Jeffrey S. Rosenthal

the Sleeping Beauty problem (2009)

Summary. We describe the importance and widespread use of Markov chain Monte Carlo (MCMC) algorithms, with an emphasis on the roles in which theoretical analysis can help with their practical...

Donax Don't Tell: Reassessing Late Holocene Land Use in Northern San Diego County (2009)

A mathematical analysis of

Rosenthal, Jeffrey S, Hildebrandt, William R, King, Jerome H

This paper considers the two competing models of late Holocene settlement and subsistence on the northern San Diego County coast. A large body of regional data derived from single component site...

Variance bounding Markov chains (2008)

Article Submitted to Journal of Symbolic Computation CROSSWORD PUZZLES: EXPERIMENTS WITH META-SEARCH IN PROPOSITIONAL REASONING (2008)

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity....

James J. Lu, Jeffrey S. Rosenthal, E. Shaffer

A new technique for improving the efficiency of propositional reasoning procedures is presented. The meta-search procedure, ND, is parameterized by a search procedure ¡ and a real number for...

I.1 Measure-Theoretic Probability.................. 1 (2008)

Summary. This is an expository paper which presents various ideas related to non-asymptotic rates of convergence for Markov chains. Such rates are of great importance for stochastic algorithms which...

Supervisor Professor, Jeffrey S. Rosenthal, Student Shuheng Zheng, Shuheng John Zheng

This research report was written during the summer of 2006 under Professor Jeffrey Rosenthal with the support of NSERC USRA. There are two major purposes to this research report. The first is to...

Waiting Time Correlations on Disorderly Streetcar Routes by (2008)

Abstract. We propose a model for disorderly streetcar routes. Through simulations and comparisons to real data, we illustrate that such routes may sometimes become supersaturated, in the sense that...

1 Comparison of Adult Offense Prediction Methods Comparison of Adult Offense Prediction Methods based on Juvenile Offense Trajectories using Cross-Validation (2008)

Summary. We provide general methods for analyzing the convergence of discrete-time, general state space Markov chains, such as those used in stochastic simulation algorithms including the Gibbs...

David M. Day, Irene Bevc, Thierry Duchesne, Jeffrey S. Rosenthal, Lianne Rossman, Frances Theodor

Considerable research has found support for the relationship between criminal offending in adolescence and criminal offending in adulthood. Estimating the strength and nature of the relationship has...

Poster presented at the 111 th Annual Convention of the American Psychological Association (2008)

David M. Day, Irene Bevc, Jeffrey S. Rosenthal, Thierry Duchesne, Lianne Rossman, Frances Theodor, ...

and Ron Richardson for their assistance. This study examined the relationship between adolescent (10-17 years) criminal offending and adult (18-33 years) offending. The sample comprised 378 Canadian...

Perfect Forward Simulation via Simulated Tempering (2008)

Stephen P. Brooksý, Yanan Fan, Jeffrey S. Rosenthal

Summary. Several authors discuss how the simulated tempering scheme provides a very simple mech-anism for introducing regenerations within a Markov chain. In this paper we explain how regenerative...

Contents (2008)

Supervisor Professor, Jeffrey S. Rosenthal, Student Olga Chilina

Authors ’ rejoinder to Markov chain Monte Carlo: Some practical implications (2008)

James Allen Fill, Motoya Machida, Duncan J. Murdoch, Jeffrey S. Rosenthal

of theoretical results

(EXT. ABS.) (2008)

perfect rejection sampling algorithm to general chains

Expressions for the Markov Chain CLT Variance 1. Introduction. (2008)

Expressions for the Markov Chain CLT Variance (2008)

1 Introduction Markov chain Monte Carlo (2008)

2003), Harris Recurrence of Metropolis-WithinGibbs and Transdimensional MCMC Algorithms (2008)

Waiting Time Correlations on Disorderly Streetcar Routes by (2008)

Abstract. A Markov chain with stationary probability distribution, which is φ-irreducible and aperiodic, will converge to its stationary distribution from almost all starting points. The property of...

Abstract. We propose a model for disorderly streetcar routes. Through simulations and comparisons to real data, we illustrate that such routes may sometimes become supersaturated, in the sense that...

A simple account (2008)

Quantitative convergence rates of Markov chains:

Summary. We analyze a random walk on the orthogonal group SO(N) given by repeat-edly rotating by a fixed angle through randomly chosen planes of R N. We derive estimates of the rate at which this...

James P. Hobert, Jeffrey S. Rosenthal

(EXT. ABS.) (2008)

James Allen Fill, Motoya Machida, Duncan J. Murdoch, Jeffrey S. Rosenthal

perfect rejection sampling algorithm to general chains

James P. Hobert, Jeffrey S. Rosenthal

and (2008)

for Markov chain Monte Carlo algorithms (2008)

Shift-coupling and convergence rates

Mary Kathryn Cowles, Jeffrey S. Rosenthal

A simulation approach to convergence rates

2002), One-shot coupling for certain stochastic recursive sequences (2008)

Supervisor Professor, Jeffrey S. Rosenthal, Student Olga Chilina

Abstract. We consider Markov chains {Γn} with transitions of the form Γn = f(Xn, Yn) Γn−1 + g(Xn, Yn), where {Xn} and {Yn} are two independent i.i.d. sequences. For two copies {Γn} and {Γ ′...

Contents (2008)

Active-Learning Strategies in Advanced Mathematics Classes (2008)

Linear-Algebraic Results Associated with Antiferromagnetic Heisenberg Chains* by (2008)

Abstract. Advanced mathematics and other theoretical sciences are often taught purely using the lecture format, which promotes passivity and isolation in students. This paper advocates the use of...

Man-duen Choi, Jeffrey S. Rosenthal, Peter Rosenthal, Y S (j

y S (j+1)

EXTREMAL INDICES, GEOMETRIC ERGODICITY OF MARKOV CHAINS, AND MCMC (2008)

Gareth O. Roberts, Jeffrey S. Rosenthal, Johan Segers

Abstract. We investigate the connections between extremal indices on the one hand and stability of Markov chains on the other hand. Both theories relate to the tail behaviour of stochastic processes,...

f-Uniform Ergodicity of Markov Chains (2008)

Supervisor Professor, Jeffrey S. Rosenthal, Olga Chilina

The present project is devoted to the discussion of properties of f-uniform ergodicity for homogeneous Markov chains. This topic is considered in many scientific articles (see, for example, [1], [2],...

James P. Hobert, Jeffrey S. Rosenthal

related to (2008)

Analysis of the Gibbs sampler for a model

Optimal Proposal Distributions and Adaptive MCMC by (2008)

for adaptive MCMC

Jeffrey S. Rosenthal, S. Brooks, A. Gelman, G. Jones

Abstract. We review recent work concerning optimal proposal scalings for Metropolis-Hastings MCMC algorithms, and adaptive MCMC algorithms for trying to improve the algorithm on the fly. 1....

On the Containment Condition for Adaptive Markov (2008)

Chain Monte, Carlo Algorithms, Yan Bai, Gareth O. Roberts, Jeffrey S. Rosenthal

1

On Variance Conditions for Markov Chain CLTs (2007)

Haggstrom, Olle; Chalmers University Of Technology; Olleh@math.chalmers.se, Rosenthal, Jeffrey S.; University Of Toronto; Jeff@math.toronto.edu

Central limit theorems for Markov chains are considered, and in particular the relationships between various expressions for asymptotic variance known from the literature. These turn out to be equal...

COMMUNICATIONS in PROBABILITY GEOMETRIC ERGODICITY AND HYBRID MARKOV CHAINS (2007)

James J. Lu, Jeffrey S. Rosenthal, Andrew E. Shaffer

Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a...

1 (2007)

Abstract. A new technique for improving the efficiency of propositional reasoning procedures is presented. The meta-search procedure, ND, is parameterized by a search procedure P and a real number...

3 (2007)

Allan Borodin, Gareth O. Roberts, Jeffrey S. Rosenthal, Panayiotis Tsaparas

Recently, there have been a number of algorithms proposed for analyzing hypertext link structure so as to determine the best "authorities " for a given topic or query. While such...

A Case Study in the Meta-Reasoning Procedure ND (2007)

James J. Lu, Jeffrey S. Rosenthal, Andrew E. Shaffer

A new technique for improving the efficiency of propositional reasoning procedures is presented. The meta-search procedure, ND, is parameterised by a search procedure P and a real number for...

Harris recurrence of Metropolis-within-Gibbs and trans-dimensional Markov chains (2007)

On Variance Conditions for Markov Chain CLTs 1. Introduction. by (2007)

A $\phi$-irreducible and aperiodic Markov chain with stationary probability distribution will converge to its stationary distribution from almost all starting points. The property of Harris...

Olle Häggström, Jeffrey S. Rosenthal

The existence of central limit theorems (CLTs) for Markov chains is well studied, and

Optimal scaling of Metropolis algorithms: is 0.234 as robust as believed. Universite de Montreal and University of Toronto, email: bedard@dms.umontreal.ca (2007)

Mylène Bédard, Jeffrey S. Rosenthal

The Metropolis algorithm with Gaussian proposal distribution is a popular sampling method; it is versatile and easy to implement. Optimal scaling theory aims to improve the speed of convergence of...

On Variance Conditions for Markov Chain CLTs 1. Introduction. by (2007)

Olle Häggström, Jeffrey S. Rosenthal

The existence of central limit theorems (CLTs) for Markov chains is well studied, and

On Variance Conditions for Markov Chain CLTs (2007)

Olle H"aggstr"om, Jeffrey S. Rosenthal

Optimal scaling of Metropolis algorithms: is 0.234 as robust as believed. Universite de Montreal and University of Toronto, email: bedard@dms.umontreal.ca (2007)

Harris recurrence of Metropolis-within-Gibbs and trans-dimensional Markov chains (2006)

Abstract The Metropolis algorithm with Gaussian proposal distribution is a popular samplingmethod; it is versatile and easy to implement. Optimal scaling theory aims to improve the speed of...

Variance Bounding Markov Chains (2006)

A ϕ-irreducible and aperiodic Markov chain with stationary probability distribution will converge to its stationary distribution from almost all starting points. The property of Harris recurrence...

Variance Bounding Markov Chains (2006)

Abstract. We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric...

Examples of adaptive MCMC (2006)

On adaptive Markov chain Monte Carlo algorithms (2005)

Abstract. We investigate the use of adaptive MCMC algorithms to automatically tune the Markov chain parameters during a run. Examples include the Adaptive Metropolis (AM) multivariate algorithm of...

Atchadé, Yves F., Rosenthal, Jeffrey S.

We look at adaptive Markov chain Monte Carlo algorithms that generate stochastic processes based on sequences of transition kernels, where each transition kernel is allowed to depend on the history...

Quantitative bounds on convergence of time-inhomogeneous Markov chains (2005)

Douc, R., Moulines, E., Rosenthal, Jeffrey S.

Convergence rates of Markov chains have been widely studied in recent years. In particular, quantitative bounds on convergence rates have been studied in various forms by Meyn and Tweedie [Ann. Appl....

Link analysis ranking: algorithms, theory, and experiments (2005)

Allan Borodin, Gareth O. Roberts, Jeffrey S. Rosenthal

The explosive growth and the widespread accessibility of the Web has led to a surge of research activity in the area of information retrieval on the World Wide Web. The seminal papers of Kleinberg...

An Introduction to Markov Chain Monte Carlo (2005)

2005), Coupling and Ergodicity of Adaptive MCMC (2005)

Theoretical rates of convergence for

2005), Coupling and Ergodicity of Adaptive MCMC (2005)

Abstract. We consider basic ergodicity properties of adaptive MCMC algorithms under minimal assumptions, using coupling constructions. We prove convergence in distribution and a weak law of large...

Quantitative bounds on convergence of time-inhomogeneous Markov chains (2004)

Abstract. We consider basic ergodicity properties of adaptive MCMC algorithms under minimal assumptions, using coupling constructions. We prove convergence in distribution and a weak law of large...

Douc, R., Moulines, E., Rosenthal, Jeffrey S.

Convergence rates of Markov chains have been widely studied in recent years. In particular, quantitative bounds on convergence rates have been studied in various forms by Meyn and Tweedie [Ann. Appl....

Moment conditions for a sequence with negative drift to be uniformly bounded in L^r (2004)

Pemantle, Robin, Rosenthal, Jeffrey S.

Suppose a sequence of random variables {X_n} has negative drift when above a certain threshold and has increments bounded in L^p. When p>2 this implies that EX_n is bounded above by a constant...

General state space Markov chains and MCMC algorithms (2004)

General state space Markov chains and MCMC algorithms (2004)

This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the...

General state space Markov chains and MCMC algorithms. (2004)

This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the...

Roberts , Gareth O., Rosenthal, Jeffrey S.

This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the...

Combinatorial identifites associated with CFTP. (2004)

Roberts , Gareth O., Rosenthal, Jeffrey S.

We explore a method of obtaining combinatorial identities by analysing partially-completed runs of the Coupling from the Past (CFTP) algorithm. In particular, using CFTP for simple symmetric random...

When Can Martingales Avoid Ruin? (2004)

Maury Bramson, Jeremy Quastel, Jeffrey S. Rosenthal

Note: After completing this paper, it was discovered that similar results had been obtained previously [B. Davis, “Divergence properties of some martingale transforms”, Annals of Mathematical...

General state space Markov chains and MCMC algorithms (2004)

On the collapsibility of lifetime regression models (2003)

This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the...

Duchesne, Thierry, Rosenthal, Jeffrey S.

In this paper we derive conditions on the internal wear process under which the resulting time to failure model will be of the simple collapsible form when the usage accumulation history is...

Geometric Convergence Rates for Time-Sampled Markov Chains (2003)

Scaling Limits for the Transient Phase of Local Metropolis-Hastings Algorithms (2003)

We consider time-sampled Markov chain kernels, of the form n fngP . We prove bounds on the total variation distance to stationarity of such chains. We are motivated by the analysis of nearperiodic...

Ole F. Christensen, Gareth O. Roberts, Jeffrey S. Rosenthal

This paper considers high-dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well-understood and it is now well-known how to scale...

Downweighting tightly knit communities in world wide web rankings (2003)

Geometric Convergence Rates for Time-Sampled Markov Chains (2003)

We propose two new algorithms for using World Wide Web link structures to determine authority values of web pages from search queries. Both algorithms postulate an underlying latent cluster...

Asymptotic Variance and Convergence Rates of Nearly-Periodic MCMC Algorithms (2003)

Abstract. We consider time-sampled Markov chain kernels, of the form P µ = � n µ{n}P n. We prove bounds on the total variation distance to stationarity of such chains. We are motivated by the...

Scaling Limits for the Transient Phase of Local Metropolis-Hastings Algorithms (2003)

Abstract. We consider nearly-periodic Markov chains, which may have excellent functional-estimation properties but poor distributional convergence rate. We show how simple modifications of the chain...

Ole F. Christensen, Gareth O. Roberts, Jeffrey S. Rosenthal

Abstract. This paper considers high-dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well-understood and it is now well-known how...

Asymptotic Variance and Convergence Rates of Nearly-Periodic MCMC Algorithms (2003)

Capitalism's growth imperative (2003)

Abstract. We consider nearly-periodic Markov chains, which may have excellent functional-estimation properties but poor distributional convergence rate. We show how simple modifications of the chain...

Gordon, Myron J., Rosenthal, Jeffrey S.

A capitalist firm operating in a competitive market is subject to a growth imperative, because uncertainty about the profit rate under a no‐growth policy makes the firm's prospects highly...

Quantitative Convergence Rates of Markov Chains: A Simple Account (2002)

Rosenthal, Jeffrey S.; University Of Toronto; Jeff@math.toronto.edu

We state and prove a simple quantitative bound on the total variation distance after k iterations between two Markov chains with different initial distributions but identical transition...

The polar slice sampler. (2002)

Stochastic justification of some simple reliability models (2002)

This paper investigates the polar slice sampler, a particular type of the Markov chain Monte Carlo algorithm known as the slice sampler. This algorithm is shown to have convergence properties which...

Thierry Duchesne, Jeffrey S. Rosenthal

In this paper we give conditions on the internal wear process under which the resulting timeto-failure model will be of the simple collapsible form (Oakes, 1995, Duchesne and Lawless, 2000) when the...

Perfect forward simulation via simulated tempering (2002)

Stephen P. Brooks, Yanan Fan, Jeffrey S. Rosenthal

Summary. Several authors discuss how the simulated tempering scheme provides a very simple mech-anism for introducing regenerations within a Markov chain. In this paper we explain how regenerative...

Achieving Limiting Distributions for Markov Chains Using Back Buttons by (2002)

Andrey Feuerverger, Jeffrey S. Rosenthal

Abstract. As a simple model for browsing the World Wide Web, we consider Markov chains with the option of moving “back ” to the previous state. We develop an algorithm which uses back buttons to...

Stochastic justification of some simple reliability models (2002)

Thierry Duchesne, Jeffrey S. Rosenthal

In this paper we derive conditions on the internal wear process under which the resulting time-to-failure model will be of the simple collapsible form (Oakes, 1995, Duchesne and Lawless, 2000) when...

Quantitative bounds on convergence of time-inhomogeneous Markov Chains (2002)

R. Douc, E. Moulines, Jeffrey S. Rosenthal

Convergence rates of Markov chains have been widely studied in recent years. In particu-lar, quantitative bounds on convergence rates have been studied in various forms by Meyn and Tweedie (1994),...

On the applicability of regenerative simulation in Markov chain Monte Carlo (2002)

Hobert, James P., Jones, Galin L., Presnell, Brett, Rosenthal, Jeffrey S.

We consider the central limit theorem and the calculation of asymptotic standard errors for the ergodic averages constructed in Markov chain Monte Carlo. Chan & Geyer (1994) established a central...

Optimal scaling for various Metropolis-Hastings algorithms (2001)

Infinite hierarchies and prior distributions (2001)

We review and extend results related to optimal scaling of Metropolis–Hastings algorithms. We present various theoretical results for the high-dimensional limit. We also present simulation studies...

Extension of Fill's perfect rejection sampling algorithm to general chains (Extended abstract) (2001)

This paper introduces a way of constructing non-informative priors for Bayesian analysis, by taking a limit of priors arising from hierarchical constructions as the number of levels in the hierarchy...

Fill, James Allen, Machida, Motoya, Murdoch, Duncan J., Rosenthal, Jeffrey S.

We provide an extension of the perfect sampling algorithm of Fill (1998) to general chains, and describe how use of bounding processes can ease computational burden. Along the way, we unearth a...

Extension of Fill's perfect rejection sampling algorithm to general chains (2001)

Fill, James Allen, Machida, Motoya, Murdoch, Duncan J., Rosenthal, Jeffrey S.

By developing and applying a broad framework for rejection sampling using auxiliary randomness, we provide an extension of the perfect sampling algorithm of Fill (1998) to general chains on quite...

Finding Authorities and Hubs From Link Structures on the World Wide Web (2001)

Borodin, Allan, Roberts, Gareth O., Rosenthal, Jeffrey S., Tsaparas, Panayiotis

Recently, there have been a number of algorithms proposed for analyzing hypertext link structure so as to determine the best "authorities" for a given topic or query. While such analysis is usually...

Finding authorities and hubs from link structures on the world wide web (2001)

Allan Borodin, Gareth O. Roberts, Jeffrey S. Rosenthal, Panayiotis Tsaparas

Recently, there have been a number of algorithms proposed for analyzing hypertext link structure so as to determine the best "authorities " for a given topic or query. While such...

Finding authorities and hubs from link structures on the world wide web (2001)

Allan Borodin, Gareth O. Roberts, Jeffrey S. Rosenthal, Panayiotis Tsaparas

Recently, there have been a number of algorithms proposed for analyzing hypertext link structure so as to determine the best "authorities " for a given topic or query. While such...

Finding authorities and hubs from link structures on the world wide web (2001)

Allan Borodin, Gareth O. Roberts, Jeffrey S. Rosenthal, Panayiotis Tsaparas

Recently, there have been a number of algorithms proposed for analyzing hypertext link structure so as to determine the best “authorities ” for a given topic or query. While such analysis is...

Markov Chains and De-initialising Processes (2001)

Infinite hierarchies and prior distributions (2001)

Abstract. We define a notion of de-initialising Markov chains. We prove that to analyse convergence of Markov chains to stationarity, it suffices to analyse convergence of a de-initialising chain....

A Case Study in the Meta-Reasoning Procedure ND (2001)

Abstract. This paper introduces a way of constructing non-informative priors for Bayesian analysis, by taking a limit of priors arising from hierarchical constructions as the number of levels in the...

James J. Lu, Jeffrey S. Rosenthal, Andrew E. Shaffer

Finding Authorities and Hubs From Link Structures on the World Wide Web (2001)

Allan Borodin Gareth, Gareth O. Roberts, Jeffrey S. Rosenthal, Panayiotis Tsaparas

Recently, there have been a number of algorithms proposed for analyzing hypertext link structure so as to determine the best "authorities" for a given topic or query. While such analysis is...

Finding authorities and hubs from link structures on the world wide web (2001)

Allan Borodin, Gareth O. Roberts, Jeffrey S. Rosenthal, Panayiotis Tsaparas

Recently, there have been a number of algorithms proposed for analyzing hypertext link structure so as to determine the best “authorities ” for a given topic or query. While such analysis is...

On the Applicability of Regenerative Simulation in Markov (2001)

Chain Monte Carlo, James P. Hobert, Galin L. Jones, Brett Presnell, Jeffrey S. Rosenthal

Suppose we want to know the value of Eπg: = � X g(x) π(dx), where π is a probability distribution with support X and g is a real-valued, π-integrable function on X. Further suppose that this

Rates of convergence for Markov chains associated with Dirichlet processes. (2000)

Roberts, Gareth O., Petrone, S., Rosenthal, Jeffrey S.

We argue that Monte Carlo algorithms are ideally suited to parallel computing, and that “parallel Monte Carlo” should be more widely used. We consider a number of issues that arise, including...

Meetings with costly participation (2000)

J. Osborne, Jeffrey S. Rosenthal, Matthew A. Turner

We study a collective decision-making process in which people interested in an issue may participate, at a cost, in a meeting, and the resulting decision is a compromise among the participants '...

Small and Pseudo-Small Sets for Markov Chains (2000)

A Note on Geometric Ergodicity and Floating-Point Roundoff Error (2000)

In this paper we examine the relationship between small sets and their generalisation, pseudo-small sets. We consider conditions which imply the equivalence of the two notions, and give examples...

Laird Breyer, Gareth O. Roberts, Jeffrey S. Rosenthal

We consider the extent to which Markov chain convergence properties are affected by the presence of computer floating-point roundoff error. Both geometric ergodicity and polynomial ergodicity are...

A Note on Geometric Ergodicity and Floating-Point Roundoff Error (2000)

Laird Breyer, Gareth O. Roberts, Jeffrey S. Rosenthal

We consider the extent to which Markov chain convergence properties are affected by the presence of computer floating-point roundoff error. Both geometric ergodicity and polynomial ergodicity are...

Extension of Fill's perfect rejection sampling algorithm to general chains (1999)

James Allen Fill, Motoya Machida, Duncan J. Murdoch, Jeffrey S. Rosenthal

By developing and applying a broad framework for rejection sampling using auxiliary randomness, we provide an extension of the perfect sampling algorithm of Fill (1998) to general chains on quite...

Convergence of slice sampler Markov chains (1999)

Finding Generators for Markov Chains via Empirical Transition Matrices (1999)

In this paper, we analyse theoretical properties of the slice sampler. We find that the algorithm has extremely robust geometric ergodicity properties. For the case of just one auxiliary variable, we...

Robert B. Israel, Jeffrey S. Rosenthal, Jason Z. Wei

. In this paper we identify conditions under which a true generator does or does not exist for an empirically observed Markov transition matrix. We show how to search for valid generators and choose...

Extension of Fill's perfect rejection sampling algorithm to general chains (Extended Abstract) (1999)

James Allen Fill, Motoya Machida, Duncan J. Murdoch, Jeffrey S. Rosenthal, Je#rey S. Rosenthal

. We provide an extension of the perfect sampling algorithm of Fill (1998) to general chains, and describe how use of bounding processes can ease computational burden. Along the way, we unearth a...

Extension of Fill's perfect rejection sampling algorithm to general chains (1999)

James Allen Fill, Motoya Machida, Duncan J. Murdoch, Jeffrey S. Rosenthal, Je#rey S. Rosenthal

By developing and applying a broad framework for rejection sampling using auxiliary randomness, we provide an extension of the perfect sampling algorithm of Fill (1998) to general chains on quite...

Extension of Fill's perfect rejection sampling algorithm to general chains (1999)

James Allen Fill, Motoya Machida, Duncan J. Murdoch, Jeffrey S. Rosenthal

By developing and applying a broad framework for rejection sampling using auxiliary randomness, we provide an extension of the perfect sampling algorithm of Fill (1998) to general chains on quite...

Extension of Fill's perfect rejection sampling algorithm to general chains (Extended Abstract) (1999)

James Allen Fill, Motoya Machida, Duncan J. Murdoch, Jeffrey S. Rosenthal

. We provide an extension of the perfect sampling algorithm of Fill (1998) to general chains, and describe how use of bounding processes can ease computational burden. Along the way, we unearth a...

The Polar Slice Sampler (1999)

Recent Progress on Computable Bounds and the Simple Slice Sampler (1999)

This paper investigates a particular type of slice sampler algorithm, the polar slice sampler. This algorithm is shown to have convergence properties which are essentially independent of the...

Gareth Roberts, Jeffrey S. Rosenthal, Jeffrey S

This paper discusses general quantitative bounds on the convergence rates of Markov chains. It then discusses application of these results to simple slice sampler algorithms. It is explained how, in...

Bayesian Models with Infinite Hierarchies (1999)

Recent Progress on Computable Bounds and the Simple Slice Sampler (1999)

This paper introduces a way of constructing non-informative priors for Bayesian analysis, by taking a limit of priors arising from hierarchical constructions as the number of levels in the hierarchy...

By Gareth Roberts, Gareth O. Roberts, Jeffrey S. Rosenthal

This paper discusses general quantitative bounds on the convergence rates of Markov chains. It then discusses application of these results to simple slice sampler algorithms. It is explained how, in...

Meetings With Costly Participation (1999)

Martin J. Osborne, Jeffrey S. Rosenthal, Matthew A. Turner

We study a collective decision-making process in which people who are interested in an issue are invited to attend a meeting, and the policy chosen is a compromise among the preferences of those who...

A review of asymptotic convergence for general state space Markov chains (1999)

Jeffrey S. Rosenthal, Jeffrey S

. We review notions of small sets, OE-irreducibility, etc., and present a simple proof of asymptotic convergence of general state space Markov chains to their stationary distributions. 1....

Parallel computing and Monte Carlo algorithms (1999)

Parallel computing and Monte Carlo algorithms (1999)

We argue that Monte Carlo algorithms are ideally suited to parallel computing, and that "parallel Monte Carlo" should be more widely used. We consider a number of issues that arise,...

Jeffrey S. Rosenthal, Parallel Computing, Monte Carlo Algorithms

We argue that Monte Carlo algorithms are ideally suited to parallel computing, and that "parallel Monte Carlo" should be more widely used. We consider a number of issues that arise,...

Extension of Fill's perfect rejection sampling algorithm to general chains (1999)

James Allen Fill, Motoya Machida, Duncan J. Murdoch, Jeffrey S. Rosenthal

By developing and applying a broad framework for rejection sampling using auxiliary randomness, we provide an extension of the perfect sampling algorithm of Fill (1998) to general chains on quite...

Parallel computing and Monte Carlo algorithms (1999)

The polar slice sampler (1999)

Abstract. We argue that Monte Carlo algorithms are ideally suited to parallel computing, and that “parallel Monte Carlo ” should be more widely used. We consider a number of issues that arise,...

Convergence of slice sampler Markov chains (1999)

This paper investigates the polar slice sampler, a particular type of the Markov chain Monte Carlo algorithm known as the slice sampler. This algorithm is shown to have convergence properties which...

Extension of Fill's perfect rejection sampling algorithm to general chains (1999)

In this paper, we analyse theoretical properties of the slice sampler. We find that the algorithm has extremely robust geometric ergodicity properties. For the case of just one auxiliary variable, we...

James Allen Fill, Motoya Machida, Duncan J. Murdoch, Jeffrey S. Rosenthal

By developing and applying a broad framework for rejection sampling using auxiliary randomness, we provide an extension of the perfect sampling algorithm of Fill (1998) to general chains on quite...

Finding Generators for Markov Chains (1999)

Robert B. Israel, Jeffrey S. Rosenthal, Jason Z. Wei, Jeremy Quastel, Peter Rosenthal, ...

via Empirical Transition Matrices, with Applications to Credit Ratings In this paper we identify conditions under which a true generator does or does not exist for an empirically observed Markov...

On convergence rates of Gibbs samplers for uniform distributions (1998)

Two convergence properties of hybrid samplers (1998)

We consider a Gibbs sampler applied to the uniform distribution on a bounded region $R \subseteq \mathbf{R}^d$. We show that the convergence properties of the Gibbs sampler depend greatly on the...

Convergence properties of perturbed Markov chains (1998)

Theoretical work on Markov chain Monte Carlo (MCMC) algorithms has so far mainly concentrated on the properties of simple algorithms, such as the Gibbs sampler, or the full-dimensional...

Roberts, Gareth O., Rosenthal, Jeffrey S., Schwartz, Peter O.

In this paper, we consider the question of which convergence properties of Markov chains are preserved under small perturbations. Properties considered include geometric ergodicity and rates of...

Efficient Use of Exact Samples (1998)

By Duncan Murdoch, Duncan J. Murdoch, Jeffrey S. Rosenthal

Propp and Wilson (1996,1998) described a protocol called coupling from the past (CFTP) for exact sampling from the steady-state distribution of a Markov chain Monte Carlo (MCMC) process. In it a past...

Moment Conditions for a Sequence With Negative Drift to Be Uniformly Bounded in (1998)

Robin Pemantle, Jeffrey S. Rosenthal

: Suppose a sequence of random variables fX n g has negative drift when above a certain threshold and has increments bounded in L p . When p ? 2 this implies that EX n is bounded above by a constant...

Efficient Use of Exact Samples (1998)

Duncan J. Murdoch, Jeffrey S. Rosenthal

Propp and Wilson (1996,1998) described a protocol called coupling from the past (CFTP) for exact sampling from the steady-state distribution of a Markov chain Monte Carlo (MCMC) process. In it a past...

Moment Conditions for a Sequence With Negative Drift to Be Uniformly Bounded in (1998)

Robin Pemantle, Jeffrey S. Rosenthal

: Suppose a sequence of random variables fX n g has negative drift when above a certain threshold and has increments bounded in L p . When p ? 2 this implies that EX n is bounded above by a constant...

A note on convergence rates of Gibbs sampling for nonparametric mixtures (1998)

Sonia Petrone, Gareth O. Roberts, Jeffrey S. Rosenthal

this paper we consider two Gibbs sampling algorithms. These have been proposed by Escobar (1994) and MacEachern (1994) for mixtures of normals and for ANOVA models. We first outline (section 2) the...

On convergence rates of Gibbs samplers for uniform distributions (1998)

Gareth O. Roberts, Jeffrey S. Rosenthal, Region R R

. We consider a Gibbs sampler applied to the uniform distribution on a bounded region R ` R d . We show that the convergence properties of the Gibbs sampler depend greatly on the smoothness of the...

A note on convergence rates of Gibbs sampling for nonparametric mixtures (1998)

Sonia Petrone, Gareth O. Roberts, Jeffrey S. Rosenthal

We consider a mixture model where the mixing distribution is random and is given a Dirichlet process prior. We describe the general structure of two Gibbs sampling algorithms that are useful for...

Sufficient Markov Chains (1998)

Convergence of slice sampler Markov chains (1998)

. We develop a theory of sufficiency for Markov chains. In particular, we prove that to analyse convergence in total variation distance, it suffices to obtain bounds on a sufficient chain. 1....

A note on convergence rates of Gibbs sampling for nonparametric mixtures (1998)

this paper, we analyse theoretical properties of the slice sampler. We find that the algorithm has extremely robust geometric ergodicity properties. For the case of just one auxiliary variable, we...

Sonia Petrone, Gareth O. Roberts, Jeffrey S. Rosenthal

We present a mathematical analysis of a class of Gibbs sampler algorithms for nonparametric mixtures, which use Dirichlet process priors and have updating steps which are partially discrete and...

A note on convergence rates of Gibbs sampling for nonparametric mixtures, Unpublished manuscript (1998)

Sonia Petrone, Gareth O. Roberts, Jeffrey S. Rosenthal

We present a mathematical analysis of a class of Gibbs sampler algorithms for nonparametric mixtures, which use Dirichlet process priors and have updating steps which are partially discrete and...

to be uniformly bounded in L (1998)

Robin Pemantle, Jeffrey S. Rosenthal

conditions for a sequence with negative drift

Efficient use of exact samples (1998)

Duncan J. Murdoch, Jeffrey S. Rosenthal

Propp and Wilson (1996,1998) described a protocol called coupling from the past (CFTP) for exact sampling from the steady-state distribution of a Markov chain Monte Carlo (MCMC) process. In it a past...

to (1998)

Duncan J. Murdoch, Jeffrey S. Rosenthal

An extension of Fill’s exact sampling algorithm

Optimal Scaling of Discrete Approximations to Langevin Diffusions (1998)

On convergence rates of Gibbs samplers for uniform distributions (1998)

Acknowledgements. We are grateful to Radford Neal for bringing references from the

Convergence properties of perturbed Markov chains (1998)

Abstract. We consider a Gibbs sampler applied to the uniform distribution on a bounded region R ⊆ R d. We show that the convergence properties of the Gibbs sampler depend greatly on the smoothness...

Gareth O. Roberts, Jeffrey S. Rosenthal, Peter O. Schwartz

Lemma 3

Geometric Ergodicity and Hybrid Markov Chains (1997)

Roberts, Gareth O.; University Of Cambridge; G.O.Roberts@statslab.cam.ac.uk, Rosenthal, Jeffrey S.; University Of Toronto; Jeff@math.toronto.edu

Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a...

Gambling Systems and Multiplication-Invariant Measures (1997)

Jeffrey S. Rosenthal, Peter O. Schwartz

Introduction. This short paper describes a surprising connection between two previously unrelated topics: the probability of winning certain gambling games, and the invariance of certain measures...

Optimal scaling of discrete approximations to Langevin diffusions (1997)

Possible biases induced by MCMC convergence diagnostics (1997)

. We consider the optimal scaling problem for proposal distributions in Hastings-Metropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that...

Mary Kathryn Cowles, Gareth O. Roberts, Jeffrey S. Rosenthal

This paper is organised as follows. In Section 2, we present an over-simplified version of a convergence diagnostic, and study analytically its performance on certain simple Markov chains. We...

Two Convergence Properties of Hybrid Samplers (1997)

Convergence properties of perturbed Markov chains (1997)

This article attempts to build on the results of Roberts and Rosenthal (1997), which consider geometric ergodicity properties of hybrid chains in terms of their constituent component algorithms. In...

Gareth O. Roberts, Jeffrey S. Rosenthal, Peter O. Schwartz, Markov Monte, Carlo Gibbs

this paper we begin an analysis of these questions. We are motivated largely by problems associated with finite precision computation (i.e. "roundoff error"). We shall often concentrate on...

Geometric Ergodicity and Hybrid Markov Chains (1997)

Geometric ergodicity and hybrid Markov chains (1997)

Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a...

Faithful couplings of Markov chains: now equals forever (1997)

Abstract. Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results...

Possible biases induced by MCMC convergence diagnostics (1997)

many insightful discussions about these and related topics. 1. Introduction. This short note considers the usual coupling approach to bounding convergence of Markov chains. It addresses the question...

Mary Kathryn Cowles, Gareth O. Roberts, Jeffrey S. Rosenthal

Convergence diagnostics are widely used to determine how many initial “burn-in ” iterations should be discarded from the output of a Markov chain Monte Carlo (MCMC) sampler in the hope that the...

Gambling Systems and Multiplication-Invariant Measures 1. Introduction. by (1997)

Jeffrey S. Rosenthal, Peter O. Schwartz

This short paper describes a surprising connection between two previously unrelated

Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes (1996)

Roberts, Gareth O.; University Of Cambridge; G.O.Roberts@statslab.cam.ac.uk, Rosenthal, Jeffrey S.; University Of Toronto; Jeff@utstat.toronto.edu

We develop quantitative bounds on rates of convergence for continuous-time Markov processes on general state spaces. Our methods involve coupling and shift-coupling, and make use of minorization and...

A cultural chronology for Solano County, California /--by Jeffrey S. Rosenthal. (1996)

Rosenthal, Jeffrey S.

Thesis (M.A.)--Sonoma State University, 1996.

Quantitative bounds for convergence rates of continuous time Markov processes (1996)

By Gareth Roberts, Gareth O. Roberts, Jeffrey S. Rosenthal

. We develop quantitative bounds on rates of convergence for continuoustime Markov processes on general state spaces. Our methods involve coupling and shiftcoupling, and make use of minorization and...

Quantitative bounds for convergence rates of continuous time Markov processes (1996)

A simulation approach to convergence rates for Markov chain Monte Carlo algorithms (1996)

. We develop quantitative bounds on rates of convergence for continuoustime Markov processes on general state spaces. Our methods involve coupling and shiftcoupling, and make use of minorization and...

Mary Kathryn Cowles, Jeffrey S. Rosenthal

Markov chain Monte Carlo (MCMC) methods, including the Gibbs sampler and the Metropolis-Hastings algorithm, are very commonly used in Bayesian statistics for sampling from complicated,...

Markov chain convergence: From finite to infinite (1996)

Markov chain convergence: From finite to infinite, Stochastic processes and their Applications 62 (1996)

Faithful couplings of Markov chains: now equals forever (1995)

Summary. Bounds on convergence rates for Markov chains are a very widely-studied topic, motivated largely by applications to Markov chain Monte Carlo algorithms. For Markov chains on finite state...

Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo (1995)

This paper is related to the problem of bounding the total variation distance k¯P

Convergence rates of Markov chains (1995)

Convergence properties of perturbed Markov chains (1995)

this paper, we attempt to describe various mathematical techniques which have been used to bound such rates of convergence. In particular, we describe eigenvalue analysis, random walks on groups,...

Gareth O. Roberts, Jeffrey S. Rosenthal, Peter O. Schwartz

this paper we begin an analysis of these questions. We are motivated largely by problems associated with finite precision computation (i.e. "roundoff error"). We shall often concentrate on...

Analysis of the Gibbs sampler for a model related to James-Stein estimators (1995)

Rates Of Convergence For Everywhere-Positive Markov Chains (1995)

this paper we investigate the convergence properties of the Gibbs sampler as applied to a particular hierarchical Bayes model. The model is related to James-Stein estimators (James and Stein, 1961;...

J. R. Baxter, Jeffrey S. Rosenthal

Introduction It is often useful to know that the distribution of a Markov process converges to a stationary distribution, and if possible to know how rapidly convergence takes place. Such rates of...

Rates of convergence for Gibbs sampling for variance components models (1995)

Rates of convergence for everywhere-positive Markov chains (1995)

Summary. This paper analyzes the Gibbs sampler applied to a standard variance compo-nent model, and considers the question of how many iterations are required for convergence. It is proved that for K...

J. R. Baxter, Jeffrey S. Rosenthal

It is often useful to know that the distribution of a Markov process converges to a stationary distribution, and if possible to know how rapidly convergence takes place. Such rates of convergence are...

Shift-Coupling and Convergence Rates of Ergodic Averages (1994)

Gareth O. Roberts, Jeffrey S. Rosenthal, Thank David Aldous, John Baxter

this paper, we avoid such difficulties by examining convergence of ergodic averages

Markov Chains, Eigenvalues, and Coupling (1994)

Active-Learning Strategies in Advanced Mathematics Classes (1994)

This paper is based on lectures given in the School of Mathematics at the University of Minnesota, and in the Department of Statistics at the University of Toronto. I am grateful to the many...

Theoretical rates of convergence for Markov chain Monte Carlo (1994)

. Advanced mathematics and other theoretical sciences are often taught purely using the lecture format, which promotes passivity and isolation in students. This paper advocates the use of certain...

Random Rotations: Characters and Random Walks on SO(N) (1994)

. We present a general method for proving rigorous, a priori bounds on the number of iterations required to achieve convergence of Markov chain Monte Carlo. We describe bounds for specific models of...

Convergence of Independent Particle Systems (1994)

We analyze a random walk on the orthogonal group SO(N) given by repeatedly rotating by a fixed angle through randomly chosen planes of R^N. We Derive...

John R. Hoffman, Jeffrey S. Rosenthal

.46>1. Introduction. A standard question in Markov process theory is the existence of, and convergence to, a stationary probability distribution. The question of rate of convergence concerns how...

Random Walks on Discrete and Continuous Circles (1994)

Minorization Conditions and Convergence Rates for Markov Chain Monte Carlo (1994)

We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise...

On generalizing the cut-off phenomenon for random walks on groups (1994)

this paper, we provide a method (Theorem 5) for proving rigorous, a priori bounds on the number of iterations required until satisfactory convergence has taken place. We feel that such bounds provide...

Random walks on discrete and continuous circles (1994)

There has been a lot of recent work on the convergence of random walks on finite or compact groups to their stationary, uniform distribution. Particular emphasis has been placed on the rate of...

Rates of Convergence for Data Augmentation on Finite Sample Spaces (1993)

Summary. We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the “generation gap ” process of Diaconis....

On Generalizing the Cut-off Phenomenon for Random Walks on Groups (1993)

this paper, we examine this rate of convergence more carefully. We restrict our attention to the case where

Convergence of Independent Particle Systems by John R. Hoffman* and (1993)

This paper presents a first step towards a more general result about the cut-off phenomenon. A large class of measures on a fairly large collection of groups (both finite and compact) are considered....

Rates of convergence for data augmentation on finite sample spaces (1993)

Summary. We consider a system of particles moving independently on a countable state space, according to a general (non-space-homogeneous) Markov process. Under mild conditions, the number of...

Convergence of pseudo-finite Markov chains. Unpublished manuscript (1992)

Tanner and Wong [TW] have defined an iterative process for obtaining closer and closer approximations to the (Bayes) posterior distribution of certain parameters given certain data. Their approach,...

On Duality of Probabilities for Card-dealing (1992)

Note: After completing this paper, it was discovered that similar ideas

Convergence of pseudo-finite Markov chains. Unpublished manuscript (1992)

Milton Sobel and Krzysztof Frankowski [1] recently described a notion of “duality” for card-dealing probabilities. They prove the equality of certain probabilities for different card-dealing...

Rates of Convergence for Gibbs Sampling for Variance Component Models (1991)

Note: After completing this paper, it was discovered that similar ideas

The Bieberbach Conjecture (1989)

This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location...

The Bieberbach Conjecture A minor thesis submitted by (1989)

This paper is organized as follows. In section 2, we present Bieberbach's proof of his conjecture for n=2, using the area theorem. (The equality part of the n=2 case is required in section 6.)...

Convergence of Slice Sampler Markov Chains

Let S denote the set of all univalent (i.e. one-to-one) analytic functions f defined in the disk |z | < 1, with f(0) = 0 and f ′ (0) = 1. Such functions may be written in the form f(z) = z + a2z...