What is a statistical model?
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This paper addresses two closely related questions, "What is a statistical model?" and "What is a parameter?" The notions that a model must "make sense," and that a parameter must "have a well-defined meaning" are deeply ingrained in applied statistical work, reasonably well understood at an instinctive level, but absent from most formal theories of modelling and inference. In this paper, these concepts are defined in algebraic terms, using morphisms, functors and natural transformations. It is argued that inference on the basis of a model is not possible unless the model admits a natural extension that includes the domain for which inference is required. For example, prediction requires that the domain include all future units, subjects or time points. Although it is usually not made explicit, every sensible statistical model admits such an extension. Examples are given to show why such an extension is necessary and why a formal theory is required. In the definition of a subparameter, it is shown that certain parameter functions are natural and others are not. Inference is meaningful only for natural parameters. This distinction has important consequences for the construction of prior distributions and also helps to resolve a controversy concerning the Box-Cox model.
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Functoriality has a role to play in the study of point cloud data, as suggested in [46].
“We argue that, as suggested in [46], it has a role to play in the study of point cloud data as well, and we give two illustrations of how this could happen, within the context of clustering.”
From Topology and data (2009) · cites this paper as [46]
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Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013) · doi:10.1201/b16018 · Cited by 27,276 · see citing works
(2005) · Springer eBooks · doi:10.1007/0-387-27255-0_9 · Cited by 20,333 · see citing works
McCullagh, P., & Nelder, J. A. (1989) · doi:10.1007/978-1-4899-3242-6 · Cited by 16,836 · see citing works
Self-citationAn Analysis of Transformations
Box, G. E. P., & Cox, D. R. (1964) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1964.tb00553.x · Cited by 15,059 · see citing works
Jeffreys, H., Moran, P. A. P., & Chatfield, C. (1922) · Nature · doi:10.1038/109132a0 · Cited by 7,837 · see citing works
Statistical Decision Theory and Bayesian Analysis
Berger, J. O. (1985) · Springer Series in Statistics · doi:10.1007/978-1-4757-4286-2 · Cited by 7,722 · see citing works
Nelder, J. A., & Wedderburn, R. W. M. (1972) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2344614 · Cited by 7,321 · see citing works
Spatial Interaction and the Statistical Analysis of Lattice Systems
Besag, J. (1974) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1974.tb00999.x · Cited by 6,067 · see citing works
Statistics and Causal Inference
Holland, P. W. (1986) · Journal of the American Statistical Association · doi:10.1080/01621459.1986.10478354 · Cited by 5,293 · see citing works
Regression Models for Ordinal Data
McCullagh, P. (1980) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1980.tb01109.x · Cited by 4,453 · see citing works
Self-citationStatistical Modeling: The Two Cultures (with comments and a rejoinder by the author)
Breiman, L. (2001) · Statistical Science · doi:10.1214/ss/1009213726 · Cited by 4,340 · see citing works
Bayesian image restoration, with two applications in spatial statistics
Besag, J. E., York, J. C., & Molli�, A. (1991) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf00116466 · Cited by 4,218 · see citing works
Ziegel, E. R., Lehmann, E. L., & Casella, G. (1999) · Technometrics · doi:10.2307/1270597 · Cited by 4,203 · see citing works
On the mathematical foundations of theoretical statistics
Fisher, R. A. (1922) · Philosophical Transactions of the Royal Society of London Series A Containing Papers of a Mathematical or Physical Character · doi:10.1098/rsta.1922.0009 · Cited by 4,055 · see citing works
Cox, D. R., & Hinkley, D. V. (1974) · doi:10.1007/978-1-4899-2887-0 · Cited by 3,089 · see citing works
The Feynman Lectures on Physics
Feynman, R. P., Leighton, R. B., Sands, M., & Treiman, S. B. (1964) · Physics Today · doi:10.1063/1.3051743 · Cited by 2,944 · see citing works
Probability and Random Processes
Grimmett, G. 1., & Stirzaker, D. (2004) · Elsevier eBooks · doi:10.1016/b978-0-12-172651-5.x5000-3 · Cited by 2,587 · see citing works
Bayesian inference for causal effects: The role of randomization
Rubin, D. B. (1978) · The Annals of Statistics · doi:10.1214/aos/1176344064 · Cited by 2,503 · see citing works
Bernardo, J. M., & Smith, A. F. M. (1994) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316870 · Cited by 2,178 · see citing works
An analysis of transformations (with discussion)
Box, G. E. P. (1964) · Journal of the Royal Statistical Society Series A (Statistics in Society) · Cited by 1,891 · see citing works
Chilès, J., & Delfiner, P. (1999) · Wiley series in probability and statistics · doi:10.1002/9780470316993 · Cited by 1,849 · see citing works
Produits tensoriels topologiques et espaces nucléaires
Grothendieck, A. (1955) · Memoirs of the American Mathematical Society · doi:10.1090/memo/0016 · Cited by 1,788 · see citing works
Generalized linear models. 2nd ed.
McCullagh, P., & Nelder, J. (1993) · Journal of the American Statistical Association · doi:10.2307/2290358 · Cited by 1,581 · see citing works
Self-citationStatistical Analysis of Non-Lattice Data
Besag, J. (1975) · The Statistician · doi:10.2307/2987782 · Cited by 1,559 · see citing works
ON STATIONARY PROCESSES IN THE PLANE
Whittle, P. J. L. (1954) · Biometrika · doi:10.1093/biomet/41.3-4.434 · Cited by 1,503 · see citing works
Group representations in probability and statistics
Diaconis, P. (1988) · doi:10.1214/lnms/1215467407 · Cited by 1,381 · see citing works
Parameter Orthogonality and Approximate Conditional Inference
Cox, D. R., & Reid, N. M. (1987) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1987.tb01422.x · Cited by 1,370 · see citing works
Lehmann, E. L. (1983) · Springer eBooks · doi:10.1007/978-1-4757-2769-2 · Cited by 1,357 · see citing works
(1958) · Medical Entomology and Zoology · Cited by 1,059 · see citing works
Furstenberg, H. (1963) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1963-0163345-0 · Cited by 950 · see citing works
Bayesian Computation and Stochastic Systems
Besag, J. E., Green, P., Higdon, D., & Mengersen, K. L. (1995) · Statistical Science · doi:10.1214/ss/1177010123 · Cited by 943 · see citing works
Simple Models for the Analysis of Association in Cross-Classifications Having Ordered Categories
Goodman, L. A. (1979) · Journal of the American Statistical Association · doi:10.1080/01621459.1979.10481650 · Cited by 840 · see citing works
On conditional and intrinsic autoregressions
BESAG, J., & KOOPERBERG, C. (1995) · Biometrika · doi:10.1093/biomet/82.4.733 · Cited by 732 · see citing works
Matérn, B. (1986) · Lecture notes in statistics · doi:10.1007/978-1-4615-7892-5 · Cited by 660 · see citing works
An empirical law describing heterogeneity in the yields of agricultural crops
Smith, H. (1938) · The Journal of Agricultural Science · doi:10.1017/s0021859600050516 · Cited by 526 · see citing works
An Analysis of Transformations Revisited
Bickel, P. J., & Doksum, K. A. (1981) · Journal of the American Statistical Association · doi:10.1080/01621459.1981.10477649 · Cited by 524 · see citing works
Barndorff-Nielsen, O. E., & Cox, D. R. (2017) · Routledge eBooks · doi:10.1201/9780203750940 · Cited by 494 · see citing works
A Class of Bivariate Distributions
Plackett, R. L. (1965) · Journal of the American Statistical Association · doi:10.1080/01621459.1965.10480807 · Cited by 492 · see citing works
Randomness and degrees of irregularity.
Pincus, S. M., & Singer, B. H. (1996) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.93.5.2083 · Cited by 483 · see citing works
Barndorff-Nielsen, O. E., & Cox, D. R. (1994) · Springer eBooks · doi:10.1007/978-1-4899-3210-5 · Cited by 473 · see citing works
Kingmán, J. F. C. (1992) · doi:10.1093/oso/9780198536932.001.0001 · Cited by 446 · see citing works
Representations for partially exchangeable arrays of random variables
Aldous, D. J. (1981) · Journal of Multivariate Analysis · doi:10.1016/0047-259x(81)90099-3 · Cited by 442 · see citing works
Analysis of Designed Experiments with Complex Aliasing
Hamada, M. S., & Wu, C. (1992) · Journal of Quality Technology · doi:10.1080/00224065.1992.11979383 · Cited by 363 · see citing works
Fraser, D. A. S. (1968) · Medical Entomology and Zoology · Cited by 355 · see citing works
A Reformulation of Linear Models
Nelder, J. A. (1977) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2344517 · Cited by 338 · see citing works
Probabilities on Algebraic Structures.
Loynes, R. M., & Grenander, U. (1964) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2344022 · Cited by 325 · see citing works
Marginalization Paradoxes in Bayesian and Structural Inference
Dawid, A. P., Stone, M., & Zidek, J. V. (1973) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1973.tb00952.x · Cited by 296 · see citing works
Arbuthnot, J. (1710) · Philosophical Transactions of the Royal Society of London · doi:10.1098/rstl.1710.0011 · Cited by 290 · see citing works
Rubin, D. B. (1986) · Journal of the American Statistical Association · doi:10.1080/01621459.1986.10478355 · Cited by 289 · see citing works
An Analysis of Transformations Revisited, Rebutted
Box, G. E. P., & Cox, D. R. (1982) · Journal of the American Statistical Association · doi:10.2307/2287791 · Cited by 281 · see citing works
Practical Data Analysis for Designed Experiments
Marx, B. D., & Yandell, B. S. (1998) · Journal of the American Statistical Association · doi:10.2307/2669639 · Cited by 278 · see citing works
Andrews, D. F., & Herzberg, A. M. (1985) · Springer series in statistics · doi:10.1007/978-1-4612-5098-2 · Cited by 265 · see citing works
Practical Data Analysis for Designed Experiments
Yandell, B. S. (1997) · Springer eBooks · doi:10.1007/978-1-4899-3035-4 · Cited by 265 · see citing works
Statistical Analysis of Field Experiments Using Neighbouring Plots
Besag, J., & Kempton, R. (1986) · Biometrics · doi:10.2307/2531047 · Cited by 246 · see citing works
Sufficiency and Approximate Sufficiency
Cam, L. L. (1964) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177700372 · Cited by 244 · see citing works
Fitting Gaussian Markov Random Fields to Gaussian Fields
Rue, H., & Tjelmeland, H. (2001) · Scandinavian Journal of Statistics · doi:10.1111/1467-9469.00058 · Cited by 222 · see citing works
Nearest Neighbour Models in the Analysis of Field Experiments
Bartlett, M. S. (1978) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1978.tb01657.x · Cited by 214 · see citing works
Goodman, L. A. (1981) · Journal of the American Statistical Association · doi:10.1080/01621459.1981.10477651 · Cited by 213 · see citing works
The Experimental Error of Field Trials
Mercer, W. B., & Hall, A. D. (1911) · The Journal of Agricultural Science · doi:10.1017/s002185960000160x · Cited by 204 · see citing works
The Analysis of Transformed Data
HINKLEY, D. V., & Runger, G. C. (1984) · Journal of the American Statistical Association · doi:10.1080/01621459.1984.10478045 · Cited by 200 · see citing works
Not all (possibly) “random” sequences are created equal
Pincus, S. M., & Kalman, R. E. (1997) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.94.8.3513 · Cited by 194 · see citing works
Bayesian Analysis of Agricultural Field Experiments
Besag, J., & Higdon, D. (1999) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00201 · Cited by 183 · see citing works
Role of Models in Statistical Analysis
Cox, D. R. (1990) · Statistical Science · doi:10.1214/ss/1177012165 · Cited by 181 · see citing works
Simple Models for the Analysis of Association in Cross-Classifications having Ordered Categories
Goodman, L. A. (1979) · Journal of the American Statistical Association · doi:10.2307/2286971 · Cited by 178 · see citing works
Cox, D. R., & Snell, E. J. (1981) · Springer eBooks · doi:10.1007/978-94-009-5838-8 · Cited by 143 · see citing works
SAS System for Linear Models (3rd ed.)
Ziegel, E. R. (1992) · Technometrics · doi:10.1080/00401706.1992.10484977 · Cited by 137 · see citing works
Topographic correlation, power-law covariance functions, and diffusion
Whittle, P. J. L. (1962) · Biometrika · doi:10.1093/biomet/49.3-4.305 · Cited by 134 · see citing works
Cartier, P. (2001) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-01-00913-2 · Cited by 127 · see citing works
Statistical issues in the analysis of disease mapping data
Pascutto, C., Wakefield, J. C., Best, N., Richardson, S. T., Bernardinelli, L., Staines, A. S., & Elliott, P. (2000) · Statistics in Medicine · doi:10.1002/1097-0258(20000915/30)19:17/18 · Cited by 123 · see citing works
Furstenberg, H. (1963) · Transactions of the American Mathematical Society · doi:10.2307/1993589 · Cited by 120 · see citing works
Homotopy theory in general categories
Huber, P. J. (1961) · Mathematische Annalen · doi:10.1007/bf01396534 · Cited by 114 · see citing works
An Analysis of Transformations Revisited
Bickel, P. J., & Doksum, K. A. (1981) · Journal of the American Statistical Association · doi:10.2307/2287831 · Cited by 111 · see citing works
The mathematics of perfect shuffles
Diaconis, P. W., Graham, R. L., & Kantor, W. M. (1983) · Advances in Applied Mathematics · doi:10.1016/0196-8858(83)90009-x · Cited by 105 · see citing works
A Unified Approach to Design of Experiments
Bailey, R. A. (1981) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2981920 · Cited by 104 · see citing works
Fiducial Theory and Invariant Estimation
Hora, R., & Buehler, R. J. (1966) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177699458 · Cited by 102 · see citing works
Extremal Families and Systems of Sufficient Statistics
Lauritzen, S. (1988) · Lecture notes in statistics · doi:10.1007/978-1-4612-1023-8 · Cited by 98 · see citing works
A Class of Bivariate Distributions
Plackett, R. L. (1965) · Journal of the American Statistical Association · doi:10.2307/2282685 · Cited by 96 · see citing works
MODELS FOR TWO-DIMENSIONAL STATIONARY STOCHASTIC PROCESSES
Heine, V. (1955) · Biometrika · doi:10.1093/biomet/42.1-2.170 · Cited by 90 · see citing works
Intrinsic autoregressions and related models on the two-dimensional lattice
Künsch, H. R. (1987) · Biometrika · doi:10.1093/biomet/74.3.517 · Cited by 87 · see citing works
Goodman, L. A. (1981) · Journal of the American Statistical Association · doi:10.2307/2287833 · Cited by 83 · see citing works
Möbius transformation and Cauchy parameter estimation
McCullagh, P. J. (1996) · The Annals of Statistics · doi:10.1214/aos/1032894465 · Cited by 79 · see citing works
Self-citationOne hundred years of the design of experiments on and off the pages of Biometrika
Atkinson, A. C. (2001) · Biometrika · doi:10.1093/biomet/88.1.53 · Cited by 73 · see citing works
On random sequences with spherical symmetry
Kingmán, J. F. C. (1972) · Biometrika · doi:10.1093/biomet/59.2.492 · Cited by 68 · see citing works
Present Position and Potential Developments: Some Personal Views
Smith, A. F. M. (1984) · Cited by 63 · see citing works
Strata for Randomized Experiments
Bailey, R. A. (1991) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1991.tb01808.x · Cited by 60 · see citing works
Detection of Ridge and Furrow Pattern by Spectral Analysis of Crop Yield
McBratney, A. B., & Webster, R. (1981) · International Statistical Review · doi:10.2307/1403036 · Cited by 59 · see citing works
The Analysis of Transformed Data
HINKLEY, D. V., & Runger, G. C. (1984) · Journal of the American Statistical Association · doi:10.2307/2288264 · Cited by 56 · see citing works
AN ESSAY TOWARDS A DYNAMICAL THEORY OF CRYSTALLINE REFLEXION AND REFRACTION
MacCullagh, J. (1972) · Elsevier eBooks · doi:10.1016/b978-0-08-015674-3.50015-4 · Cited by 55 · see citing works
Conditional Inference and Cauchy Models
McCullagh, P. J. (1992) · Biometrika · doi:10.1093/biomet/79.2.247 · Cited by 48 · see citing works
Self-citationBox‐Cox transformations in linear models: Large sample theory and tests of normality
Chen, G., Lockhart, R., & Stephens, M. A. (2002) · Canadian Journal of Statistics · doi:10.2307/3315946 · Cited by 45 · see citing works
Nonlinear Regression, Quasi Likelihood, and Overdispersion in Generalized Linear Models
Tjur, T. (1998) · The American Statistician · doi:10.1080/00031305.1998.10480567 · Cited by 41 · see citing works
Present Position and Potential Developments: Some Personal Views: Bayesian Statistics
Smith, A. F. M. (1984) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2981680 · Cited by 41 · see citing works
Molière (2023) · BCU · doi:10.22005/bcu.294698 · Cited by 34 · see citing works
Local versus global association for bivariate ordered responses
Dale, J. R. (1984) · Biometrika · doi:10.1093/biomet/71.3.507 · Cited by 33 · see citing works
An examination of Fairfield Smith's law of environmental variation
Pearce, S. C. (1976) · The Journal of Agricultural Science · doi:10.1017/s0021859600026538 · Cited by 30 · see citing works
Probabilities on algebraic structures
Grenander, U. (1968) · Cited by 26 · see citing works
Local Asymptotic Normality of Ranks and Covariates in Transformation Models
Bickel, P. J., & Ritov, Y. (1997) · Springer eBooks · doi:10.1007/978-1-4612-1880-7_3 · Cited by 24 · see citing works
Invariance and Factorial Models
McCullagh, P. J. (2000) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00229 · Cited by 19 · see citing works
Self-citationA Black Box or a Comprehensive Model
Fraser, D. A. S. (1968) · Technometrics · doi:10.1080/00401706.1968.10490557 · Cited by 19 · see citing works
Nonlinear Regression, Quasi Likelihood, and Overdispersion in Generalized Linear Models
Tjur, T. (1998) · The American Statistician · doi:10.2307/2685928 · Cited by 12 · see citing works
Reduction of regression models under symmetry
Helland, I. S. (2001) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/287/04783 · Cited by 10 · see citing works
Statistical inference under a fixed symmetry group
Helland, I. S. (1998) · NORA - Norwegian Open Research Archives · Cited by 10 · see citing works
Note on the Surface of Constant Association
Pearson, K. (1913) · Biometrika · doi:10.2307/2331905 · Cited by 7 · see citing works
Quotient spaces and statistical models
McCullagh, P. J. (1999) · Canadian Journal of Statistics · doi:10.2307/3316103 · Cited by 6 · see citing works
Self-citationA Black Box or a Comprehensive Model
Fraser, D. A. S. (1968) · Technometrics · doi:10.2307/1267040 · Cited by 4 · see citing works
Cox, D. R. (1986) · Journal of the American Statistical Association · doi:10.1080/01621459.1986.10478356 · Cited by 4 · see citing works
Quantum Mechanics from Symmetry and Statistical Modeling
Helland, I. S. (1999) · International Journal of Theoretical Physics · doi:10.1023/a:1026676913271 · Cited by 3 · see citing works
The Research of Jack Kiefer Outside the Area of Experimental Design
Brown, L. D. (1984) · The Annals of Statistics · doi:10.1214/aos/1176346495 · Cited by 2 · see citing works
Quantum Theory from Symmetries in a General Statistical Parameter SpacePreprint
Helland, I. S. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9908076 · Cited by 1 · see citing works
Present Position and Potential Developments: Some Personal Views: Probability and Random Processes
Kingmán, J. F. C. (1984) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2981679 · Cited by 1 · see citing works
Flagged first, then by citations
Research works printed but not linked: 4
- ANDREWS, D. F. and HERZBERG, A. (1985). Data. Springer, New York.
- BILLINGSLEY, P. (1986). Probability and Measure, 2nd ed. Wiley, New York.
- DE FINETTI, B. (1975). Theory of Probability 2. Wiley, New York.
- MAC LANE, S. (1998). Categories for the Working Mathematician, 2nd ed. Springer, New York.
Cited by
Sorted by citations
Carlsson, G. (2009) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-09-01249-x · Cited by 2,302 · see citing works
Machine Learning: New Ideas and Tools in Environmental Science and Engineering
Zhong, S., Zhang, K., Bagheri, M., Burken, J. G., Gu, A. Z., Li, B., Ma, X., Marrone, B. L., Ren, Z. J., Schrier, J., et al. (2021) · Environmental Science & Technology · doi:10.1021/acs.est.1c01339 · Cited by 974 · see citing works
The Focused Information Criterion
Claeskens, G., & Hjort, N. L. (2003) · Journal of the American Statistical Association · doi:10.1198/016214503000000819 · Cited by 381 · see citing works
A Comprehensive Review on Generative AI for Education
Mittal, U., Sai, S., Chamola, V., & Sangwan, D. (2024) · IEEE Access · doi:10.1109/access.2024.3468368 · Cited by 383 · see citing works
Maximum Likelihood Estimation in Semiparametric Regression Models with Censored Data
Zeng, D., & Lin, D. Y. (2007) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1369-7412.2007.00606.x · Cited by 315 · see citing works
Fisher Lecture: Dimension Reduction in Regression
Cook, R. D. (2007) · Statistical Science · doi:10.1214/088342306000000682 · Cited by 287 · see citing works
Q-statistic and T2-statistic PCA-based measures for damage assessment in structures
Delgado, L. E. M., Rodellar, J., Fernández, A., & Güemes, A. (2010) · Structural Health Monitoring · doi:10.1177/1475921710388972 · Cited by 240 · see citing works
A review on lubricant condition monitoring information analysis for maintenance decision support
Wakiru, J., Pintelon, L. M., Muchiri, P., & Chemweno, P. K. (2018) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2018.08.039 · Cited by 207 · see citing works
On Quantum Statistical Inference
Barndorff-Nielsen, O. E., Gill, R. D., & Jupp, P. E. (2003) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00415 · Cited by 197 · see citing works
The Box–Cox Transformation: Review and Extensions
Atkinson, A. C., Riani, M., & Corbellini, A. (2021) · Statistical Science · doi:10.1214/20-sts778 · Cited by 187 · see citing works
Spatial occupancy models for large data sets
Johnson, D. S., Conn, P. B., Hooten, M. B., Ray, J. C., & Pond, B. A. (2012) · Ecology · doi:10.1890/12-0564.1 · Cited by 171 · see citing works
Fritz, T. (2020) · Advances in Mathematics · doi:10.1016/j.aim.2020.107239 · Cited by 143 · see citing works
Interaction Screening for Ultrahigh-Dimensional Data
Hao, N., & Zhang, H. H. (2014) · Journal of the American Statistical Association · doi:10.1080/01621459.2014.881741 · Cited by 133 · see citing works
A Theory of Statistical Models for Monte Carlo Integration
Kong, A., McCullagh, P. J., Meng, X., Nicolae, D. L., & Tan, Z. (2003) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00404 · Cited by 124 · see citing works
“These are fully fledged statistical models in the sense of the definition given by McCullagh (2002), no more or no less artificial than any other statistical model.”
BackgroundSelf-citation2.2 Nine Considerations for Constructing and Running Geomorphological Models
Malamud, B. D., & Baas, A. C. W. (2013) · Elsevier eBooks · doi:10.1016/b978-0-12-374739-6.00024-5 · Cited by 123 · see citing works
Adaptive dropout for high-dimensional expensive multiobjective optimization
Lin, J., He, C., & Cheng, R. (2021) · Complex & Intelligent Systems · doi:10.1007/s40747-021-00362-5 · Cited by 109 · see citing works
Structured variable selection and estimation
Yuan, M., Joseph, V. R., & Zou, H. (2009) · The Annals of Applied Statistics · doi:10.1214/09-aoas254 · Cited by 109 · see citing works
“Interested readers are also referred to McCullagh (2002) for a rigorous discussion about what criteria a sensible statistical model should obey.”
BackgroundZobel‐Roos, S., Schmidt, A., Mestmäcker, F., Mouellef, M., Huter, M., Uhlenbrock, L., Kornecki, M., Lohmann, L., Ditz, R., & Strube, J. (2019) · Processes · doi:10.3390/pr7020094 · Cited by 87 · see citing works
“Statistical models: Are part of the evaluation of experimental data generated according to DoE experimental plans, which could be statistically evaluated according to accuracy and prediction by aid of statistical models [51,68].”
MethodMalouf, R. (2010) · doi:10.1002/9781444324044.ch5 · Cited by 86 · see citing works
Thinking avant la lettre: A Review of 4E Cognition
Carney, J. (2020) · Evolutionary Studies in Imaginative Culture · doi:10.26613/esic.4.1.172 · Cited by 82 · see citing works
Fractional Gaussian fields: A survey
Lodhia, A., Sheffield⋆, S., Sun, X., & Watson, S. S. (2016) · Probability Surveys · doi:10.1214/14-ps243 · Cited by 70 · see citing works
On Some Principles of Statistical Inference
Reid, N. M., & Cox, D. R. (2014) · International Statistical Review · doi:10.1111/insr.12067 · Cited by 67 · see citing works
“McCullagh (2002) emphasises the importance of careful delineation of design, covariate and treatment variables as an essential part of the correct specification of a statistical model.”
BackgroundGaussian Random Field Models for Spatial Data
Haran, M. (2011) · Chapman & Hall/CRC eBooks · doi:10.1201/b10905-19 · Cited by 66 · see citing works
3D object recognition and classification: a systematic literature review
Carvalho, L. E., & von Wangenheim, A. (2019) · Pattern Analysis and Applications · doi:10.1007/s10044-019-00804-4 · Cited by 61 · see citing works
“– Statistical models: this is a type of mathematical model that embeds a set of assumptions related to a sampled data, often representing, in considerably idealized form, the data-generating process [192].”
BackgroundScaling Multidimensional Inference for Structured Gaussian Processes
Gilboa, E., Saatçi, Y., & Cunningham, J. P. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.192 · Cited by 53 · see citing works
Recovering dynamic networks in big static datasets
Wu, R., & Jiang, L. (2021) · Physics Reports · doi:10.1016/j.physrep.2021.01.003 · Cited by 53 · see citing works
Likelihood-Free Parameter Estimation with Neural Bayes Estimators
Sainsbury-Dale, M., Zammit‐Mangion, A., & Huser, R. (2023) · The American Statistician · doi:10.1080/00031305.2023.2249522 · Cited by 53 · see citing works
“A parametric statistical model is a set of probability distributions on a sample space S , where the probability distributions are parameterized via some p -dimensional parameter vector θ on a parameter space (cid:2) (McCullagh 2002).”
MethodOn the Unidentifiability of the Fixed-Effects 3PL Model
Martı́n, E. S., González, J., & Tuerlinckx, F. (2014) · Psychometrika · doi:10.1007/s11336-014-9404-2 · Cited by 50 · see citing works
On the Well-posedness of Bayesian Inverse Problems
Latz, J. (2020) · SIAM/ASA Journal on Uncertainty Quantification · doi:10.1137/19m1247176 · Cited by 49 · see citing works
PLS-SEM and reflective constructs: A response to recent criticism and a constructive path forward
Guenther, P., Guenther, M., Ringle, C. M., Zaefarian, G., & Cartwright, S. (2025) · Industrial Marketing Management · doi:10.1016/j.indmarman.2025.05.003 · Cited by 61 · see citing works
Römer, U., Hartmann, S., Tröger, J., Anton, D., Wessels, H., Flaschel, M., & Lorenzis, L. D. (2024) · Applied Mechanics Reviews · doi:10.1115/1.4066118 · Cited by 48 · see citing works
Box‐Cox transformations in linear models: Large sample theory and tests of normality
Chen, G., Lockhart, R., & Stephens, M. A. (2002) · Canadian Journal of Statistics · doi:10.2307/3315946 · Cited by 45 · see citing works
False confidence, non-additive beliefs, and valid statistical inference
Martin, R. (2019) · International Journal of Approximate Reasoning · doi:10.1016/j.ijar.2019.06.005 · Cited by 48 · see citing works
“ides the difficulty and importance of specifying a good model. General discussion and guidelines on modeling are given, e.g., in Cox and Hinkley (1974), Box (1980), and McCullagh and Nelder (1983), and McCullagh (2002) gives a more technical discussion. Here it will suffice to consider the model PX|θ, θ∈ Θ, as describing…”
Zwiernik, P. (2015) · Chapman & Hall/CRC eBooks · doi:10.1201/b18981-9 · Cited by 41 · see citing works
Philosophy of Probability and Statistical Modelling
Suárez, M. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108985826 · Cited by 40 · see citing works
Caffo, B. S., Peng, R. D., Dominici, F., Louis, T. A., & Zeger, S. L. (2011) · Chapman & Hall/CRC eBooks · doi:10.1201/b10905-21 · Cited by 38 · see citing works
A Note on High-Dimensional Linear Regression With Interactions
Hao, N., & Zhang, H. H. (2016) · The American Statistician · doi:10.1080/00031305.2016.1264311 · Cited by 37 · see citing works
Model Selection Using Information Theory and the MDL Principle
Stine, R. A. (2004) · Sociological Methods & Research · doi:10.1177/0049124103262064 · Cited by 37 · see citing works
Toward a Causal Interpretation of the Common Factor Model
van Bork, R., Wijsen, L. D., & Rhemtulla, M. (2017) · Disputatio · doi:10.1515/disp-2017-0019 · Cited by 34 · see citing works
Statistical Inference under Symmetry
Helland, I. S. (2004) · International Statistical Review · doi:10.1111/j.1751-5823.2004.tb00245.x · Cited by 34 · see citing works
Minimax Rates in Network Analysis: Graphon Estimation, Community Detection and Hypothesis Testing
Gao, C., & Ma, Z. (2020) · Statistical Science · doi:10.1214/19-sts736 · Cited by 33 · see citing works
Marmolejo‐Ramos, F., Tejo, M., Brabec, M., Kužílek, J., Joksimovíc, S., Kovanović, V., González, J., Kneib, T., Bühlmann, P., Kook, L., et al. (2022) · Wiley Interdisciplinary Reviews Data Mining and Knowledge Discovery · doi:10.1002/widm.1479 · Cited by 32 · see citing works
“From a strict statistical modeling viewpoint (McCullagh, 2002), GAMLSS are used to analyze nonlinear relationships between the distributions of outcomes and covariates (features, in ML parlance) and where the covariates' effects are additively weighted.”
MethodWakiru, J., Pintelon, L. M., Muchiri, P., & Chemweno, P. K. (2018) · International Journal of Production Economics · doi:10.1016/j.ijpe.2018.12.014 · Cited by 32 · see citing works
A causal theory of error scores.
van Bork, R., Rhemtulla, M., Sijtsma, K., & Borsboom, D. (2022) · Psychological Methods · doi:10.1037/met0000521 · Cited by 32 · see citing works
MEANINGFUL STATISTICAL MODEL FORMULATIONS FOR REPEATED MEASURES
Molenberghs, G., & Verbeke, G. N. (2004) · Lirias (KU Leuven) · Cited by 30 · see citing works
Evidence for conformal invariance of crop yields
McCullagh, P. J., & Clifford, D. J. (2006) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2006.1667 · Cited by 28 · see citing works
“The arguments leading to the conformal model (McCullagh 2002, p. 1307) are specific to planar processes, considered also as processes on the sphere by stereographic projection, but are not otherwise crop specific.”
BackgroundSelf-citationMultivariate skew-normal at linear mixed models for multi-outcome longitudinal data
Lin, T., & Wang, W. (2013) · Statistical Modelling · doi:10.1177/1471082x13480283 · Cited by 28 · see citing works
Sadeghieh, T., Waddell, L. A., Ng, V., Hall, A., & Sargeant, J. M. (2020) · PLoS ONE · doi:10.1371/journal.pone.0227678 · Cited by 28 · see citing works
Persistent Clustering and a Theorem of J. Kleinberg
Carlsson, G., & Memoli, F. (2008) · arXiv · doi:10.48550/arxiv.0808.2241 · Cited by 28 · see citing works
“In [ McC02 ], the idea of using categorical and functorial ideas in statistics has been proposed as a formalism for defining what is meant by statistical models.”
BackgroundCosta, R., Fraga, H., Malheiro, A. C., & Santos, J. A. (2015) · Ciência e técnica vitivinícola/Ciência e técnica vitivinícola · doi:10.1051/ctv/20153001029 · Cited by 27 · see citing works
Anh-Likelihood Method for Spatial Mixed Linear Models Based on Intrinsic Auto-Regressions
Dutta, S., & Mondal, D. (2014) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12084 · Cited by 25 · see citing works
“Whereas the subsequent works of McCullagh (2002), Besag (2002), Besag and Mondal (2005) and McCullagh and Clifford (2006) have provided new perspectives on spatial modelling via continuum random fields, Lee and Nelder (1996, 2001) and Lee et al. (2006) revived Henderson’s (1950, 1975) h-likelihood…”
BackgroundEdge exchangeable models for network dataPreprint
Crane, H., & Dempsey, W. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1603.04571 · Cited by 27 · see citing works
Design of genetic algorithms for topology control of unmanned vehicles
Sahin, C. S., Urrea, E., Uyar, M. Ü., Conner, M., Bertoli, G., & Pizzo, C. (2010) · International Journal of Applied Decision Sciences · doi:10.1504/ijads.2010.036100 · Cited by 26 · see citing works
“It is mathematically thought of as a pair of (X, P) where X = (x 1 , x 2 ,..., x n ) n is the number of observations is the set of possible observations and P is the set of possible probability distribution on X (McCullagh, 2002).”
BackgroundOlea, J. L. M., Ortoleva, P., Pai, M. M., & Prat, A. (2022) · The Quarterly Journal of Economics · doi:10.1093/qje/qjac015 · Cited by 26 · see citing works
Helland, I. S. (2021) · Springer eBooks · doi:10.1007/978-3-030-81923-1_2 · Cited by 26 · see citing works
Gradation of complexity and predictability of hydrological processes
Sang, Y., Singh, V. P., Wen, J., & Liu, C. (2015) · Journal of Geophysical Research Atmospheres · doi:10.1002/2014jd022844 · Cited by 26 · see citing works
“A statistical model is a tool for estimating probability distributions of potential outcomes; the random variation is usually based on fluctuations observed in historical data for a selected period using standard probabilistic techniques [McCullagh, 2002].”
MethodA framework for statistical network modelingPreprint
Crane, H., & Dempsey, W. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1509.08185 · Cited by 26 · see citing works
Chi-p distribution: characterization of the goodness of the fitting using Lp norms
Livadiotis, G. (2014) · Journal of Statistical Distributions and Applications · doi:10.1186/2195-5832-1-4 · Cited by 24 · see citing works
“Introduction The fitting of a given dataset f i σ f i N i¼1 to the values V if gNi¼1 of a statistical model V(X; α) in the domain X∈Dx⊆ℜ (McCullagh 2002; Adèr 2008), involves finding the optimal parameter value α = α* in α ∈ Dα ⊆ℜ that minimizes the total square deviations (TSD) between model and…”
Non-Gaussian Statistical Models and Their Applications
Ma, Z. (2011) · KTH Publication Database DiVA (KTH Royal Institute of Technology) · Cited by 24 · see citing works
A prior-free framework of coherent inference and its derivation of simple shrinkage estimators
Bickel, D. R., & Padilla, M. (2013) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2013.08.011 · Cited by 23 · see citing works
Identification of parametric Rasch-type models
Martı́n, E. S., & Rolin, J. (2012) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2012.06.014 · Cited by 23 · see citing works
Maclaren, O. J., & Nicholson, R. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1904.02826 · Cited by 23 · see citing works
Best Practice Guidelines for Publishing Rigorous Research in Counseling
Giordano, A. L., Schmit, M. K., & Schmit, E. L. (2021) · Journal of Counseling & Development · doi:10.1002/jcad.12360 · Cited by 21 · see citing works
Informal statistical models and modeling
Dvir, M., & Ben‐Zvi, D. (2021) · Mathematical Thinking and Learning · doi:10.1080/10986065.2021.1925842 · Cited by 21 · see citing works
“Formally, a statistical model is often viewed as a set of probability distributions or a function allocating any specific set of possible parameters to a probability distribution (McCullagh, 2002), meaning it depicts the likelihood of any possible outcome, resulting from specific conditions.”
BackgroundStackelberg Game Theory-Based Optimization of High-Order Robust Control for Fuzzy Dynamical Systems
Li, C., Chen, Y., Zhao, H., & Sun, H. (2020) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2020.3018139 · Cited by 20 · see citing works
Schwade, F. (2021) · Decision Support Systems · doi:10.1016/j.dss.2021.113587 · Cited by 20 · see citing works
On the Accuracy of the Sine Power Lomax Model for Data Fitting
Nagarjuna, V. B. V., Vardhan, R. V., & Chesneau, C. (2021) · Modelling—International Open Access Journal of Modelling in Engineering Science · doi:10.3390/modelling2010005 · Cited by 20 · see citing works
“This theme is fully developed in [1,2], among others.”
BackgroundFoliations-Webs-Hessian Geometry-Information Geometry-Entropy and Cohomology
Boyom, M. N. (2016) · Entropy · doi:10.3390/e18120433 · Cited by 19 · see citing works
Conditional independence of multivariate binary data with an application in caries research
García‐Zattera, M. J., Jara, A., Lesaffre, E. M. E. H., & Declerck, D. (2006) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2006.11.021 · Cited by 19 · see citing works
Taming singularities of the quantum Fisher information
Goldberg, A. Z., Romero, J. L., Sanz, Á. S., & Sánchez-Soto, L. L. (2021) · International Journal of Quantum Information · doi:10.1142/s0219749921400049 · Cited by 18 · see citing works
Prediction of treatment outcome in clinical trials under a personalized medicine perspective
Berchialla, P., Lanera, C., Sciannameo, V., Gregori, D., & Baldi, I. (2022) · Scientific Reports · doi:10.1038/s41598-022-07801-4 · Cited by 19 · see citing works
“A Statistical Model (SM) is a family of probability distributions, which embody the data generating mechanism process, indexed by a set of parameters 19 .”
BackgroundBayesian Models for Astrophysical Data
Hilbe, J. M., de Souza, R. S., & Ishida, É. E. O. (2017) · Cambridge University Press eBooks · doi:10.1017/cbo9781316459515 · Cited by 67 · see citing works
Algebraic statistical modelsPreprint
Drton, M., & Sullivant, S. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0703609 · Cited by 18 · see citing works
A review of failure prognostics for predictive maintenance of offshore wind turbines
Zhang, W., Vatn, J., & Rasheed, A. (2022) · Journal of Physics Conference Series · doi:10.1088/1742-6596/2362/1/012043 · Cited by 17 · see citing works
Students’ construction and use of statistical models: a socio-critical perspective
Zapata‐Cardona, L. (2018) · ZDM · doi:10.1007/s11858-018-0967-8 · Cited by 17 · see citing works
What is the Purpose of Statistical Modelling?
Hand, D. J. (2019) · Harvard Data Science Review · doi:10.1162/99608f92.4a85af74 · Cited by 15 · see citing works
Three enigmatic examples and inference from likelihood
Fraser, D. A. S., Wong, A. C. M., & Sun, Y. (2009) · Canadian Journal of Statistics · doi:10.1002/cjs.10008 · Cited by 15 · see citing works
“In the discussion, McCullagh raised questions whether the choice β/σ was “physically meaningful” and mentioned the notion of a natural subparameter (McCullagh, 2002); the resulting claim was that β/σ did not represent a characteristic of the context being investigated and was rather an artefact of…”
BackgroundResultProbability, Information and Statistical Physics
Kuzemsky, A. L. (2015) · International Journal of Theoretical Physics · doi:10.1007/s10773-015-2779-8 · Cited by 15 · see citing works
Small‐scale Inference: Empirical Bayes and Confidence Methods for as Few as a Single Comparison
Bickel, D. R. (2014) · International Statistical Review · doi:10.1111/insr.12064 · Cited by 14 · see citing works
Extended statistical modeling under symmetry; the link toward quantum mechanics
Helland, I. S. (2006) · The Annals of Statistics · doi:10.1214/009053605000000868 · Cited by 20 · see citing works
A Monad for Probabilistic Point Processes
Dash, S., & Staton, S. (2021) · Electronic Proceedings in Theoretical Computer Science · doi:10.4204/eptcs.333.2 · Cited by 14 · see citing works
“[6, 8, 9, 10, 11, 18, 19, 23, 27]).”
On Some Assumptions of the Null Hypothesis Statistical Testing
Patriota, A. G. (2016) · Educational and Psychological Measurement · doi:10.1177/0013164416667979 · Cited by 14 · see citing works
Discussion on the Paper by Barndorff-Nielsen, Gill and Jupp
Accardi, L., Belavkin, V. P., Kent, J. T., Brody, D. C., Bingham, N. H., Frey, J. G., Helland, I. S., Larsson, J.-Å., Majumdar, N., Minozzo, M., et al. (2003) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00416 · Cited by 14 · see citing works
“This has alreadybeenproposed for completely different reasons by McCullagh (2002).”
BackgroundUncertainty Quantification for In Silico Chemistry
Frömbgen, T., Surzhikova, E., Dölz, J., Proppe, J., Kirchner, B., & Jacob, C. R. (2026) · Chemical Reviews · doi:10.1021/acs.chemrev.5c00931 · Cited by 14 · see citing works
Nzekwe, C. J., Kim, S., & Mostafa, S. A. (2024) · Journal of Data Science · doi:10.6339/24-jds1127 · Cited by 13 · see citing works
Three Strategies for the Critical Use of Statistical Methods in Psychological Research
Campitelli, G., Macbeth, G., Ospina, R., & Marmolejo‐Ramos, F. (2016) · Educational and Psychological Measurement · doi:10.1177/0013164416668234 · Cited by 13 · see citing works
Stehlík, M., Aguirre, P., Girard, S., Jordanova, P. K., Kiseľák, J., Torres, S., Sadovský, Z., & Rivera, A. (2016) · Ecological Complexity · doi:10.1016/j.ecocom.2016.11.002 · Cited by 13 · see citing works
Statistical Properties of an Unassisted Image Quality Index for SAR Imagery
Gómez, L., Ospina, R., & Frery, A. C. (2019) · Remote Sensing · doi:10.3390/rs11040385 · Cited by 12 · see citing works
“Albeit an expressive estimator, the distribution of M is not known and, therefore, cannot be used as a statistical model [42] for prediction and testing [43,44].”
MethodWhen should modes of inference disagree? Some simple but challenging examples
Fraser, D. A. S., Reid, N. M., & Lin, W. (2018) · The Annals of Applied Statistics · doi:10.1214/18-aoas1160sf · Cited by 12 · see citing works
Lew, M. J. (2019) · Handbook of experimental pharmacology · doi:10.1007/164_2019_286 · Cited by 12 · see citing works
“tion of errors in his observations, and about facts that are assumed to be known for the purposes of statistical calculations. |[Colquhoun, 1971, p. v] Statistical models can take a variety of forms [McCullagh, 2002], but the model for the familiar Student’s t-test for independent samples is reasonably representative.…”
BackgroundSensitivity of Regular EstimatorsPreprint
Mukhin, Y. (2018) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.1805.08883 · Cited by 12 · see citing works
Revisiting the Large n (Sample Size) Problem: How to Avert Spurious Significance Results
Spanos, A. (2023) · Stats · doi:10.3390/stats6040081 · Cited by 11 · see citing works
González, J., & von Davier, M. (2013) · Journal of Educational Measurement · doi:10.1111/jedm.12018 · Cited by 11 · see citing works
Crane, H. (2015) · Bernoulli · doi:10.3150/14-bej617 · Cited by 11 · see citing works
A frequentist framework of inductive reasoningPreprint
Bickel, D. R. (2016) · Cited by 11 · see citing works
Noventa, S., Ye, S., Kelava, A., & Spoto, A. (2024) · Psychometrika · doi:10.1007/s11336-024-09950-z · Cited by 10 · see citing works
“A statistical model is identifiable if no two different sets of parameters values are observation-ally equivalent, i.e., they yield the same likelihood of the observed outcomes (see, e.g., Bamber and Van Santen, 2000; McCullagh, 2002, for a detailed introduction to the topic).”
BackgroundLinear Regression with Optimal Rotation
Livadiotis, G. (2019) · Stats · doi:10.3390/stats2040028 · Cited by 10 · see citing works
Manisera, M., & Zuccolotto, P. (2015) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2015.05.011 · Cited by 10 · see citing works
Multi-Party Inference and Uncongeniality
Meng, X. (2011) · International Encyclopedia of Statistical Science · doi:10.1007/978-3-642-04898-2_381 · Cited by 10 · see citing works
General Fitting Methods Based on Lq Norms and their Optimization
Livadiotis, G. (2020) · Stats · doi:10.3390/stats3010002 · Cited by 9 · see citing works
- Authors
- McCullagh, P.
- Affiliations
- University of Chicago (US)
- Corresponding author
- McCullagh, Peter
- ORCID
- McCullagh, Peter
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2002-10-01
- Volume
- 30
- Issue
- 5
- Pages
- 1225-1310
- ISSN
- 0090-5364 (ISSN-L)
- 2168-8966
- OpenAlex
- W2049954094
- Cited by
- 248
- References
- 103
- Citations by year
- 2026: 9 · 2025: 22 · 2024: 13 · 2023: 5 · 2022: 10 · 2021: 23 · 2020: 17 · 2019: 16 · 2018: 18 · 2017: 12 · 2016: 12 · 2015: 16 · 2014: 12 · 2013: 10 · 2012: 7
- FWCI
- 5.37
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Statistics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- CBS Research Portal (Copenhagen Business School) (submittedVersion)
- Funders
- National Science Foundation (0071726, 9705347)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- statistical models, parameters, natural parameters, morphisms, functors, natural transformation, model extension, prediction, prior distributions
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