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Obituary: Richard Lewis Tweedie

Published online by Cambridge University Press:  14 July 2016

William T. M. Dunsmuir ,
Sean P. Meyn  and
Gareth Roberts
William T. M. Dunsmuir
Affiliation:
University of Minnesota, Minneapolis
Sean P. Meyn
Affiliation:
University of Illinois at Urbana-Champaign
Gareth Roberts
Affiliation:
Lancaster University
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Obituary
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 441 - 454
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Copyright © Applied Probability Trust 2002 

References

References

Publication of R.L. Tweedie

Item authored or co-authored by R.L. Tweedie, listed chronologically.

[1] Tweedie, R. L. (1971). Stationary measures for random walk on a half line. Z. Wahrscheinlichkeitsth. 20, 28–46.Google Scholar
[2] Tweedie, R. L. (1971). Truncation procedures for non-negative matrices. J. Appl. Prob. 8, 311–320.Google Scholar
[3] Tweedie, R. L. (1973). The calculation of limit probabilities for denumerable Markov processes from infinitesimal properties. J. Appl. Prob. 10, 84–99.CrossRefGoogle Scholar
[4] Tweedie, R. L. (1974). A representation for invariant measures for transient Markov chains. Z. Wahrschein-lichkeitsth. 28, 99–112.CrossRefGoogle Scholar
[5] Tweedie, R. L. (1974). Some ergodic properties of the Feller minimal process. Quart. J. Math. Oxford 25, 485–495.Google Scholar
[6] Tweedie, R. L. (1974). R-theory for Markov chains on a general state-space. I. Solidarity properties and R-recurrent chains. Ann. Prob. 2, 840–864.Google Scholar
[7] Tweedie, R. L. (1974). R-theory for Markov chains on a general state-space. II. r-subinvariant measures for r-transient chains. Ann. Prob. 2, 865–878.Google Scholar
[8] Tweedie, R. L. (1974). Quasi-stationary distributions for Markov chains on a general state-space. J. Appl. Prob. 11, 726–741.Google Scholar
[9] Tweedie, R. L. (1975). Truncation approximation of the limit probabilities for denumerable semi-Markov processes. J. Appl. Prob. 12, 161–163.CrossRefGoogle Scholar
[10] Pollard, D. B. and Tweedie, R. L. (1975). R-theory for Markov chains on a topological state-space. I. J. London Math. Soc. 10, 389–400.Google Scholar
[11] Tweedie, R. L. (1975). Sufficient conditions for regularity, recurrence, and ergodicity of Markov processes. Math. Proc. Camb. Phil. Soc. 78, 125–136.CrossRefGoogle Scholar
[12] Tweedie, R. L. (1975). Sufficient conditions for ergodicity and recurrence of Markov chains on a general state-space. Stoch. Process. Appl. 3, 385–403.Google Scholar
[13] Tweedie, R. L. (1975). The robustness of positive recurrence and recurrence of Markov chains under perturbations of the transition probabilities. J. Appl. Prob. 12, 744–752.Google Scholar
[14] Tweedie, R. L. (1975). Relations between ergodicity and mean drift for Markov chains. Austral. J. Statist. 17, 96–102.CrossRefGoogle Scholar
[15] Saunders, I. W. and Tweedie, R. L. (1976). The settlement of Polynesia by CYBER 76. Math. Scientist 1, 15–26.Google Scholar
[16] Pollard, D. B. and Tweedie, R. L. (1976). R-theory for Markov chains on a topological state-space. II. Z. Wahrscheinlichkeitsth. 34, 269–278.CrossRefGoogle Scholar
[17] Tweedie, R. L. (1976). Criteria for classifying general Markov chains. Adv. Appl. Prob. 8, 737–771.Google Scholar
[18] McArthur, N. A., Saunders, I. W. and Tweedie, R. L. (1976). Small population isolates: a simulation study. J. Polynesian Soc. 85, 307–326.Google Scholar
[19] Nummelin, E. and Tweedie, R. L. (1976). Geometric ergodicity for a class of Markov chains. Ann. Sci. Univ. Clermont 61, 145–153.Google Scholar
[20] Tweedie, R. L. (1977). Modes of convergence of Markov chain transition probabilities. J. Math. Anal. Appl. 60, 280–291.Google Scholar
[21] Tweedie, R. L. (1977). Hitting times for Markov chains with application to state dependent queues. Bull. Austral. Math. Soc. 17, 97–107.Google Scholar
[22] Tweedie, R. L. (1977). Criteria for classifying general Markov chains (abstract). Adv. Appl. Prob. 9, 208–210.Google Scholar
[23] Tweedie, R. L. and Westcott, M. (1978). First-passage times in skip-free processes. Stoch. Process. Appl. 7, 191–204.Google Scholar
[24] Nummelin, E. and Tweedie, R. L. (1978). Geometric ergodicity and R-positivity for general Markov chains. Ann. Prob. 6, 404–420.Google Scholar
[25] Isaacson, D. and Tweedie, R. L. (1978). Criteria for strong ergodicity of Markov chains. J. Appl. Prob. 15, 87–95.Google Scholar
[26] Arjas, E., Nummelin, E. and Tweedie, R. L. (1978). Uniform limit theorems for non-singular renewal and Markov renewal processes. J. Appl. Prob. 15, 112–125.Google Scholar
[27] Laslett, G. M., Pollard, D. B. and Tweedie, R. L. (1978). Techniques for establishing ergodic and recurrent properties of continuous-valued Markov chains. Naval. Res. Logistics Quart. 25, 455–472.Google Scholar
[28] Tweedie, R. L. (ed.) (1978). Proc. Conf. Spatial Patterns Process., Canberra, 12-14 May 1977 (Adv. Appl. Prob. 10 Spec. Suppl.). Applied Probability Trust, Sheffield.Google Scholar
[29] Tuominen, P. and Tweedie, R. L. (1979). Markov chains with continuous components. Proc. London Math. Soc. 38, 89–114.CrossRefGoogle Scholar
[30] Tweedie, R. L. (1979). Topological aspects of Doeblin decompositions for Markov chains. Z. Wahrschein-lichkeitsth. 46, 299–305.Google Scholar
[31] Tuominen, P. and Tweedie, R. L. (1979). The recurrence structure of general Markov processes. Proc. London Math. Soc. 39, 554–576.Google Scholar
[32] Tweedie, R. L. (1979). Computerised anthropology—finding and settling Polynesian islands. Math. Spectrum 11, 75–81.Google Scholar
[33] Schuh, H.-J. and Tweedie, R. L. (1979). Parameter estimation using transform estimation in time-evolving models. Math. Biosci. 45, 37–67.Google Scholar
[34] Tuominen, P. and Tweedie, R. L. (1979). Exponential decay and ergodicity of general Markov processes and their discrete skeletons. Adv. Appl. Prob. 11, 784–803.Google Scholar
[35] Tuominen, P. and Tweedie, R. L. (1979). Exponential ergodicity in Markovian queueing and dam models. J. Appl. Prob. 16, 867–880.Google Scholar
[36] Arjas, E., Nummelin, E. and Tweedie, R. L. (1980). Semi-Markov processes on a general state-space: a-theory and quasi-stationary properties. J. Austral. Math. Soc. A 30, 187–200.Google Scholar
[37] Athreya, K. B., Tweedie, R. L. and Vere-Jones, D. (1980). Asymptotic behaviour of point processes with Markov-dependent intervals. Math. Nachr. 99, 301–313.Google Scholar
[38] Tweedie, R. L. (1980). Perturbations of countable Markov chains. Ann. Inst. Statist. Math. A. 32, 283–290.Google Scholar
[39] Young, R. R., Anderson, N., Overend, D., Tweedie, R. L., Malafant, K. W. J. and Preston, G. A. N. (1980). The effect of temperature on times to hatching of eggs of the nematode Ostertagia Circumcinta . Parasitology 81, 477–491.Google Scholar
[40] Young, R. R., Nicholson, R. M., Tweedie, R. L. and Schuh, H.-J. (1980). Quantitative modeling and prediction of development times of the free living stages of Ostertagia ostertagi under controlled and field conditions. Parasitology 81, 493–505.Google Scholar
[41] Low, W. A., Tweedie, R. L., Edwards, C. B. H., Hodder, R. M., Malafant, K. W. J. and Cunningham, R. B. (1981). The influence of environment on daily maintenance behaviour of free-ranging shorthorn cows in Central Australia. I: general introduction and descriptive analysis of day-long activities. Appl. Animal Ethol. 7, 11–26.Google Scholar
[42] Low, W. A., Tweedie, R. L., Edwards, C. B. H., Hodder, R. M., Malafant, K. W. J. and Cunningham, R. B. (1981). The influence of environment on daily maintenance behaviour of free-ranging shorthorn cows in Central Australia. II: multivariate analysis of duration and incidence of activities. Appl. Animal Ethol. 7, 27–38.Google Scholar
[43] Low, W. A., Tweedie, R. L., Edwards, C. B. H., Hodder, R. M., Malafant, K. W. J. and Cunningham, R. B. (1981). The influence of environment on daily maintenance behaviour of free-ranging shorthorn cows in Central Australia. III: detailed analysis of sequential behavior patterns and integrated discussion. Appl. Animal Ethol. 7, 39–56.CrossRefGoogle Scholar
[44] Tweedie, R. L. (1981). Criteria for ergodicity, exponential ergodicity and strong ergodicity of Markov processes. J. Appl. Prob. 18, 122–130.Google Scholar
[45] Tweedie, R. L. (1982). Operator-geometric stationary distributions for Markov chains, with application to queueing models. Adv. Appl. Prob. 14, 368–391.CrossRefGoogle Scholar
[46] Brockwell, P. J., Resnick, S. I. and Tweedie, R. L. (1982). Storage processes with general release rule and additive input. Adv. Appl. Prob. 14, 392–433.Google Scholar
[47] Malafant, K. W. J., and Tweedie, R. L. (1982). Computer production of kinetograms. Appl. Animal Ethol. 8, 179–187.Google Scholar
[48] Trajstman, A. C., and Tweedie, R. L. (1982). Techniques for estimating parameters in Bartoszynski's virus model. Math. Biosci. 58, 277–307.CrossRefGoogle Scholar
[49] Tweedie, R. L. (1982). Criteria for rates of convergence of Markov chains, with application to queueing and storage theory. In Papers in Probability, Statistics and Analysis (London Math. Soc. Lecture Notes 79), eds Kingman, J. F. C. and Reuter, G. E. H., Cambridge University Press, pp. 260–276.Google Scholar
[50] Feigin, P. D., Belyea, C. and Tweedie, R. L. (1983). Weighted area techniques for explicit parameter estimation in hierarchical models. Austral. J. Statist. 25, 1–16.Google Scholar
[51] Theodorescu, R. and Tweedie, R. L. (1983). Solidarity properties and a Doeblin decomposition for a class of non-Markovian stochastic processes. Metrika 30, 37–47.CrossRefGoogle Scholar
[52] Sennott, L. I., Humblet, P. and Tweedie, R. L. (1983). Mean drifts and the non-ergodicity of Markov chains. Operat. Res. 31, 783–789.Google Scholar
[53] Tweedie, R. L. (1983). The existence of moments for stationary Markov chains. J. Appl. Prob. 20, 191–196.Google Scholar
[54] Leedow, M. I. and Tweedie, R. L. (1983). Weighted area techniques for the estimation of the parameters of a growth curve. Austral. J. Statist. 25, 310–320.Google Scholar
[55] Henstridge, J. D. and Tweedie, R. L. (1984). A model for the growth pattern of mutton birds. Biometrics 40, 917–925.Google Scholar
[56] Tweedie, R. L. and Hall, N. (1984). A rotational sampling framework for NSW health statistics (abstract). Community Health Studies 8, 144.Google Scholar
[57] Arjas, E., Haara, P. and Tweedie, R. L. (1984). A system model with interacting components: renewal-type results (abstract). Adv. Appl. Prob. 16, 7–8.Google Scholar
[58] Feigin, P. D. and Tweedie, R. L. (1985). Random coefficient autoregressive processes: a Markov chain analysis of stationarity and finiteness of moments. J. Time Ser. Anal. 6, 1–14.Google Scholar
[59] Seneta, E. and Tweedie, R. L. (1985). Moments for stationary and quasi-stationary distributions of Markov chains. J. Appl. Prob. 22, 148–155.Google Scholar
[60] Arjas, E., Haara, P. and Tweedie, R. L. (1985). Reliability in multi-component systems: structure and convergence to stationary behaviour. Optimisation 16, 297–311.Google Scholar
[61] Feigin, P. D. and Tweedie, R. L. (1985). Markov-chain ergodicity and time-series models (abstract). Stoch. Process. Appl. 19, 17.Google Scholar
[62] Tweedie, R. L. (1986). The existence of moments for Markov and semi-Markov processes with application to birth-death and stress release models. In Proc. 1st Pacific Statist. Cong., eds Francis, I., Manly, B. J. F., Lam, F. C., North-Holland, Amsterdam, pp. 147–149.Google Scholar
[63] Hall, J., Hall, N. and Tweedie, R. L. (1986). A longitudinal study of health changes following the introduction of Medicare. In Economics and Health 1985, Proc. 7th Austral. Conf. Health Econom. (Austral. Studies Health Service Administration 56), eds Butler, J.. and Doessel, D. P., University of New South Wales, pp. 81–102.Google Scholar
[64] Tweedie, R. L. (1986). Recurrence criterion. In Encyclopaedia of Statistical Sciences, Vol. 7, eds Kotz, S., Johnson, N. L. and Read, C. B., John Wiley, New York, pp. 656–658.Google Scholar
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[66] Tweedie, R. L. (1986). In and out of applied probability in Australia. In The Craft of Probabilistic Modelling (Appl. Prob. Ser.), ed. Gani, J., Springer, New York, pp. 291–308.CrossRefGoogle Scholar
[67] Tweedie, R. L. (1987). Statistical consulting in Australia. Liaison 2, 37–40.Google Scholar
[68] Tweedie, R. L. (1988). Invariant measures for Markov chains with no irreducibility assumptions. In A Celebration of Applied Probability (J. Appl. Prob. Spec. Vol. 25A), ed. Gani, J., Applied Probability Trust, Sheffield, pp. 275–285.Google Scholar
[69] Tweedie, R. L. (1988). Return state. In Encyclopaedia of Statistical Sciences, Vol. 8, eds Kotz, S., Johnson, N. L. and Read, C. B., John Wiley, New York, pp. 124–125.Google Scholar
[70] Tweedie, R. L. (1989). Shaping tomorrow's university. In Proc. SOST’89, eds Clark, R. and Cameron, J., ACS, Sydney, pp. 427–439.Google Scholar
[71] Feigin, P. D. and Tweedie, R. L. (1989). Linear functionals and Markov chains associated with the Dirichlet process. Math. Proc. Camb. Phil. Soc. 105, 579–585.Google Scholar
[72] Tweedie, R. L. (1989). Total quality management and information technology. Internat. J. Value-Based Manag. 2, 111–125.Google Scholar
[73] Dunsmuir, W. T. M., Tweedie, R. L., Flack, L. and Mengersen, K. E. (1989). Modelling of transitions between employment states for young Australians. Austral. J. Statist. 31A, 165–196.Google Scholar
[74] Tweedie, R. L. (1990). Criteria for rates of convergence to stationarity in Markovian queueing models with application to the GSPP/GSPP/1 queue. In Proc. 4th Austral. Teletraffic Res. Seminar, ed. Harris, R. J., Bond University.Google Scholar
[75] Tweedie, R. L. (1991). Pitman Medal awarded to E. J. Hannan. Austral. J. Statist. 33, 1–4 Google Scholar
[76] Brockwell, P. J., Liu, J. and Tweedie, R. L. (1992). On the existence of a stationary threshold autoregressive-moving average model. J. Time Ser. Anal. 13, 95–107.Google Scholar
[77] Tweedie, R. L. (1992). Comments on the Committee for New Researchers Guidelines. Statist. Sci. 7, 263–264.Google Scholar
[78] Meyn, S. P. and Tweedie, R. L. (1992). Stability of Markovian processes I: criteria for discrete-time chains. Adv. Appl. Prob. 24, 542–574.Google Scholar
[79] Tweedie, R. L. and Mengersen, K. L. (1992). Lung cancer and passive smoking: reconciling the biochemical and epidemiological approaches. British J. Cancer 66, 700–705.Google Scholar
[80] Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability. Springer, London.Google Scholar
[81] Meyn, S. P. and Tweedie, R. L. (1993). The Doeblin decomposition. Contemp. Math. 149, 211–225.Google Scholar
[82] Meyn, S. P. and Tweedie, R. L. (1993). Generalised resolvents and Harris recurrence of Markov processes. Contemp. Math. 149, 227–250.CrossRefGoogle Scholar
[83] Meyn, S. P. and Tweedie, R. L. (1993). Stability of Markovian processes II: continuous-time and sampled chains. Adv. Appl. Prob. 25, 487–517.Google Scholar
[84] Meyn, S. P. and Tweedie, R. L. (1993). Stability of Markovian processes III: Foster-Lyapunov criteria for continuous-time processes. Adv. Appl. Prob. 25, 518–548.Google Scholar
[85] Tweedie, R. L., Zhu, ζ. Y. and Choy, S. L. (1993). Parameter estimation using Laplace transforms in the M/M/1 queue. Tech. Rep. 93/6, Department of Statistics, Colorado State University.Google Scholar
[86] Tweedie, R. L. (1994). Computable convergence rates and geometric ergodicity for Markovian queueing systems. In Proc. 31st Allerton Conf. Commun. Control Comput. (October 1993), eds Sarwate, D. P. and van Dooren, P., University of Illinois Press, Champaign, IL, pp. 404–412.Google Scholar
[87] Meyn, S. P. and Tweedie, R. L. (1994). State-dependent criteria for convergence of Markov chains. Ann. Appl. Prob. 4, 149–168.Google Scholar
[88] Spieksma, F. M. and Tweedie, R. L. (1994). Strengthening ergodicity to geometric ergodicity for Markov chains. Commum. Statist. Stoch. Models 10, 45–74.Google Scholar
[89] Tweedie, R. L., Mengersen, K. L. and Eccleston, J. A. (1994). Garbage in, garbage out: can statisticians quantify the effects of poor data? Chance 7, 20–27.Google Scholar
[90] Tweedie, R. L. (1994). Topological conditions enabling use of Harris methods in discrete and continuous time. Acta Appl. Math. 34, 175–188.Google Scholar
[91] Stramer, O. and Tweedie, R. L. (1994). Stability and instability of continuous time Markov processes. In Probability, Statistics and Optimization: a Tribute to Peter Whittle, ed. Kelly, F. P., John Wiley, London, pp. 173–183.Google Scholar
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[94] Tuominen, P. and Tweedie, R. L. (1994). Subgeometric rates of convergence of f-ergodic Markov chains. Adv. Appl. Prob. 26, 775–798.Google Scholar
[95] Biggerstaff, B., Tweedie, R. L. and Mengersen, K. L. (1994). Passive smoking in the workplace: classical and Bayesian meta-analyses. Internat. Arch. Occupational Environmental Health 66, 269–277.Google Scholar
[96] Tweedie, R. L. and Mengersen, K. L. (1995). Meta-analytic approaches to dose-response relationships, with application in studies of lung cancer and exposure to environmental tobacco smoke. Statist. Medicine 14, 545–569.Google Scholar
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[98] Down, D., Meyn, S. P. and Tweedie, R. L. (1995). Exponential and uniform ergodicity of Markov processes. Ann. Prob. 23, 1671–1691.Google Scholar
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[100] Mengersen, K. L. and Tweedie, R. L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24, 101–121.Google Scholar
[101] Lund, R. and Tweedie, R. L. (1996). Geometric convergence rates for stochastically ordered Markov chains. Math. Operat. Res. 21, 182–194.Google Scholar
[102] Roberts, G. O. and Tweedie, R. L. (1996). Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83, 95–110.Google Scholar
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[104] Stramer, O., Brockwell, P. J. and Tweedie, R. L. (1996). Continuous-time threshold AR(1) models. Adv. Appl. Prob. 28, 728–746.Google Scholar
[105] Stramer, O., Tweedie, R. L. and Brockwell, P. J. (1996). Existence and stability of continuous time threshold ARMA precesses. Statist. Sinica 6, 715–732.Google Scholar
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[108] Roberts, G. O. and Tweedie, R. L. (1996). Exponential convergence of Langevin diffusions and their discrete approximations. Bernoulli 2, 341–363.Google Scholar
[109] Tweedie, R. L. (1996). Electronic publishing in the IMS: a step forward. IMS Bull. 25, 627–629.Google Scholar
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[111] Chen, P. and Tweedie, R. L. (1997). Orthogonal measures and absorbing sets for Markov chains. Math. Proc. Camb. Phil. Soc. 121, 101–113.Google Scholar
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[123] Tweedie, R. L. (1998). Truncation approximations of invariant measures for Markov chains. J. Appl Prob. 35, 517–536.Google Scholar
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[128] Stramer, O. and Tweedie, R. L. (1999). Langevin-type models I: diffusions with given stationary distributions, and their discretizations. Methodol. Comput. Appl. Prob. 1, 283–306.Google Scholar
[129] Stramer, O. and Tweedie, R. L. (1999). Langevin-type models II: self-targeting candidates for MCMC algorithms. Methodol. Comput. Appl. Prob. 1, 307–328.Google Scholar
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[135] Grunwald, G. K., Hyndman, R. J., Tedesco, L. and Tweedie, R. L. (2000). Non-Gaussian conditional linear AR(1) models. Austral. N. Z. J. Statist. 42, 479–495.Google Scholar
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