Appendix P — References

P.1 Bibliography

Agresti, A. 2012. Categorical Data Analysis. Wiley Series in Probability and Statistics. Wiley.

Aldous, David. 1983. “Random Walks on Finite Groups and Rapidly Mixing Markov Chains.” In Séminaire de Probabilités XVII 1981/82: Proceedings, 243–97. Springer.

Aldrich, John. 2008. “R. A. Fisher on Bayes and Bayes’ Theorem.” Bayesian Analysis 3 (March). https://doi.org/10.1214/08-BA306.

Autolatry. 2015. “Why Square Brackets for Expectation.” Mathematics Stack Exchange. https://math.stackexchange.com/q/1302543.

Banerjee, S., A. E. Gelfand, and B. P. Carlin. 2026. Hierarchical Modeling and Analysis for Spatial Data. CRC Press LLC.

Battaglia, Tobias Gerstenberg, Tomer D Ullman, and B Joshua. n.d. “Intuitive Physics as Probabilistic Inference Kevin a. Smith, Jessica b. Hamrick, Adam n. Sanborn, Peter w.”

Bayesian Nonparametrics. 2010. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press.

Belsley, David A., Edwin Kuh, and Roy E. Welsch. 1980. Regression Diagnostics. John Wiley & Sons, Inc. https://doi.org/10.1002/0471725153.

Bernoulli, J. 1713. Ars Conjectandi [the Art of Conjecturing]. Impensis Thurnisiorum.

Bishop, C. M. 2006. Pattern Recognition and Machine Learning. Information Science and Statistics. Springer (India) Private Limited. https://www.microsoft.com/en-us/research/uploads/prod/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf.

Blundell, Charles, Julien Cornebise, Koray Kavukcuoglu, and Daan Wierstra. 2015. “Weight Uncertainty in Neural Networks.” https://doi.org/10.48550/ARXIV.1505.05424.

Box, G. E. P., G. M. Jenkins, G. C. Reinsel, and G. M. Ljung. 2015. Time Series Analysis: Forecasting and Control. Wiley Series in Probability and Statistics. Wiley.

Bressoud, D. M. 2008. A Radical Approach to Lebesgue’s Theory of Integration. Classroom Resource Materials. Cambridge University Press.

Brockwell, Peter J, and Richard A Davis. 1991. Time Series: Theory and Methods. Springer science & business media.

Broemeling, Lyle D. 2019. Bayesian Analysis of Time Series. CRC Press.

Carlin, B. P., and T. A. Louis. 2008. Bayesian Methods for Data Analysis. Chapman & Hall/CRC Texts in Statistical Science. CRC Press.

Carter, C. K., and R. Kohn. 1994. “On Gibbs Sampling for State Space Models.” Biometrika 81 (3): 541–53. https://doi.org/10.1093/biomet/81.3.541.

Casella, G., and R. L. Berger. 2002. Statistical Inference. Duxbury Advanced Series in Statistics and Decision Sciences. Thomson Learning. http://home.ustc.edu.cn/~zt001062/MaStmaterials/George%20Casella&Roger%20L.Berger--Statistical%20Inference.pdf.

Chen, J. 2023. Statistical Inference Under Mixture Models. ICSA Book Series in Statistics. Springer Nature Singapore.

Cook, R. Dennis. 1977. “Detection of Influential Observation in Linear Regression.” Technometrics 19 (1): 15. https://doi.org/10.2307/1268249.

Cowpertwait, P. S. P., and A. V. Metcalfe. 2009. Introductory Time Series with r. Use r! Springer New York.

Cressie, N., and C. K. Wikle. 2011. Statistics for Spatio-Temporal Data. CourseSmart Series. Wiley.

Davidson-Pilon, Cameron. 2015. Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference. Addison-Wesley Data & Analytics Series. Pearson Education.

Dempster, Arthur P, Nan M Laird, and Donald B Rubin. 1977. “Maximum Likelihood from Incomplete Data via the EM Algorithm.” Journal of the Royal Statistical Society: Series B (Methodological) 39 (1): 1–22.

Durbin, J. 1960. “The Fitting of Time-Series Models.” Revue de l’Institut International de Statistique / Review of the International Statistical Institute 28 (3): 233–44. http://www.jstor.org/stable/1401322.

Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199641178.001.0001.

Ebbinghaus, H. D., and J. H. Ewing. 1991. Numbers. Graduate Texts in Mathematics. Springer New York.

Finetti, Bruno de. 1937. “La Prévision: Ses Lois Logiques, Ses Sources Subjectives.” Annales de l’Institut Henri Poincaré 7 (1): 1–68.

———. 2017. “Theory of Probability.” Edited by Antonio Machí and Adrian Smith. Wiley Series in Probability and Statistics, January. https://doi.org/10.1002/9781119286387.

Fisher, R. A. 1925. Statistical Methods for Research Workers. 1st ed. Edinburgh Oliver & Boyd.

Frazier, Peter I. 2018. “A Tutorial on Bayesian Optimization.” https://arxiv.org/abs/1807.02811.

Fruhwirth-Schnatter, S., G. Celeux, and C. P. Robert. 2019. Handbook of Mixture Analysis. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. CRC Press.

Frühwirth-Schnatter, S. 2006. Finite Mixture and Markov Switching Models. Springer Series in Statistics. Springer New York.

Gelman, Andrew, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. 2013. Bayesian Data Analysis, Third Edition. Chapman & Hall/CRC Texts in Statistical Science. Taylor & Francis.

Gelman, Andrew, and Jennifer Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Analytical Methods for Social Research. Cambridge University Press.

Gelman, Andrew, Aleks Jakulin, Maria Grazia Pittau, and Yu-Sung Su. 2008. “A Weakly Informative Default Prior Distribution for Logistic and Other Regression Models.” The Annals of Applied Statistics 2 (4). https://doi.org/10.1214/08-aoas191.

Geman, Stuart, and Donald Geman. 1984. “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images.” IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-6 (6): 721–41. https://doi.org/10.1109/tpami.1984.4767596.

Ghosh, Joyee, Yingbo Li, and Robin Mitra. 2018. “On the Use of Cauchy Prior Distributions for Bayesian Logistic Regression.” Bayesian Analysis 13 (2). https://doi.org/10.1214/17-ba1051.

Golan, J. S. 2012. The Linear Algebra a Beginning Graduate Student Ought to Know. Mathematics and Statistics. Springer Netherlands.

Gramacy, Robert B. 2020. Surrogates: Gaussian Process Modeling, Design, and Optimization for the Applied Sciences. Chapman & Hall/CRC the r Series. CRC Press. https://bookdown.org/rbg/surrogates/.

Hairer, E., and G. Wanner. 2008. Analysis by Its History. Undergraduate Texts in Mathematics. Springer New York.

Hamilton, J. D. 2020. Time Series Analysis. Princeton University Press. https://books.google.co.il/books?id=BeryDwAAQBAJ.

Härdle, Wolfgang Karl, and Léopold Simar. 2019. Applied Multivariate Statistical Analysis. Springer International Publishing. https://doi.org/10.1007/978-3-030-26006-4.

Harvey, A. C. 1990. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.

Hewitt, Edwin, and Leonard J Savage. 1955. “Symmetric Measures on Cartesian Products.” Transactions of the American Mathematical Society 80 (2): 470–501.

Hobbs, N. Thompson, and Mevin B. Hooten. 2015. Bayesian Models: A Statistical Primer for Ecologists. STU - Student edition. Princeton University Press. http://www.jstor.org/stable/j.ctt1dr36kz.

Hoff, Peter D. 2009. A First Course in Bayesian Statistical Methods. Springer New York. https://doi.org/10.1007/978-0-387-92407-6.

Jackman, Simon. 2009. “Bayesian Analysis for the Social Sciences.” Wiley Series in Probability and Statistics, October. https://doi.org/10.1002/9780470686621.

James, G., D. Witten, T. Hastie, and R. Tibshirani. 2013. An Introduction to Statistical Learning: With Applications in r. Springer Texts in Statistics. Springer New York.

Jeffreys, H. 1983. Theory of Probability. International Series of Monographs on Physics. Clarendon Press.

Johnson, R. A., and D. W. Wichern. 2001. Applied Multivariate Statistical Analysis. Pearson Modern Classics for Advanced Statistics Series. Prentice Hall.

Kalman, Rudolph Emil. 1960. “A New Approach to Linear Filtering and Prediction Problems.”

Kruschke, John K. 2011. Doing Bayesian Data Analysis: A Tutorial with R and BUGS. Burlington, MA: Academic Press. http://www.amazon.com/Doing-Bayesian-Data-Analysis-Tutorial/dp/0123814855.

Levinson, Norman. 1946. “The Wiener (Root Mean Square) Error Criterion in Filter Design and Prediction.” Journal of Mathematics and Physics 25 (1-4): 261–78. https://doi.org/https://doi.org/10.1002/sapm1946251261.

Lunn, D., C. Jackson, N. Best, A. Thomas, and D. Spiegelhalter. 2012. The BUGS Book: A Practical Introduction to Bayesian Analysis. Chapman & Hall/CRC Texts in Statistical Science. Taylor & Francis.

Martin, Osvaldo A., Ravin Kumar, and Junpeng Lao. 2021. Bayesian Modeling and Computation in Python. Boca Raton.

McElreath, Richard. 2015. Statistical Rethinking, a Course in r and Stan.

McKinney, Wes. 2022. Python for Data Analysis: Data Wrangling with Pandas, NumPy, and Jupyter. 3rd ed. O’Reilly Media.

McLachlan, G. J., and D. Peel. 2004. Finite Mixture Models. Wiley Series in Probability and Statistics. Wiley.

Moivre, Abraham De. 1718. The Doctrine of Chances. H. Woodfall. https://tellingstorieswithdata.com.

Morita, Satoshi, Peter F Thall, and Peter Müller. 2008. “Determining the Effective Sample Size of a Parametric Prior.” Biometrics 64 (2): 595–602.

Nielsen, A. 2019. Practical Time Series Analysis: Prediction with Statistics and Machine Learning. O’Reilly Media.

Ostermann, A., and G. Wanner. 2012. Geometry by Its History. Undergraduate Texts in Mathematics. Springer Berlin Heidelberg.

Pearson, E. S., W. S. Gosset, R. L. Plackett, and G. A. Barnard. 1990. Student: A Statistical Biography of William Sealy Gosset. Clarendon Press.

Petris, G., S. Petrone, and P. Campagnoli. 2009. Dynamic Linear Models with r. Use r! Springer New York. https://link.springer.com/book/10.1007/b135794.

Pfaff, B. 2008. Analysis of Integrated and Cointegrated Time Series with r. Use r! Springer New York.

Poisson, S. -D. 2019. “English Translation of Poisson’s "Recherches Sur La Probabilité Des Jugements En Matière Criminelle Et En Matière Civile" / "Researches into the Probabilities of Judgements in Criminal and Civil Cases".” https://arxiv.org/abs/1902.02782.

Polya, G. 1945. How to Solve It. Princeton University Press. https://doi.org/10.1515/9781400828678.

Prado, Raquel, Gabriel Huerta, and Mike West. 2000. “Bayesian Time-Varying Autoregressions: Theory, Methods and Applications.” Resenhas Do Instituto de Matemática e Estatı́stica Da Universidade de São Paulo 4 (4): 405–22. https://www2.stat.duke.edu/~mw/MWextrapubs/Prado2001.pdf.

Prado, R., M. A. R. Ferreira, and M. West. 2023. Time Series: Modeling, Computation, and Inference. Chapman & Hall/CRC Texts in Statistical Science. CRC Press.

Ramsey, Frank P. 1926. “Truth and Probability.” In The Foundations of Mathematics and Other Logical Essays, edited by R. B. Braithwaite, 156–98. McMaster University Archive for the History of Economic Thought. https://EconPapers.repec.org/RePEc:hay:hetcha:ramsey1926.

Rasmussen, Carl Edward, and Christopher K. I. Williams. 2006. Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning Series. MIT Press. https://gaussianprocess.org/gpml/.

Ravishanker, N., B. Raman, and R. Soyer. 2022. Dynamic Time Series Models Using r-INLA: An Applied Perspective. CRC Press.

Remmert, R., and R. B. Burckel. 2012. Theory of Complex Functions. Graduate Texts in Mathematics. Springer New York.

Rios Insua, David, Fabrizio Ruggeri, and Michael P Wiper. 2012. Bayesian Analysis of Stochastic Process Models. John Wiley & Sons.

Särkkä, S. 2013. Bayesian Filtering and Smoothing. Bayesian Filtering and Smoothing. Cambridge University Press. https://books.google.co.il/books?id=5VlsAAAAQBAJ.

Schott, James R. 2016. Matrix Analysis for Statistics. Wiley Series in Probability and Statistics. Wiley.

Sheather, Simon. 2009. A Modern Approach to Regression with r. Springer New York. https://doi.org/10.1007/978-0-387-09608-7.

Soch, Joram et al. 2024. The Book of Statistical Proofs. Zenodo. https://doi.org/10.5281/ZENODO.4305949.

Spanos, A. 2019. Probability Theory and Statistical Inference. Cambridge University Press.

Spiegelhalter, David J., Nicola G. Best, Bradley P. Carlin, and Angelika Van Der Linde. 2002. “Bayesian Measures of Model Complexity and Fit.” Journal of the Royal Statistical Society Series B: Statistical Methodology 64 (4): 583–639. https://doi.org/10.1111/1467-9868.00353.

Storch, H. von, and F. W. Zwiers. 2002. Statistical Analysis in Climate Research. Cambridge University Press.

Theodoridis, S. 2015. Machine Learning: A Bayesian and Optimization Perspective. Elsevier Science.

Trench, William F. 1964. “An Algorithm for the Inversion of Finite Toeplitz Matrices.” Journal of the Society for Industrial and Applied Mathematics 12 (3): 515–22. http://ramanujan.math.trinity.edu/wtrench/research/papers/TRENCH_RP_6.PDF.

VanderPlas, Jake. 2016. Python Data Science Handbook: Essential Tools for Working with Data. 1st ed. O’Reilly Media, Inc. https://jakevdp.github.io/PythonDataScienceHandbook/.

Visser, I., and M. Speekenbrink. 2022. Mixture and Hidden Markov Models with r. Use r! Springer International Publishing.

Walker, Gilbert Thomas. 1931. “On Periodicity in Series of Related Terms.” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 131 (818): 518–32. https://doi.org/10.1098/rspa.1931.0069.

Weckerle, Melissa. 2022. “Statistics professor wins prestigious professional statistics society award Baskin School of Engineering.” https://engineering.ucsc.edu/news/statistics-professor-wins-zellner-medal.

West, M., and J. Harrison. 2013. Bayesian Forecasting and Dynamic Models. Springer Series in Statistics. Springer New York.

Wiesenfarth, Manuel, and Silvia Calderazzo. 2020. “Quantification of Prior Impact in Terms of Effective Current Sample Size.” Biometrics 76 (1): 326–36. https://doi.org/https://doi.org/10.1111/biom.13124.

Wikipedia contributors. 2023a. “68–95–99.7 Rule — Wikipedia.” https://en.wikipedia.org/w/index.php?title=68%E2%80%9395%E2%80%9399.7_rule.

———. 2023b. “Functional (Mathematics) — Wikipedia, the Free Encyclopedia.” https://en.wikipedia.org/w/index.php?title=Functional_(mathematics)&oldid=1148699341.

———. 2024a. “Autoregressive Model — Wikipedia, the Free Encyclopedia.” https://en.wikipedia.org/w/index.php?title=Autoregressive_model&oldid=1233171855#Estimation_of_AR_parameters.

———. 2024b. “Levinson Recursion — Wikipedia, the Free Encyclopedia.” https://en.wikipedia.org/w/index.php?title=Levinson_recursion&oldid=1229942891.

———. 2025. “Wold’s Theorem — Wikipedia, the Free Encyclopedia.” https://en.wikipedia.org/w/index.php?title=Wold%27s_theorem&oldid=1295347901.

Wikle, C. K., A. Zammit-Mangion, and N. Cressie. 2019. Spatio-Temporal Statistics with r. Chapman & Hall/CRC the r Series. CRC Press.

Yao, W., and S. Xiang. 2024. Mixture Models: Parametric, Semiparametric, and New Directions. Chapman & Hall/CRC Monographs on Statistics and Applied Probability. CRC Press.

Yule, George Udny. 1927. “VII. On a Method of Investigating Periodicities Disturbed Series, with Special Reference to Wolfer’s Sunspot Numbers.” Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 226 (636-646): 267–98. https://doi.org/10.1098/rsta.1927.0007.

Zohar, Shalhav. 1969. “Toeplitz Matrix Inversion: The Algorithm of w. F. Trench.” J. ACM 16: 592–601. https://api.semanticscholar.org/CorpusID:3115290.