “analogy by proximity”. This can be handled naturally along ... More


Aspiration-based Adaptive Rules

Jonathan Bendor, Daniel Diermeier, David A. Siegel, and Michael M. Ting

in A Behavioral Theory of Elections

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691135076
eISBN:
9781400836802
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691135076.003.0002
Subject:
Political Science, American Politics

This chapter discusses some general properties of aspiration-based adaptive rules (ABARs). It begins with an overview of propensity and aspiration-based adjustment, using axioms to represent three ... More


Inference

Jesper Møller

in New Perspectives in Stochastic Geometry

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232574
eISBN:
9780191716393
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232574.003.0009
Subject:
Mathematics, Geometry / Topology

This contribution concerns statistical inference for parametric models used in stochastic geometry and based on quick and simple simulation free procedures as well as more comprehensive methods based ... More


Random Walks and Rapid Mixing

Cristopher Moore and Stephan Mertens

in The Nature of Computation

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199233212
eISBN:
9780191775079
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233212.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Random sampling is a technique for dealing with possible states or solutions having an exponentially large space. The best method of random sampling generally involves a random walk or a Markov ... More


Markov chains

Eric Renshaw

in Stochastic Population Processes: Analysis, Approximations, Simulations

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199575312
eISBN:
9780191728778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575312.003.0005
Subject:
Mathematics, Applied Mathematics, Mathematical Biology

This chapter considers Markov chains and branching processes. It covers two-state Markov chain, examples of m-state Markov chains, the Ehrenfest model, and branching processes.


Models of nucleotide substitution

ZIHENG YANG

in Computational Molecular Evolution

Published in print:
2006
Published Online:
April 2010
ISBN:
9780198567028
eISBN:
9780191728280
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567028.003.0001
Subject:
Biology, Evolutionary Biology / Genetics

This chapter discusses models of nucleotide substitution and calculation of the distance between a pair of sequences. It introduces the theory of Markov chains and the maximum likelihood method, ... More


Bayesian methods

ZIHENG YANG

in Computational Molecular Evolution

Published in print:
2006
Published Online:
April 2010
ISBN:
9780198567028
eISBN:
9780191728280
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567028.003.0005
Subject:
Biology, Evolutionary Biology / Genetics

This chapter provides a brief introduction to the theory and computation of Bayesian statistics and its applications to molecular evolution. It uses simple examples, such as distance estimation under ... More


Bayesian computation (MCMC)

Ziheng Yang

in Molecular Evolution: A Statistical Approach

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199602605
eISBN:
9780191782251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199602605.003.0007
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Evolutionary Biology / Genetics

This chapter provides a detailed introduction to modern Bayesian computation. The Metropolis–Hastings algorithm is illustrated using a simple example of distance estimation between two sequences. A ... More


Parsimony and Bayesian phylogenetics

Pablo A. Goloboff and Diego Pol

in Parsimony, Phylogeny, and Genomics

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199297306
eISBN:
9780191713729
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199297306.003.0008
Subject:
Biology, Evolutionary Biology / Genetics

The intent of a statistically-based phylogenetic method is to estimate tree topologies and values of possibly relevant parameters, as well as the uncertainty inherent in those estimations. A method ... More


Time‐varying parameters and state space models

Timo Teräsvirta, Dag Tjøstheim, and W. J. Granger

in Modelling Nonlinear Economic Time Series

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199587148
eISBN:
9780191595387
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199587148.003.0009
Subject:
Economics and Finance, Econometrics

Linear state space models have become popular in time series, and there are applications to many fields. The Kalman filter is often a fundamental tool. In this chapter it is shown that there are ... More


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