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Volumn 23, Issue 3, 2008, Pages 287-312

Quantifying the fraction of missing information for hypothesis testing in statistical and genetic studies

Author keywords

Cox regression; EM algorithm; Entropy; Fisher information; Genetic linkage studies; Haplotype based association studies; Kullback Leibler information; Noninformative prior; Partial likelihood; Relative information

Indexed keywords


EID: 59349096892     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/07-STS244     Document Type: Article
Times cited : (9)

References (63)
  • 1
    • 0033909546 scopus 로고    scopus 로고
    • A general test of association for quantitative traits in nuclear families
    • ABECASIS, G. R., CARDON, L. R. and COOKSON, W. O. C. (2000). A general test of association for quantitative traits in nuclear families. Amer. J. Human Genetics 66 279-292.
    • (2000) Amer. J. Human Genetics , vol.66 , pp. 279-292
    • ABECASIS, G.R.1    CARDON, L.R.2    COOKSON, W.O.C.3
  • 2
    • 0033362231 scopus 로고    scopus 로고
    • Direct power comparisons between simple lod scores and npl scores for linkage analysis in complex diseases
    • ABREU, P., GREENBERG, D. and HODGE, S. (1999). Direct power comparisons between simple lod scores and npl scores for linkage analysis in complex diseases. Amer. J. Human Genetics 65 847-857.
    • (1999) Amer. J. Human Genetics , vol.65 , pp. 847-857
    • ABREU, P.1    GREENBERG, D.2    HODGE, S.3
  • 3
    • 85042251872 scopus 로고
    • Goodness of prediction fit
    • MR0391353
    • AITCHISON, J. (1975). Goodness of prediction fit. Biometrika 62 547-554. MR0391353
    • (1975) Biometrika , vol.62 , pp. 547-554
    • AITCHISON, J.1
  • 4
    • 59349116206 scopus 로고    scopus 로고
    • AKAIKE, H. (1985). Prediction and entropy. In Celebration of Statistics: The ISI Centenary 1-24 (A. Atkinson and S. Fienberg, eds.). Springer, New York. MR0816143
    • AKAIKE, H. (1985). Prediction and entropy. In Celebration of Statistics: The ISI Centenary Volume 1-24 (A. Atkinson and S. Fienberg, eds.). Springer, New York. MR0816143
  • 5
    • 0000410232 scopus 로고
    • Minimum, variance estimation without regularity assumptions
    • MR0044084
    • CHAPMAN, D. C. and ROBBINS, H. (1951). Minimum, variance estimation without regularity assumptions. Ann. Math. Statist. 22 581-586. MR0044084
    • (1951) Ann. Math. Statist , vol.22 , pp. 581-586
    • CHAPMAN, D.C.1    ROBBINS, H.2
  • 7
    • 13144261748 scopus 로고    scopus 로고
    • Identification of novel susceptibility loci for inflammatory bowel disease
    • CHO, J. H., NICOLAE, D. L., GOLD, L. H. and FIELDS, C. T. ET AL. (1998). Identification of novel susceptibility loci for inflammatory bowel disease. Proc. Natl. Acad. Sci. USA 95 7502-7507.
    • (1998) Proc. Natl. Acad. Sci. USA , vol.95 , pp. 7502-7507
    • CHO, J.H.1    NICOLAE, D.L.2    GOLD, L.H.3    FIELDS, C.T.4    ET AL.5
  • 8
    • 0031003687 scopus 로고    scopus 로고
    • Alternative test for linkage between two loci
    • CLEVES, M. A. and ELSTON, R. C. (1997). Alternative test for linkage between two loci. Genetic Epidemiology 14 117-131.
    • (1997) Genetic Epidemiology , vol.14 , pp. 117-131
    • CLEVES, M.A.1    ELSTON, R.C.2
  • 9
    • 84889281816 scopus 로고    scopus 로고
    • COVER, T. M. and THOMAS, J. A. (1991). Elements of Information Theory. Wiley, New York. MR1122806
    • COVER, T. M. and THOMAS, J. A. (1991). Elements of Information Theory. Wiley, New York. MR1122806
  • 10
    • 59349087806 scopus 로고    scopus 로고
    • COX, D. R. and HINKLEY, D. (1974). Theoretical Statistics. Chapman and Hall, London. MR0370837
    • COX, D. R. and HINKLEY, D. (1974). Theoretical Statistics. Chapman and Hall, London. MR0370837
  • 11
    • 0033711876 scopus 로고    scopus 로고
    • Bias in multipoint linkage analysis arising from map misspecification
    • DAW, E. W., THOMPSON, E. A. and WIJSMAN, E. M. (2000). Bias in multipoint linkage analysis arising from map misspecification. Genetic Epidemiology 19 366-380.
    • (2000) Genetic Epidemiology , vol.19 , pp. 366-380
    • DAW, E.W.1    THOMPSON, E.A.2    WIJSMAN, E.M.3
  • 12
    • 21944455810 scopus 로고    scopus 로고
    • The direct use of likelihood for significance testing
    • DEMPSTER, A. P. (1997). The direct use of likelihood for significance testing. Statist. Comput. 7 247-252.
    • (1997) Statist. Comput , vol.7 , pp. 247-252
    • DEMPSTER, A.P.1
  • 13
    • 0002629270 scopus 로고
    • Maximum likelihood from incomplete data via the EM algorithm (with discussion)
    • MR0501537
    • DEMPSTER, A. P., LAIRD, N. M. and RUBIN, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39 1-37. MR0501537
    • (1977) J. Roy. Statist. Soc. Ser. B , vol.39 , pp. 1-37
    • DEMPSTER, A.P.1    LAIRD, N.M.2    RUBIN, D.B.3
  • 14
    • 0029150074 scopus 로고
    • A comparison of linkage disequilibrium measures for fine-scale mapping
    • DEVLIN, B. and RISCH, N. (1995). A comparison of linkage disequilibrium measures for fine-scale mapping. Genomics 29 311-322.
    • (1995) Genomics , vol.29 , pp. 311-322
    • DEVLIN, B.1    RISCH, N.2
  • 15
    • 4544335122 scopus 로고    scopus 로고
    • Guidelines for genotyping in genomewide linkage studies: Single-Nucleotide Polymorphism maps versus microsatellite maps
    • EVANS, D. E. and CARDON, L. R. (2004). Guidelines for genotyping in genomewide linkage studies: Single-Nucleotide Polymorphism maps versus microsatellite maps. Amer. J. Human Genetics 75 687-692.
    • (2004) Amer. J. Human Genetics , vol.75 , pp. 687-692
    • EVANS, D.E.1    CARDON, L.R.2
  • 16
    • 0029130796 scopus 로고
    • Maximum-likelihood estimation of molecular haplotype frequencies in a diploid population
    • EXCOFFIER, L. and SLATKIN, M. (.1995). Maximum-likelihood estimation of molecular haplotype frequencies in a diploid population. Mol. Biol. Evol. 12 921-927.
    • (1995) Mol. Biol. Evol , vol.12 , pp. 921-927
    • EXCOFFIER, L.1    SLATKIN, M.2
  • 17
    • 0023235253 scopus 로고
    • Haplotype relative risks: An easy reliable way to construct a proper control sample for risk calculations
    • FALK, C. T. and RUBINSTEIN, P. (1987). Haplotype relative risks: an easy reliable way to construct a proper control sample for risk calculations. Ann. Human Genetics 51 227-233.
    • (1987) Ann. Human Genetics , vol.51 , pp. 227-233
    • FALK, C.T.1    RUBINSTEIN, P.2
  • 18
    • 33744815939 scopus 로고    scopus 로고
    • Improved minimax predictive densities under Kullback-Leibler loss
    • MR2275235
    • GEORGE, E., FENG, L. and XU, X. (2006). Improved minimax predictive densities under Kullback-Leibler loss. Ann. Statist. 34 78-91. MR2275235
    • (2006) Ann. Statist , vol.34 , pp. 78-91
    • GEORGE, E.1    FENG, L.2    XU, X.3
  • 20
    • 0141819194 scopus 로고    scopus 로고
    • The gene encoding phosphodiesterase 4d confers risk of ischemic stroke
    • GRETARSDOTTIR, S., THORLEIFSSON, G. and REYNISDOTTIR, S. T. ET AL. (2003). The gene encoding phosphodiesterase 4d confers risk of ischemic stroke. Nature Genetics 35 131-138.
    • (2003) Nature Genetics , vol.35 , pp. 131-138
    • GRETARSDOTTIR, S.1    THORLEIFSSON, G.2    REYNISDOTTIR, S.T.3    ET AL.4
  • 22
    • 0029372419 scopus 로고
    • HAPLO: A program using the EM algorithm to estimate the frequencies of multi-site haplotypes
    • HAWLEY, M. and KIDD, K. (1995). HAPLO: A program using the EM algorithm to estimate the frequencies of multi-site haplotypes. J. Heredity 86 409-411.
    • (1995) J. Heredity , vol.86 , pp. 409-411
    • HAWLEY, M.1    KIDD, K.2
  • 23
    • 33846596193 scopus 로고    scopus 로고
    • Refining the impact of TCF7L2 gene variants on type 2 diabetes and adaptive evolution
    • HELGASON, A., PALSSON, S., THORLEIFSSON, G. and GRANT, S. F. ET AL. (2007). Refining the impact of TCF7L2 gene variants on type 2 diabetes and adaptive evolution. Nature Genetics 39 218-225.
    • (2007) Nature Genetics , vol.39 , pp. 218-225
    • HELGASON, A.1    PALSSON, S.2    THORLEIFSSON, G.3    GRANT, S.F.4    ET AL.5
  • 24
    • 0030728925 scopus 로고    scopus 로고
    • Allele-sharing models: Lod scores and accurate linkage tests
    • KONG, A. and COX, N. J. (1997). Allele-sharing models: Lod scores and accurate linkage tests. Amer. J. Human Genetics 61 1179-1188.
    • (1997) Amer. J. Human Genetics , vol.61 , pp. 1179-1188
    • KONG, A.1    COX, N.J.2
  • 25
    • 0030861903 scopus 로고    scopus 로고
    • The use of a genetic map of biallelic markers in linkage studies
    • KRUGLYAK, L. ( 1997). The use of a genetic map of biallelic markers in linkage studies. Nature Genetics 17 21-24.
    • (1997) Nature Genetics , vol.17 , pp. 21-24
    • KRUGLYAK, L.1
  • 26
    • 0029886532 scopus 로고    scopus 로고
    • Parametric and nonparametric linkage analysis: A unified multipoint approach
    • KRUGLYAK, L., DALY, M. J., REEVE-DALY, M. P. and LANDER, E. S. (1996). Parametric and nonparametric linkage analysis: A unified multipoint approach. Amer. J. Human Genetics 58 1347-1363.
    • (1996) Amer. J. Human Genetics , vol.58 , pp. 1347-1363
    • KRUGLYAK, L.1    DALY, M.J.2    REEVE-DALY, M.P.3    LANDER, E.S.4
  • 27
    • 0033912563 scopus 로고    scopus 로고
    • Haplotype fine mapping by evolutionary trees
    • LAM, J. C., ROEDER, K. and DEVLIN, B. (2000). Haplotype fine mapping by evolutionary trees. Amer. J. Human Genetics 66 659-673.
    • (2000) Amer. J. Human Genetics , vol.66 , pp. 659-673
    • LAM, J.C.1    ROEDER, K.2    DEVLIN, B.3
  • 28
    • 0000803318 scopus 로고
    • Construction of multilocus genetic linkage maps in humans
    • LANDER, E. S. and GREEN, P. (1987). Construction of multilocus genetic linkage maps in humans. Proc. Natl. Acad. Sci. USA 84 2363-2367.
    • (1987) Proc. Natl. Acad. Sci. USA , vol.84 , pp. 2363-2367
    • LANDER, E.S.1    GREEN, P.2
  • 29
    • 0036724540 scopus 로고    scopus 로고
    • Analytical sample size and power calculations for a general class of family-based association tests: Dichotomous traits
    • LANGE, C. and LAIRD, N. M. (2002a). Analytical sample size and power calculations for a general class of family-based association tests: Dichotomous traits. Amer. J. Human Genetics 71 575-584.
    • (2002) Amer. J. Human Genetics , vol.71 , pp. 575-584
    • LANGE, C.1    LAIRD, N.M.2
  • 30
    • 0036668724 scopus 로고    scopus 로고
    • On a general class of conditional tests for family-based association studies in genetics: The asymptotic distribution, the conditional power and optimality considerations
    • LANGE, C. and LAIRD, N. M. (2002b). On a general class of conditional tests for family-based association studies in genetics: The asymptotic distribution, the conditional power and optimality considerations. Genetic Epidemiology 23 .165-180.
    • (2002) Genetic Epidemiology , vol.23 , pp. 165-180
    • LANGE, C.1    LAIRD, N.M.2
  • 31
    • 0028913523 scopus 로고
    • An E-M algorithm and testing strategy for multiple locus haplotypes
    • LONG, J. C., WILLIAMS, R. C. and URBANEK, M. (1995). An E-M algorithm and testing strategy for multiple locus haplotypes. Amer. J. Human Genetics 59 799-810.
    • (1995) Amer. J. Human Genetics , vol.59 , pp. 799-810
    • LONG, J.C.1    WILLIAMS, R.C.2    URBANEK, M.3
  • 32
    • 0033910787 scopus 로고    scopus 로고
    • A test for linkage and association in general pedigrees: The pedigree disequilibrium test
    • MARTIN, E. R., MONKS, S. A., WARREN, L. L. and KAPLAN, N. L. (2000). A test for linkage and association in general pedigrees: The pedigree disequilibrium test. Amer. J. Human Genetics 67 146-154.
    • (2000) Amer. J. Human Genetics , vol.67 , pp. 146-154
    • MARTIN, E.R.1    MONKS, S.A.2    WARREN, L.L.3    KAPLAN, N.L.4
  • 33
    • 12144286180 scopus 로고    scopus 로고
    • Parallel genotyping of over 10,000 snps using a one-primer assay on a high-density oligonucleotide array
    • MATSUZAKI, H., LOI, H. and DONG, S. ET AL. (2004). Parallel genotyping of over 10,000 snps using a one-primer assay on a high-density oligonucleotide array. Genome Research 14 414-425.
    • (2004) Genome Research , vol.14 , pp. 414-425
    • MATSUZAKI, H.1    LOI, H.2    DONG, S.3    ET AL.4
  • 34
    • 0033358667 scopus 로고    scopus 로고
    • Assesment of linkage disequilibrium by the decay of haplotype sharing, with application to fine-scale genetic mapping
    • MCPEEK, M. S. and STRAHS, A. (1999). Assesment of linkage disequilibrium by the decay of haplotype sharing, with application to fine-scale genetic mapping. Amer. J. Human Genetics 65 858-875.
    • (1999) Amer. J. Human Genetics , vol.65 , pp. 858-875
    • MCPEEK, M.S.1    STRAHS, A.2
  • 35
    • 21344477603 scopus 로고
    • On the rate of convergence of the ECM algorithm
    • MR1272086
    • MENG, X.-L. (1994). On the rate of convergence of the ECM algorithm. Ann. Statist. 22 326-339. MR1272086
    • (1994) Ann. Statist , vol.22 , pp. 326-339
    • MENG, X.-L.1
  • 36
    • 14344249153 scopus 로고    scopus 로고
    • MENG, X.-L. (2000). Discussion of Optimization transfer using surrogate objective functions by K. Lange, D. Hunter and I. Yang. J. Comput. Graph. Statist. 9 35-43. MR1819865
    • MENG, X.-L. (2000). Discussion of "Optimization transfer using surrogate objective functions" by K. Lange, D. Hunter and I. Yang. J. Comput. Graph. Statist. 9 35-43. MR1819865
  • 37
    • 0345673603 scopus 로고    scopus 로고
    • A congenial overview and investigation of multiple imputation inference under uncongeniality
    • R. Groves, D. Dillman, J. Eltinge and R. Little, eds, Wiley, New York
    • MENG, X.-L. (2001). A congenial overview and investigation of multiple imputation inference under uncongeniality. In Survey Nonresponse (R. Groves, D. Dillman, J. Eltinge and R. Little, eds.) 343-356. Wiley, New York.
    • (2001) Survey Nonresponse , pp. 343-356
    • MENG, X.-L.1
  • 38
    • 84864615423 scopus 로고
    • Using EM to obtain asymptotic variance-covariance matrices: The SEM algorithm
    • MENG, X.-L. and RUBIN, D. B. (1991). Using EM to obtain asymptotic variance-covariance matrices: The SEM algorithm. J. Amer. Statist. Assoc. 86 899-909.
    • (1991) J. Amer. Statist. Assoc , vol.86 , pp. 899-909
    • MENG, X.-L.1    RUBIN, D.B.2
  • 39
    • 0000251971 scopus 로고
    • Maximum likelihood estimation via the ECM algorithm: A general framework
    • MR1243503
    • MENG, X.-L. and RUBIN, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika 80 267-278. MR1243503
    • (1993) Biometrika , vol.80 , pp. 267-278
    • MENG, X.-L.1    RUBIN, D.B.2
  • 41
    • 18244387717 scopus 로고    scopus 로고
    • The EM algorithm an old folk song sung to a fast new tune (with discussion)
    • MR1452025
    • MENG, X.-L. and VAN DYK, D. A. (1997). The EM algorithm an old folk song sung to a fast new tune (with discussion). J. Roy. Statist. Soc. Ser. B 59 511-567. MR1452025
    • (1997) J. Roy. Statist. Soc. Ser. B , vol.59 , pp. 511-567
    • MENG, X.-L.1    VAN DYK, D.A.2
  • 42
    • 2342635193 scopus 로고    scopus 로고
    • Genomewide linkage analysis of bipolar disorder by use of a high-density single- nucleotidepolymorphism (snp) genotyping assay: A comparison with microsatellite marker assays and finding of significant linkage to chromosome 6q22
    • MLDDLETON, F. A. ET AL. (2004). Genomewide linkage analysis of bipolar disorder by use of a high-density single- nucleotidepolymorphism (snp) genotyping assay: A comparison with microsatellite marker assays and finding of significant linkage to chromosome 6q22. Amer. J. Human Genetics 74 886-897.
    • (2004) Amer. J. Human Genetics , vol.74 , pp. 886-897
    • MLDDLETON, F.1    ET AL, A.2
  • 43
    • 0036177752 scopus 로고    scopus 로고
    • Fine-scale mapping of disease loci via shattered coalescent modeling of genealogies
    • MORRIS, A. P., WHITTAKER, J. C. and BALDING, D. J. (2002). Fine-scale mapping of disease loci via shattered coalescent modeling of genealogies. Amer. J. Human Genetics 70 686-707.
    • (2002) Amer. J. Human Genetics , vol.70 , pp. 686-707
    • MORRIS, A.P.1    WHITTAKER, J.C.2    BALDING, D.J.3
  • 45
    • 33845198883 scopus 로고    scopus 로고
    • Testing untyped alleles (TUNA) - applications to genome-wide association studies
    • NICOLAE, D. L. (2006a). Testing untyped alleles (TUNA) - applications to genome-wide association studies. Genetic Epidemiology 30 718-727.
    • (2006) Genetic Epidemiology , vol.30 , pp. 718-727
    • NICOLAE, D.L.1
  • 46
    • 33845186299 scopus 로고    scopus 로고
    • Quantifying the amount of missing information in genetic association studies
    • NICOLAE, D. L. (2006b). Quantifying the amount of missing information in genetic association studies. Genetic Epidemiology 30 703-717.
    • (2006) Genetic Epidemiology , vol.30 , pp. 703-717
    • NICOLAE, D.L.1
  • 47
    • 2942638335 scopus 로고    scopus 로고
    • Measuring the relative information in allele-sharing linkage studies
    • MR2066271
    • NICOLAE, D. L. and KONG, A. (2004). Measuring the relative information in allele-sharing linkage studies. Biometrics 60 368-275. MR2066271
    • (2004) Biometrics , vol.60 , pp. 368-275
    • NICOLAE, D.L.1    KONG, A.2
  • 48
    • 4444332735 scopus 로고    scopus 로고
    • Bayesian haplotype inference for multiple linked single-nucleotide polymorphisms
    • NIU, T., QIN, Z. S., XU, X. and LIU, J. S. (2002). Bayesian haplotype inference for multiple linked single-nucleotide polymorphisms. Amer. J. Human Genetics 71 1242-1247.
    • (2002) Amer. J. Human Genetics , vol.71 , pp. 1242-1247
    • NIU, T.1    QIN, Z.S.2    XU, X.3    LIU, J.S.4
  • 50
    • 0035234944 scopus 로고    scopus 로고
    • Major strengths and weaknesses of the lod score method
    • OTT, J. (2001). Major strengths and weaknesses of the lod score method. Adv. Genetics 42 125-132.
    • (2001) Adv. Genetics , vol.42 , pp. 125-132
    • OTT, J.1
  • 51
    • 33745279392 scopus 로고    scopus 로고
    • Evaluating and improving power in whole-genome association studies using fixed marker sets
    • PE'ER, I., DE BARKER, P. I., MALLER, J., YELENSKY, R., ALTSHULER, D. and DALY, M. J. (2006). Evaluating and improving power in whole-genome association studies using fixed marker sets. Nature Genetics 38 663-667.
    • (2006) Nature Genetics , vol.38 , pp. 663-667
    • PE'ER, I.1    DE BARKER, P.I.2    MALLER, J.3    YELENSKY, R.4    ALTSHULER, D.5    DALY, M.J.6
  • 53
    • 0017133178 scopus 로고
    • Inference and missing data
    • MR0455196
    • RUBIN, D. B. (1976). Inference and missing data. Biometrika 63 581-592. MR0455196
    • (1976) Biometrika , vol.63 , pp. 581-592
    • RUBIN, D.B.1
  • 55
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • MR0026286
    • SHANNON, C. E. (1949). A mathematical theory of communication. Bell Syst. Tech. J. 27 623-656. MR0026286
    • (1949) Bell Syst. Tech. J , vol.27 , pp. 623-656
    • SHANNON, C.E.1
  • 56
    • 0035071957 scopus 로고    scopus 로고
    • A new statistical method for haplotype reconstruction from population data
    • STEPHENS, M., SMITH, N. J. and DONNELLY, P. (2001). A new statistical method for haplotype reconstruction from population data. Amer. J. Human Genetics 68 978-989.
    • (2001) Amer. J. Human Genetics , vol.68 , pp. 978-989
    • STEPHENS, M.1    SMITH, N.J.2    DONNELLY, P.3
  • 57
    • 0032447006 scopus 로고    scopus 로고
    • Multipoint linkage analysis using affected relative pairs and partially informative markers
    • MR1671602
    • TENG, J. and SIEGMUND, D. O. (1998). Multipoint linkage analysis using affected relative pairs and partially informative markers. Biometrics 54 .1247-1265. MR1671602
    • (1998) Biometrics , vol.54 , pp. 1247-1265
    • TENG, J.1    SIEGMUND, D.O.2
  • 58
    • 0026494911 scopus 로고
    • A haplotype-based 'haplotype relative risk' approach to detecting allelic associations
    • TERWILLIGER, J. D. and OTT, J. (1992). A haplotype-based 'haplotype relative risk' approach to detecting allelic associations. Human Heredity 42 337-346.
    • (1992) Human Heredity , vol.42 , pp. 337-346
    • TERWILLIGER, J.D.1    OTT, J.2
  • 59
    • 30344443851 scopus 로고    scopus 로고
    • A comparison between microsatellite and single-nucleotide polymorphism, markers with respect to two measures of information content
    • THALAMUTHU, A., MUKHOPADHYAY, I., RAY, A. and WEEKS, D. E. (2005). A comparison between microsatellite and single-nucleotide polymorphism, markers with respect to two measures of information content. BMC Genetics 6 (Suppl 1) S27.
    • (2005) BMC Genetics , vol.6 , Issue.SUPPL. 1
    • THALAMUTHU, A.1    MUKHOPADHYAY, I.2    RAY, A.3    WEEKS, D.E.4
  • 60
    • 79959503826 scopus 로고    scopus 로고
    • The international hapmap project
    • THE INTERNATIONAL HAPMAP CONSORTIUM
    • THE INTERNATIONAL HAPMAP CONSORTIUM (2003). The international hapmap project. Nature 426 789-796.
    • (2003) Nature , vol.426 , pp. 789-796
  • 61
    • 0028301661 scopus 로고
    • A class of tests for linkage using affected pedigree members
    • WHITTEMORE, A. S. and HALPERN, J. (1994). A class of tests for linkage using affected pedigree members. Biometrics 50 118-127.
    • (1994) Biometrics , vol.50 , pp. 118-127
    • WHITTEMORE, A.S.1    HALPERN, J.2
  • 62
    • 59349121602 scopus 로고    scopus 로고
    • Some aspects of the history of Bayesian information processing. Technical report, The Graduate School of Business, Univ. Chicago
    • ZELLNER, A. (2003). Some aspects of the history of Bayesian information processing. Technical report, The Graduate School of Business, Univ. Chicago.
    • (2003)
    • ZELLNER, A.1
  • 63
    • 15544365509 scopus 로고    scopus 로고
    • Coalescent-based association mapping and fine mapping of complex trait loci
    • ZÖLLNER, S. and PRITCHARD, J. K. (2005). Coalescent-based association mapping and fine mapping of complex trait loci. Genetics 169 1071-1092.
    • (2005) Genetics , vol.169 , pp. 1071-1092
    • ZÖLLNER, S.1    PRITCHARD, J.K.2


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