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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


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


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


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


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


Random Walks and Rapid Mixing

Christopher 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


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


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.


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