Cambridge University Press 978-0-521-14577-0 - Probability and Mathematical Genetics Edited by N. H. Bingham and C. M. Goldie Index More information Index ABC, approximate Bayesian almost complete, 141 computation almost complete Abecasis, G. R., 220 metrizabilityalmost-complete Abel Memorial Fund, 380 metrizability, see metrizability Abou-Rahme, N., 430 α-stable, see subordinator AB-percolation, see percolation Alsmeyer, G., 114 Abramovitch, F., 86 alternating renewal process, see renewal accumulate essentially, 140, 161, 163, theory 164 alternating word, see word Addario-Berry, L., 120, 121 AMSE, average mean-square error additive combinatorics, 138, 162–164 analytic set, 147 additive function, 139 ancestor gene, see gene adjacency relation, 383 ancestral history, 92, 96, 211, 256, 360 Adler, I., 303 ancestral inference, 110 admixture, 222, 224 Anderson, C. W., 303, 305–306 adsorption, 465–468, 477–478, 481, see Anderson, R. D., 137 also cooperative sequential Andjel, E., 391 adsorption model (CSA) Andrews, G. E., 372 advection-diffusion, 398–400, 408–410 anomalous spreading, 125–131 a.e., almost everywhere Antoniak, C. E., 324, 330 Affymetrix gene chip, 326 Applied Probability Trust, 33 age-dependent branching process, see appointments system, 354 branching process approximate Bayesian computation Aldous, D. J., 246, 250–251, 258, 328, (ABC), 214 448 approximate continuity, 142 algorithm, 116, 219, 221, 226–228, 422, Archimedes of Syracuse see also computational complexity, weakly Archimedean property, coupling, Kendall–Møller 144–145 algorithm, Markov chain Monte area-interaction process, see point Carlo (MCMC), phasing algorithm process perfect simulation algorithm, 69–71 arithmeticity, 172 allele, 92–103, 218, 222, 239–260, 360, arithmetic progression, 138, 157, 366, see also minor allele frequency 162–163 (MAF) Arjas, E., 350 allelic partition distribution, 243, 248, Aronson, D. G., 400 250 ARP, alternating renewal process two-allele model, 214 Arratia, R., 102, 106–109, 247, 328 two-allele process, 360, 363 a.s., almost sure(ly) allocation process, 467, 480–481 Askey, R,, 372 Allstat, 303, 317 Asmussen, S., 346 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-14577-0 - Probability and Mathematical Genetics Edited by N. H. Bingham and C. M. Goldie Index More information 510 Index assay, 205, 326 Bayesian inference, 22, 65, 214, assessment, see computer-based test 222–223 associated random walk, see random Bayesian nonparametric modelling, walk 321–323, 325–326 asymptotic independence, 352, 356 Bayesian partition, 340 Athreya, K. B., 346 Bayesian statistics, 36–38, 40–41, 251, Atiyah, M. F., 20–21, 23, 26 254, 265, 319 Atkinson, F. V., 239 Bayes’s theorem, 81 attraction/repulsion, see point process: BayesThresh method, see wavelet clustering Beagle, see phasing algorithm Austin, T., 59 Beal, M. J., 329 Auton, A., 223 Beaumont, M. A., 214 autonomous equation, 495, 498 Beder, B., 259 auto-Poisson process, see Poisson, S. D. Beerli, P., 214 autoregressive process, 352 Belkhir, K., 221–222 average mean-square error (AMSE), see Bellman, R. E. error Bellman–Harris process, 113, 116, 118 Awadalla, P., 223 Ben Arous, G., 452–453, 458 Axiom, see computer algebra Beneˇs, V. E., 420 Benjamini, I., 392–393 Bachmann, M., 122 Benjamini, Y., 86 Baddeley, A. J., 67, 71–73, 75 Bensoussan, A., 400 Bailleul, I., 452 Bergelson, V., 138, 157, 159, 161, 163 Baire, R.-L. Berkson, J., 189 Baire category theorem, 137 Bertoin, J., 46, 265, 273, 378 Baire function, 138 Bessel, F. W. Baire property, 138, 140 Bessel process, 271 Baire set, 138–164 beta distribution, 270–276, 280–284, Baire space, 142 328–329, 334, 359–360, 364–365, Baire’s theorem, 141 374 balanced incomplete block design, 30 bivariate beta distribution, 368–370 Balding, D. J., 214 Bhamidi, S., 55 Balister, P. N., 384 bias, 193, 196 ballot theorem, 38 Bibby, J. M., 353 balls in cells, 301 binary branching Brownian motion, see Baltr¯unas, A., 173 Brownian motion Banach, S. Bingham, N. H., 194 Banach space, 164 biomass, 137 bandwidth, 189–190, 195–199 birth-and-death model, see Barbour, A. D., 247, 328, 362, 448 mathematical genetics Barry, J., 186 birth-and-death process, 67 Bartlett, M. S., 25, 27, 32–33 bitopology, see topology base, 240 Bj¨ornberg, J. E., 391 base measure, 322, 328, 334 Blackwell, D., 322, 330 Batchelor, G. K., 24, 28 Blei, D. M., 329 Bather, J. A., 21, 23, 25, 32 blind transmission, 484–486, 489 Baudoin, F., 461 Blin-Stoyle, R. J., 31 Bayes, T., see also approximate blood group, 239 Bayesian computation (ABC), Bobecka, K., 273 conjugacy, hyperparameter, Bochner, S., 360–361, 368, 370, posterior predictive distribution, 372–373, 378 posterior sampling, posterior Bollob´as, B., 384 simulation, predictive density Bolthausen, E., 388 Bayesian curve fitting, 326 Bonald, T., 424–425 Bayesian density estimation, 326 Bond, S., 317 Bayesian hierarchical model, 36, 78, Bonhomme, S., 186 326 Bonnefont, M., 461 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-14577-0 - Probability and Mathematical Genetics Edited by N. H. Bingham and C. M. Goldie Index More information Index 511 Borovkov, A. A., 416 Butucea, C., 186 Borwein, D., 137–138, 157 Cambridge, University of, xv–xvi, 19, boundary bias, 190 33, 170 Bousch, T., 466 Mathematical Tripos, 19–24 Bowcock, A. M., 221 Pembroke College, 17, 19, 26 boxcar function, 195 Statistical Laboratory, 22, 24, 29, 34 Bradley, R. C., 356 Campbell, P. J., 92 Bramson, M. D., 118, 120–121, 391, 416 Camps, A., 21 branching process, 137, 260, 346, 493, cancer, 91–110 498, 502, 505–508, see also Cane, V. R., 24, 29 Bellman–Harris process, branching Cannings, C., 242 Brownian motion, branching Cannings model, 248 random walk (BRW), extinction, capacity, 406, see also channel capacity, Galton–Watson process, Markov network capacity, Newtonian branching process, Yule process capacity age-dependent branching process, Carath´eodory, C., 348 114–115 Carpio, K. J. E., 181 continuous-state branching process, Carroll, R. J., 186–187, 191 378 Cartwright, M. L., 20 general branching process, 116, 119 cascade, see multiplicative cascade multitype age-dependent branching Cassels, J. W. S., 29 process, 114 Catalan, E. C. supercritical branching process, 115 Catalan number, 51 weighted branching process, 116 category measure, 147 branching random walk (BRW), 47, Cauchy, A. L. 114–131, see also anomalous Cauchy problem, 398, 401, 408–409 spreading, extinction, spreading Cayley, A. out, spreading speed Cayley’s formula, 51 irreducible BRW, 124, 130 CDP, coloured Dirichlet process multitype BRW, 117, 124–131 cell, 91–97, 100, 110, 206 reducible BRW, 125–131 CFTP, coupling from the past two-type BRW, 125–131 Chafa¨ı, D., 461 Breiman, L., 347 channel, see also Gaussian channel Bressler, G., 489 capacity, 485, 488–490 Briggs, A., 31–32 coding, 484 Bristol, University of, xvi, 19, 381 memoryless channel, 485 British Columbia, University of, 394 characteristic function, 188, 191, Broadbent, S. R., 381 193–194, 197 Brookmeyer, R., 186 characteristic polynomial, 386 Brown, R. charge-state model, see mathematical branching Brownian motion, 118, 120, genetics 123, 128 Chen, H., 422 Brownian differential, 454 Chen, L., see Stein–Chen approximation Brownian excursion, 53 Chen, M. F., 451 Brownian motion, 51, 60, 271, 361, Chinese restaurant process (CRP), 46, 374, 398–411, 417–443, 447–461, 97–99, 276 467 Christ’s College, Finchley, xv, 18 Brownian network, 418, 426–442 chromosome, 93, 206–212, 214–231 Brownian snake, 53 Chung, K. L., 25, 28, 31 Browning, B. L., 216 clairvoyancy, see compatibility, demon, Browning, S. R., 216 embedding, scheduling BRW, branching random walk clopen, 147 Brydges, D., 502 close-packed lattice, see lattice bulk deletion, see deletion CLT, central limit theorem Buonaccorsi, J. P., 187 cluster(ing), 328, 333–340, see also Burdzy, K., 449 point process burn-in, 230–233, 340 background cluster model, 335–337 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-14577-0 - Probability and Mathematical Genetics Edited by N. H. Bingham and C. M. Goldie Index More information 512 Index cluster size, 324 convex optimization, 423, 425, 433, 437, co-adapted coupling, see coupling 439 coagulation, 273, see also coalescence, cooperative sequential adsorption model Smoluchowski coagulation equation (CSA), 465 coalescence, 39, 46–50, 54, 83, 206–223, Coppersmith, D., 384 265, 361, 364, 367, 375, see also copula, 41 Kingman coalescent, Li and copying, 212, 216–219, 225–227 Stephens model Corander, J., 221–222 inference, 205, 213–215, 220 correlation, 352 n-coalescents, 211 sequence, 368–372 coalescent tree, 210, 214, 217, 361, 366, coupling, 384n, 385, 447–461 376 co-adapted coupling, 447–454, coding, 485–488, see also channel coding 460–461 cofinality, 139 control, 454–458 co-immersed coupling, see coupling: coupling from the past (CFTP), 65, co-adapted 78, 82, 88 coin tossing, 136, 381 dominated CFTP algorithm, 65, 74n collision, 384–385 dominated coupling from the past, colour, 139, 330, 333–336 67–69 coloured Dirichlet process (CDP), 334 γ-coupling, 451 colouring, 268, 272, 275–276, 278, 334, maximal coupling, 447–450, 460–461 360, 368 mirror coupling, 451 combinatorics, 59, see also additive reflection coupling, 447, 450–453, combinatorics 458–460 compatibility rotation coupling, 447, 453, 460 clairvoyant compatibility, 384–385 shift-coupling, 450 complementary slackness, 423, 425 synchronous coupling, 447, 452–453, complete monotonicity, 375 458–460 complete neutrality, 273 time, 447, 452, 454, 458–461 completion, 140 coupon collecting, 271, 282, 300–303 composition, 266–267, 274, 278–280, 287 covariate, 320, 326, 329, 336–337, 339 compound Poisson process, see Poisson, Cox, D. R., 27, 33 S. D. Cox process, 71, 170–173, 181 computational complexity, 69–70, 76, Cram´er,C. H., 346 85, 205 Cranston, M., 451–453, 458, 461 computational statistics, see statistics Crick, F.