1. Distribuciones de probabilidad multivariadas
    • Distribución conjunta, marginal y condicional.
    • Independencia y factorización.

Referencias: Ross (1998)

  1. Redes bayesianas
    • Representación gráfica de independencias.
    • Modelos locales.
    • Aprendizaje de estructura de redes bayesianas.

Referencias: Koller and Friedman (2009), Whittaker (2009), Nagarajan, Scutari, and Lebre (2013), Hastie, Tibshirani, and Friedman (2001), Scutari and Ness (2019), Højsgaard (2016).

  1. Redes markovianas
    • Modelos log-lineales.
    • Modelos gráficos gaussianos.

Referencias: Wasserman (2004), Bishop (2006), Whittaker (2009)

  1. Variables latentes
    • Algoritmo Esperanza-Maximización.
    • Datos faltantes.
    • Clase latentes, mezclas gaussianas y análisis de factores.
    • Modelos markovianos de estados ocultos.

Referencias: Wasserman (2004), Gelman and Hill (2007), Rubin (1987)

  1. Modelos para datos espaciales y temporales
    • Estadística espacial.
    • Modelos de espacio de estados.

Referencias: Banerjee (2003)

  1. Modelos jerárquicos
    • Introducción al análisis bayesiano
    • MCMC
    • JAGS
    • Modelos jerárquicos

Referencias: Gelman and Hill (2007), Gelman et al. (2013), Kruschke (2015)


Banerjee, S. 2003. Hierarchical Modeling and Analysis for Spatial Data. Chapman & Hall/Crc Monographs on Statistics & Applied Probability. CRC Press. https://books.google.com.mx/books?id=YqpZKTp-Wh0C.

Bishop, Christopher M. 2006. Pattern Recognition and Machine Learning (Information Science and Statistics). Berlin, Heidelberg: Springer-Verlag.

Gelman, A., J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, and D.B. Rubin. 2013. Bayesian Data Analysis, Third Edition. Chapman & Hall/Crc Texts in Statistical Science. Taylor & Francis. https://books.google.com.mx/books?id=ZXL6AQAAQBAJ.

Gelman, Andrew, and Jennifer Hill. 2007. Data Analysis Using Regression and Multilevel/Hierarchical Models. Vol. Analytical methods for social research. New York: Cambridge University Press.

Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. 2001. The Elements of Statistical Learning. Springer Series in Statistics. New York, NY, USA: Springer New York Inc.

Højsgaard, Søren. 2016. GRain: Graphical Independence Networks. https://CRAN.R-project.org/package=gRain.

Koller, Daphne, and Nir Friedman. 2009. Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning. The MIT Press.

Kruschke, John. 2015. Doing Bayesian Data Analysis (Second Edition). Boston: Academic Press.

Nagarajan, Radhakrishnan, Marco Scutari, and Sophie Lebre. 2013. Bayesian Networks in R with Applications in Systems Biology. New York: Springer.

Ross, Sheldon M. 1998. A First Course in Probability. Fifth. Upper Saddle River, N.J.: Prentice Hall.

Rubin, D. B. 1987. Multiple Imputation for Nonresponse in Surveys. Wiley.

Scutari, Marco, and Robert Ness. 2019. Bnlearn: Bayesian Network Structure Learning, Parameter Learning and Inference. https://CRAN.R-project.org/package=bnlearn.

Wasserman, Larry. 2004. All of Statistics: A Concise Course in Statistical Inference. Springer Texts in Statistics. New York: Springer. https://doi.org/10.1007/978-0-387-21736-9.

Whittaker, Joe. 2009. Graphical Models in Applied Multivariate Statistics. Wiley Publishing.