Papers

Publications

[1] Griffiths, R.C. (1969). The canonical correlation coefficients of bivariate gamma distributions. Ann. Math. Statist. 40, 1401-1408.

[2] Griffiths, R.C. (1969). A class of infinitely divisible bivariate gamma distributions. Sankhya 31, 473-476.

[3] Griffiths, R.C. (1970). Infinitely divisible multivariate gamma distributions. Sankhya, 32, 393-404.

[4] Griffiths, R.C. (1970). Positive definite sequences and canonical correlation coefficients. Austral. J. Statist. 12, 162-165.

[5] Griffiths, R.C. (1971). Orthogonal polynomials on the multinomial distribution. Austral. J. Statist. 13, 27-35. Corrigenda (1972) Austral. J. Statist. 14, 270.

[6] Griffiths, R.C. (1972). Linear dependence in bivariate distributions. Austral. J. Statist. 14, 182-187.

[7] Griffiths, R.C. (1973). An expansion for the permanent of a doubly stochastic matrix. J. Aust. Math. Soc. 15, 504-509.

[8] Griffiths, R.C. (1974). Permanents of random doubly stochastic matrices. Can. J. Math. 26, 600-607.

[9] Griffiths, R.C. (1974). A characterization of the multinomial distribution. Austral. J. Statist. 16, 53-56.

[10] Griffiths, R.C. (1975). Orthogonal polynomials on the negative multinomial distribution. J. Multivariate Anal. 5, 271-277.

[11] Griffiths, R.C. (1978). On a bivariate triangular distribution. Austral. J. Statist. 20, 183-185.

[12] Griffiths, R.C. and Milne, R.K. (1978). A class of bivariate Poisson processes. J. Multivariate Anal. 8, 380-395.

[13] Griffiths, R.C., Milne, R.K. and Wood, R. (1979). Aspects of correlation in bivariate Poisson distributions and processes. Austral. J. Statist. 21, 238-255.

[14] Griffiths, R.C. (1979). On the distribution of allele frequencies in a diffusion model. Theor. Popul. Biol. 15, 140-158.

[15] Griffiths, R.C. (1979). A transition density expansion for a multi-allele diffusion model. Adv. Appl. Prob. 11, 310-325.

[16] Griffiths, R.C. (1979). Exact sampling distributions from the infinite neutral alleles model. Adv. Appl. Prob. 11, 326-354.

[17] De Silva, B. and Griffiths, R.C. (1980). A test of independence for bivariate symmetric stable distributions. Austral. J. Statist. 22, 172-177.

[18] Griffiths, R.C. (1980). Lines of descent in the diffusion approximation of neutral Wright-Fisher models. Theor. Popul. Biol. 17, 37-50.

[19] Griffiths, R.C. (1980). Allele frequencies in multi-dimensional Wright-Fisher models with a general symmetric mutation structure. Theor. Popul. Biol. 17, 51-70.

[20] Griffiths, R.C. (1980). Genetic identity between populations when mutation rates vary within and across loci. J. Math. Biol. 10, 195-204.

[21] Griffiths, R.C. (1981). Transient distribution of the number of segregating sites in a neutral infinite-sites model with no recombination. J. Appl. Prob. 18, 42-51.

[22] Griffiths, R.C. (1981). The number of heterozygous loci between two randomly chosen completely linked sequences of loci in two subdivided population models. J. Math. Biol. 12, 251-261.

[23] Griffiths, R.C. (1981). Neutral two-locus multiple allele models with recombination. Theor. Popul. Biol. 19, 169-186.

[24] Griffiths, R.C. (1982). The number of alleles and segregating sites in a sample from the infinite-alleles model. Adv. Appl. Prob. 14, 225-239.

[25] Griffiths, R.C., McKechnie, S.W. and McKenzie, J.A. (1982). Multiple mating and sperm displacement in a natural population of Drosophila melanogaster. Theor. Appl. Genet. 62, 89-96.

[26] Chakraborty, R. and Griffiths, R.C. (1982). Correlation of heterozygosity and the number of alleles in different frequency classes. Theor. Popul. Biol. 21, 205-218.

[27] Griffiths, R.C. and Li, W.H. (1983). Simulating allele frequencies in a population and the genetic differentiation of populations under mutation pressure. Theor. Popul. Biol. 23, 19-33.

[28] Griffiths, R.C. (1983). Allele frequencies with genic selection. J. Math. Biol. 17, 1-10.

[29] Griffiths, R.C. (1984). Characterization of infinitely divisible multivariate gamma distributions. J. Multivariate Anal. 15, 13-20.

[30] Griffiths, R.C. (1984). Asymptotic line-of-descent distributions. J. Math. Biol. 21, 67-75.

[31] Griffiths, R.C. (1985). Orthogonal expansions. In: Kotz, S., Johnson, N.L. and Read, C.B. (Eds.), Encyclopedia of Statistical Sciences, Volume 6, Multivariate Analysis. Wiley, New York, pp. 530-536.

[32] Griffiths, R.C. (1986). Family trees and D.N.A. sequences. In: Francis, I.S., Manly, B.F.J. and Lam, F.C. (Eds.), Proceedings of the Pacific Statistical Congress. Elsevier Science (North Holland), Amsterdam, pp. 225-227.

[33] Griffiths, R.C. and Milne, R.K. (1986). Structure of exchangeable infinitely divisible sequences of Poisson random vectors. Stochastic Process. Appl. 22, 145-160.

[34] Ethier, S.N. and Griffiths, R.C. (1987). The infinitely-many-sites-model as a measure valued diffusion. Ann. Prob. 15, 515-545.

[35] Griffiths, R.C. and Milne, R.K. (1987). A class of infinitely divisible multivariate negative binomial distributions. J. Multivariate Anal. 22, 13-23.

[36] Griffiths, R.C. (1987). Counting genealogical trees. J. Math. Biol. 25, 422-432.

[37] Griffiths, R.C. and Pakes, A.G. (1988). An infinite alleles version of the simple branching process. Adv. App. Prob. 20, 489-524.

[38] Griffiths, R.C. (1988). On the distribution of points in a Poisson-Dirichlet process. J. Appl. Prob. 25, 336-345.

[39] Griffiths, R.C. (1989). Genealogical-tree probabilities in the infinitely-many-sites model. J. Math. Biol. 27, 667-680.

[40] Griffiths, R.C. and Watterson, G.A. (1990). The number of alleles in multigene families. Theor. Popul. 

Biol. 37, 110-123.

[41] Ethier, S.N. and Griffiths, R.C. (1990). The neutral two-locus model as a measure valued diffusion. Adv. Appl. Prob. 22, 773-786.

[42] Ethier, S.N. and Griffiths, R.C. (1990). On the two-locus sampling distribution. J. Math. Biol. 29, 131-159.

[43] Ethier, S.N. and Griffiths, R.C. (1991). Harmonic measure for random genetic drift. In: Pinsky, M.A. (Ed.), Diffusion Processes and Related Problems in Analysis, Volume 1. Progress in Probability Series, Volume 22. Birkhäuser, Boston, pp. 73-81.

[44] Griffiths, R.C. (1991). The two-locus ancestral graph. In: Basawa, I.V. and Taylor, R.L. (Eds.), Selected Proceedings of the Symposium on Applied Probability, Sheffield, 1989. IMS Lecture Notes - Monograph Series, Volume 18. Institute of Mathematical Statistics, Hayward, California, pp. 100-117.

[45] Griffiths, R.C. (1991). Two chromosomes with multigene families. Theor. Popul. Biol. 39, 263-273.

[46] Griffiths, R.C. (1991). Which locus has the oldest allele? J. Math. Biol. 29, 763-777.

[47] Griffiths, R.C. (1992). Distribution of the number of alleles in multigene families. J. Appl. Prob. 29, 759-769.

[48] Ewens, W.J., Griffiths, R.C., Ethier, S.N., Wilcox, S.A., and Marshall Graves, J.A. (1992). Statistical Analysis of in situ hybridization data: Derivation of the zmax test. Genomics 12, 675-682.

[49] Ethier, S.N. and Griffiths, R.C. (1993). The transition function of a Fleming-Viot process. Ann. Prob. 21, 1571-1590.

[50] Ethier, S.N. and Griffiths, R.C. (1993). The transition function of a measure-valued branching diffusion with immigration. In: Cambanis, S., Ghosh, J.K., Karandikar, R.L. and Sen, P.K. (Eds.), Stochastic Processes: A Festschrift in Honour of Gopinath Kallianpur. Springer Verlag, Berlin, pp.71-79.

[51] Nath, H.B. and Griffiths, R.C. (1993). The coalescent in two colonies with symmetric migration. J. Math. Biol. 31, 841-852.

[52] Griffiths, R.C. and Tavaré, S. (1994). Simulating probability distributions in the coalescent. Theor. Popul. Biol. 46, 131-159.

[53] Griffiths, R.C. and Tavaré, S. (1994). Sampling theory for neutral alleles in a varying environment. Phil. Trans. R. Soc. Lond. B 344, 403-410.

[54] Griffiths, R.C. and Tavaré, S. (1994). Ancestral inference in population genetics. Statistical Science 9, 307-319.

[55] Griffiths, R.C. and Tavaré, S. (1995). Unrooted genealogical tree probabilities in the infinitely-many-sites model. Mathematical Biosciences 127, 77-98.

[56] Gilfillan, C.P., Silberberg, S., Scrivenor, P., Griffiths, R.C., McCloud, P.I. and Burger, H.G. (1995). Determinants of forearm mineral density and its correlation with fracture history in women. Maturitas 20, 199-208.

[57] Griffiths, R.C. and Tavaré, S. (1996). Markov chain inference methods in population genetics. Math. Comput. Modelling 23, 8/9, 141-158.

[58] Donnelly, P., Tavaré, S., Balding, D. and Griffiths, R.C. (1996). Estimating the age of the common ancestor of men from the ZFY intron (Technical comment), Science 272, 1357-1359.

[59] Nath, H.B. and Griffiths, R.C. (1996). Estimation in an island model using simulation. Theor. Popul. Biol. 50, 227-253.

[60] Griffiths, R.C. and Marjoram, P. (1996). Ancestral inference from samples of DNA sequences with recombination. Journal of Computational Biology 3, 479-502.

[61] Tavaré, S., Balding, D., Griffiths, R.C. and Donnelly, P. (1997). Inferring coalescence times from DNA sequence data. Genetics 145, 505-518.

[62] Griffiths, R.C. and Tavaré, S. (1997). Computational methods for the coalescent. In: Donnelly, P. and Tavaré, S. (Eds.), Progress in Population Genetics and Human Evolution, IMA Volumes in Mathematics and its Applications, Volume 87. Springer Verlag, Berlin, pp. 165-182.

[63] Griffiths, R.C. and Marjoram, P. (1997). An ancestral recombination graph. In: Donnelly, P. and Tavaré, S. (Eds.), Progress in Population Genetics and Human Evolution, IMA Volumes in Mathematics and its Applications, Volume 87. Springer Verlag, Berlin, pp. 257-270.

[64] Harding, R.M., Fullerton, S.M., Griffiths, R.C., Bond, J., Cox, M.J., Schneider, J.A., Moulin, D. and Clegg, J.B. (1997). Archaic African and Asian lineages in the genetic ancestry of modern humans. Am. J. Hum. Genet. 60, 772-798.

[65] Harding, R.M., Fullerton, S.M., Griffiths, R.C. and Clegg, J.B. (1997). A gene tree for beta-globin sequences from Melanesia. J. Mol. Evol. 44 (Supplement 1): S133-S138.

[66] Griffiths, R.C. and Tavaré, S. (1998). The age of a mutation in a general coalescent tree. Stochastic Models. 14, 273-295.

[67] Hammer M. F., Karafet, T., Rasanayagam, A., Wood, E. T., Altheide, T. K., Jenkins, T., Griffiths, R. C., Templeton, A. R., and Zegura, S. L. (1998). Out of Africa and back again: Nested cladistic analysis of human Y chromosome variation. Mol. Biol. Evol. 15, 427-441.

[68] Karafet, T.M., Zegura, S.L., Posukh, O., Osipova, L., Bergen, A., Long, J., Goldman, D., Klitz, W., Harihara, S., de Knijff, P., Wiebe, V., Griffiths, R.C., Templeton, A.R. and Hammer, M.F. (1999). Ancestral Asian source(s) of New World Y-chromosome founder haplotypes. Am. J. Hum. Genet. 64, 817-831.

[69] Griffiths, R.C. (1999). Time to the ancestor along sequences with recombination. Theor. Popul. Biol. 55, 137-144.

[70] Griffiths, R.C. and Tavaré S. (1999). The ages of mutations in gene trees. Ann. Appl. Prob. 9, 567-590.

[71] Griffiths, R.C. (1999). Ancestral inference from gene trees in a subdivided population. Bulletin of the International Statistical Institute. 52nd Session, ISI99, Helsinki. Book 1. pp. 353-356.

[72] Barbour, A.D., Ethier, S.N. and Griffiths, R.C. (2000). A transition function expansion for a diffusion model with selection. Ann. Appl. Prob. 10, 123-162.

[73] Bahlo, M. and Griffiths, R.C. (2000). Inference from gene trees in a subdivided population. Theor. Popul. Biol. 57, 79-95.

[74] Griffiths, R.C. (2001). Ancestral inference from gene trees. In: Donnelly, P. and Foley, R. (Eds.), Genes, Fossils, and Behaviour: an Integrated Approach to Human Evolution, IOS Press, Amsterdam, pp.137-172.

[75] Bahlo, M. and Griffiths, R.C. (2001). Coalescence time for two genes from a subdivided population. J. Math. Biol. 43, 397-410.

[76] Griffiths, R.C. (2002). Ancestral inference from gene trees. In: Veuille, M. and Slatkin, M. (Eds.), Modern Developments in Theoretical Population Genetics: the Legacy of Gustave Malécot, Oxford University Press, New York, pp. 94-117.

[77] Stone, A. C., Griffiths, R.C., Zegura, S. L. and Hammer, M. F. (2002). High levels of Y-chromosome nucleotide diversity in the genus Pan. PNAS 99, 43-49.

[78] Griffiths, R.C. and Tavaré, S. (2003). The genealogy of a neutral mutation. In: Green, P.J., Hjort, N.L. and Richardson, S. (Eds.), Highly Structured Stochastic Systems. Oxford University Press, Oxford, pp. 393-413.

[79] Myers, S.R. and Griffiths, R.C. (2003). Bounds on the minimum number of recombination events in a sample history. Genetics 163, 375-394.

[80] Griffiths, R.C. (2003). The frequency spectrum of a mutation, and its age, in a general diffusion model. Theor. Popul. Biol. 64, 241-251.

[81] De Iorio, M. and Griffiths, R.C. (2004). Importance sampling on coalescent histories. I. Adv. Appl. Prob. 36, 417-433.

[82] De Iorio, M. and Griffiths, R.C. (2004). Importance sampling on coalescent histories. II Subdivided population models. Adv. Appl. Prob. 36, 434-454.

[83] Coop, G. and Griffiths, R.C. (2005). Ancestral inference on gene trees under selection. Theor. Popul. Biol. 66, 219-232.

[84] De Iorio, M., Griffiths, R.C., Lebois, R. and Rousset, F. (2005). Stepwise mutation likelihood computation by sequential importance sampling in subdivided population models. Theor. Popul. Biol. 68, 41-53.

[85] Griffiths, R.C. and Lessard, S. (2005). Ewens' sampling formula and related formulae: Combinatorial proofs, extensions to variable population size and applications to ages of alleles. Theor. Popul. Biol. 68, 167-177.

[86] Clark, T., De Iorio, M., Griffiths, R.C., Farrall, M. (2005). Finding associations in dense genetic maps: a genetic algorithm approach. Hum. Hered. 60, 97-108.

[87] Griffiths, R. C. (2006). Coalescent lineage distributions. Adv. Appl. Prob. 38, 405-429

[88] Clark, T., De Iorio, M. and Griffiths, R.C. (2007). Bayesian logistic regression using a perfect phylogeny. Biostat. 8, 32-52.

[89] Griffiths, R. C. and Spanò , D. (2007). Record indices and age-ordered frequencies in Exchangeable Gibbs Partitions. Electronic Journal of Probability, 1101-1130.

[90] Clark, T. G., De Iorio, M., Griffiths, R. C. (2008). An evolutionary algorithm to find associations in dense genetic maps. IEEE Transactions on Evolutionary Computation, 12, No. 3, 297-306.

[91] Griffiths, R. C., Jenkins, P. A., Song, Y. S. (2008). Importance sampling and the two-locus model with subdivided population structure. Adv. Appl. Prob. 40, 473-500.

[92] Griffiths, R. C., Griffiths, Y. J. (2008). Ancestral inference from Microsatellite data by sequential importance sampling in subdivided populations. In Simulations, Genetics and Human Prehistory, ed. Matsumura, S., Forster, P., Renfrew, C, McDonald Institute Monographs , Chapter 13, p125-134.

[93] Etheridge, A. M., Griffiths, R. C. (2009). A coalescent dual process in a Moran model with genic selection. Theor. Popul. Biol. 75,320-330.

[94] Griffiths, B. (2009). Stochastic processes with orthogonal polynomial eigenfunctions. J. Comput. Appl. Math. 23, 739-744.

[95] Etheridge, A. M., Griffiths, R. C., Taylor, J. E. (2010). A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit. Theor. Popul. Biol. 78 77-92.

[96] Griffiths, R. C. and Spanò, D. (2010). Diffusion processes and coalescent trees. Chapter 15 358-375. In: Probability and Mathematical Genetics, Papers in Honour of Sir John Kingman. LMS Lecture Note Series 378. ed Bingham, N. H. and Goldie, C. M., Cambridge University Press.

[97] Sainudiin, R., Thornton, K., Harlow, J. Booth, J., Stillman, M., Yoshida, R., Griffiths, R., McVean, G., Donnelly, P. (2010). Experiments with the Site Frequency Spectrum. Bulletin of Mathematical Biology 1-44.

[98] Jenkins, P. A., Griffiths, R. C. (2011). Inference from samples of DNA sequences using a two-locus model. Journal of Computational Biology 18, 109-127.

[99] Griffiths, R. C., Spanò D. (2011). Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials. Bernoulli 17, 1095-1125.

[100] Diaconis, P. and Griffiths, R. C. (2012). Exchangeable pairs of Bernoulli random variables, Krawtchouk polynomials and Ehrenfest urns. Aust. N. Z. J. Stat. 54, 81-101.

[101] Griffiths, R. C., Spanò D. (2013). Orthogonal Polynomial Kernels and Canonical Correlations for Dirichlet measures. Bernoulli 19, 548-598.

[102] Schraiber, J. G., Griffiths, R. C., Evans, S. N. (2013). Analysis and rejection sampling of Wright-Fisher diffusion bridges. Theor. Popul. Biol. 89 , 64-74.

[103] Diaconis, P., Griffiths, R. C. (2014). An introduction to multivariate Krawtchouk polynomials and their applications. Journal of Statistical Planning and Inference 154, 39-53.

[104] Griffiths R. C. (2014). The Lambda-Fleming-Viot process and a connection with Wright-Fisher diffusion. Adv. Appl. Prob. 46, 1009-1035.

[105] Griffiths R. C. (2016). Lancaster distributions and Markov chains with Multivariate Poisson-Charlier, Meixner and Hermite-Chebycheff polynomial eigenvectors. J. Approx. Theory 207, 139-164.

[106] Griffiths R. C. (2016). Multivariate Krawtchouk polynomials and composition birth and death processes. Symmetry 8, 33-52.

[107] Griffiths R. C. and Mano, S. (2016). The star-shaped Lambda-coalescent and Fleming-Viot process Stochastic Models. 32, 606-631.

[108] Griffiths R. C., Jenkins P. A., Lessard, S. (2016). A coalescent dual process for a Wright-Fisher diffusion with recombination and its applications to haplotype partitioning. Theor. Popul. Biol. 112, 126-138.

[109] Griffiths R. C. (2016). A Multi-type Lambda-Coalescent. In Branching processes and their applications Proceedings of WBPA15. Lecture notes in Statistics Volume 219. Ed. Editors: Inés M. del Puerto, Miguel González, Cristina Gutiérrez, Rodrigo Martínez, Carmen Minuesa, Manuel Molina, Manuel Mota, Alfonso Ramos E-Book

[110] Griffiths, R. C. Jenkins, P. A., Spanò D. (2018). Wright-Fisher diffusion bridges. Theor. Popul. Biol. 112, 126-138.

[111] Griffiths, R.C. and Tavaré S., (2018). Ancestral distributions in the coalescent. Theor. Popul. Biol. 122, 12-21.

[113] Burden, C. J. and Griffiths, R. C. (2018). Stationary distribution of a 2-island 2-allele Wright- Fisher diffusion model with slow mutation and migration rates. Theor. Popul. Biol. 124, 70-80.

[114] Burden, C. J. and Griffiths, R. C. (2019). The stationary distribution of a Wright-Fisher diffusion model with general small mutation rates.  J. Math. Biol. 78, 1211-1224.

[115] Diaconis, P. and Griffiths, R. C. (2019). Reproducing kernel polynomials on the multinomial distribution.  J. Approx. Theory, 242, 1-30.

[116] Burden, C. J. and Griffiths, R. C. (2019).  The transition distribution of a sample from a Wright-Fisher diffusion with general small mutation rates. J. Math. Biol.  79, 2315-2342.

[117] Griffiths, R. and Hamza, K. (2020).  A universal approach to matching marginals and sums. Electron. Commun. Probab. 25, paper no. 78, 12pp.

[118]  Collevecchio, A and Griffiths, R. C. (2020). A Class of Random Walks on the Hypercube. In In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius (pp. 265–298).  Springer International Publishing.

[119] Griffiths, R. and Hamza, K. (2021).  Matching the distributions of the marginals and the sums for the Meixner class. Theory of Prob. Appl.  66, 430-444.

[120]  Burden, C. J. and Griffiths, R. C. (2023). The stationary and quasi-stationary properties of neutral multi-type branching process diffusions. Stoch.  Models.  39, 185-218.

[121] Collevecchio, A. and Griffiths, R. (2023).  A class of non-reversible long-range random walks and Bernoulli autoregression. J.  Theor. Probab. 36, 623-645.

[122] Griffiths, Robert,  (2023).  "Coalescent Theory", In Oxford Bibliographies in Evolutionary Biology. Ed. Douglas Futuyma. New York: Oxford University Press.

[123] Griffiths, R.C., Jenkins, P.A.(2023).  An estimator for the recombination rate from a continuously observed diffusion of haplotype frequencies. J. Math. Biol. 86, 98 (2023). 

[124] Burden, C. J. and Griffiths, R. C. (2024).  Coalescence and sampling distributions for Feller diffusions.  Theor. Popul. Biol. 155, 67-76. 

Invited and Contributed Discussion

[125] Griffiths, R.C. (2000). Discussion note on Inference in molecular population genetics by M. Stephens, and P. Donnelly. J. R. Statist. Soc. B, 62, 638-639.

[126] Griffiths, R.C. (2002). Discussion note on Assessing population differentiation and isolation from single-nucleotide polymorphism data by G. Nicholson, A.V. Smith, F. Jónsson, Ó. Gústafsson, K. Stefánsson and P. Donnelly. J. R. Statist. Soc. B, 64, 742-743.

[127] Griffiths, R.C. (2003). Discussion on Inferences from DNA data: population histories, evolutionary processes and forensic match probabilities by I.A. Wilson, M.E. Weale and D.J. Balding. J. R. Statist. Soc. A, 166, 192-193.

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