Bayesian Parameter Estimation

This page contains resources about Bayesian Parameter Estimation, Bayesian Parameter Learning and Bayes Estimator.

Subfields and Concepts

 * For complete (fully observed data):
 * Dirichlet distribution (or other priors)
 * For incomplete (hidden/missing data):
 * Markov Chain Monte Carlo (MCMC)
 * Viterbi Algorithm
 * Variational Bayes
 * Stochastic Gradient Variational Bayes (SGVB) Estimator
 * Bayesian Hierarchical Modelling / Hierarchical Bayes Model
 * Hyperparameter
 * Hyperprior
 * Bayesian Decision Theory
 * Bayesian Point Estimation
 * Bayesian Signal Processing
 * Bayes Risk
 * Bayesian Score
 * Posterior variance (when MSE is used)
 * Bayes Risk Function / Posterior Expected Loss (i.e. Posterior Expectation Value of Loss Function)
 * Posterior mean / Minimum MSE (MMSE) estimator / Bayes least squared error (BLSE) estimator / Squared error loss
 * Posterior median / Median-unbiased estimator / Absolute error loss
 * Posterior mode
 * Bayes estimator
 * MMSE / BLSE estimator
 * Median-unbiased estimator
 * Bayes estimator for conjugate priors (eg. exponential family)
 * Maximum Likelihood Estimation (MLE)
 * Asymptotics of Maximum Likelihood
 * Cramer-Rao bound / Cramer-Rao lower bound
 * Fisher information
 * Uninformative priors / Noninformative priors / Maximum entropy priors
 * Jeffreys prior
 * Maximum Entropy (Maxent) Models / Entropic priors
 * Exponential family
 * Beta distribution
 * Bayesian Online Parameter Estimation
 * Recursive Bayesian Estimation / Bayes filter
 * Kalman filter (special case of Bayes filter)
 * Wiener filter (special case of Kalman filter)
 * Bayesian Density Estimation
 * Nonparametric Empirical Bayes (NPEB)
 * Parametric Empirical Bayes Point Estimation
 * Iterative proportional fitting (IPF)
 * Nonparametric Methods
 * Kernel Density Estimation (KDE)
 * k-Nearest Neighbours
 * Bayesian Nonparametrics

Books and Book Chapters

 * Theodoridis, S. (2015). "Chapter 12: Bayesian Learning" Machine Learning: A Bayesian and Optimization Perspective. Academic Press.
 * Aster, R. C., Borchers, B., & Thurber, C. (2012). "Chapter 11: Bayesian Methods". Parameter estimation and inverse problems. Academic Press
 * Barber, D. (2012). "Section 9.1: Learning as Inference". Bayesian Reasoning and Machine Learning. Cambridge University Press.
 * Barber, D. (2012). "Chapter 18: Bayesian Linear Models". Bayesian Reasoning and Machine Learning. Cambridge University Press.
 * Duda, R. O., Hart, P. E., & Stork, D. G. (2012). "Chapter 2: Bayesian Decision Theory". Pattern Classification. John Wiley & Sons.
 * Murphy, K. P. (2012). "Section 5.7: Bayesian Decision Theory". Machine Learning: A Probabilistic Perspective. MIT Press.
 * Koller, D., & Friedman, N. (2009). "Chapter 17: Parameter Estimation". Probabilistic Graphical Models. MIT Press.
 * Theodoridis, S., Pikrakis, A., Koutroumbas, K., & Cavouras, D. (2008). "Chapter 2: Bayesian Decision Theory". Pattern Recognition. 4th Ed. Academic Press.
 * Bishop, C. M. (2006). "Chapter 2: Probability Distributions". Pattern Recognition and Machine Learning. Springer.
 * MacKay, D. J. (2003). "Chapter 24: Exact Marginalization". Information Theory, Inference and Learning Algorithms. Cambridge University Press.
 * MacKay, D. J. (2003). "Chapter 36: Decision Theory". Information Theory, Inference and Learning Algorithms. Cambridge University Press.
 * Bretthorst, G. L. (1998). Bayesian spectrum analysis and parameter estimation. Springer Science & Business Media.
 * Berger, J. O. (1993). Statistical decision theory and Bayesian analysis. 2nd Ed. Springer Science & Business Media.

Scholarly Articles

 * Caticha, A. (2010). Entropic inference. arXiv preprint arXiv:1011.0723.
 * Caticha, A., & Preuss, R. (2004). Maximum entropy and Bayesian data analysis: Entropic prior distributions. Physical Review E, 70(4), 046127.
 * Ghahramani, Z. (2003). "Graphical models: Parameter learning". In Handbook of Brain Theory and Neural Networks.
 * Malouf, R. (2002). A comparison of algorithms for maximum entropy parameter estimation. In proceedings of the 6th conference on Natural language learning-Volume 20 (pp. 1-7). Association for Computational Linguistics.

Other resources

 * Bayesian parameter estimation - Metacademy
 * Maximum Entropy Modelling