Abstract
The necessary mathematical background for the textbook is reviewed in this chapter. This includes second year calculus, matrix algebra, probability and statistics. Because linear models in particular depend heavily on matrices, it deemed necessary to review some topics of matrix analysis, such as matrix differentiation. Rather than just stating results, which can be found in the literature, for pedagogical reasons we develop some of the arguments in order to set the tone and provide a more coherent account. Probability and distribution theory are reviewed and several discrete and continuous distributions are briefly discussed. In a similar fashion we set the statistics background, with a focus on Bayesian inference. Some statistical topics such as Markov chain Monte Carlo and particle filters are introduced in later chapters.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society Series B, 39, 1–38.
Fahrmeir, L., & Tutz, G. (2001). Multivariate statistical modelling based on generalized linear models. New York: Springer.
Gamerman, D., & Lopes, H. F. (2006). Markov chain Monte Carlo: Stochastic simulation for Bayesian inference (2nd ed.). New York: Chapman and Hall.
Harville, D. A. (1997). Matrix Algebra from a Statistician’s perspective. New York: Springer.
Horn, R. A., & Johnson, C. R. (2013). Matrix analysis (2nd ed.). Cambridge: Cambridge University Press.
Lang, S. (1987). Calculus of several variables (3rd ed.). New York: Springer.
Leonard, T., & Hsu, J. S. J. (1999). Bayesian methods. Cambridge: Cambridge University Press.
Magnus, J. R., & Neudecker, H. (1988). Matrix differential calculus with applications in statistics and econometrics. New York: Wiley.
O’Hagan, A., & Forster, J. J. (2004). Bayesian inference (Kendall’s advanced theory of statistics: Volume 2B) (2nd ed.). London: Arnold.
Press, S. J. (1989). Bayesian statistics: Principles, models, and applications. New York: Wiley.
Robert, C. P. (2007). The Bayesian choice: From decision-theoretic foundations to computational implementation (2nd ed.). New York: Springer.
Spivak, M. (1995). Calculus (3rd ed.). Cambridge: Cambridge University Press.
Trosset, M. W. (2009). An introduction to statistical inference and its applications with R. Chapman and Hall.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Triantafyllopoulos, K. (2021). Matrix Algebra, Probability and Statistics. In: Bayesian Inference of State Space Models. Springer Texts in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-76124-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-76124-0_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-76123-3
Online ISBN: 978-3-030-76124-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)