## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## A probabilistic toolbox

*Marc Mézard and Andrea Montanari*

### in Information, Physics, and Computation

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780198570837
- eISBN:
- 9780191718755
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570837.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The three fields that form the subject of this book all deal with large sets of random variables. Not surprisingly, they possess common underlying structures and techniques. This chapter describes ... More