Bayesian Parameter Estimation

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

Subfields and Concepts[edit]

  • Statistical Signal Processing / Estimation Theory
    • Bayesian Decision Theory
    • Bayesian Point Estimation
    • Bayesian Score
    • Maximum Likelihood Estimation (MLE)
    • Asymptotics of Maximum Likelihood
    • Cramer-Rao bound / Cramer-Rao lower bound
    • Fisher information
  • For complete (fully observed data):
    • Dirichlet distribution (or other priors)
  • For incomplete (hidden/missing data):
  • Bayesian Parametric Models
    • Bayesian Linear (Regression) Model
    • Bayesian Multivariate Linear (Regression) Model
  • Bayesian Nonparametric Models
  • Bayesian Smoothing Splines
  • Posterior Risk / Bayes Risk
    • 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 (e.g. exponential family)
  • Bayesian Hierarchical Modelling / Hierarchical Bayes
    • Hyperparameter
    • Hyperprior
  • Empirical Bayes / Maximum marginal likelihood estimator (MMLE) / Evidence Approximation
    • Nonparametric Empirical Bayes (NPEB)
    • Parametric Empirical Bayes Point Estimation
  • Full Bayes
  • Uninformative priors / Noninformative priors / Maximum entropy priors
    • Jeffreys prior
  • Maximum Entropy (Maxent) Models / Entropic priors
  • Exponential family
  • Beta distribution
  • Bayesian Online Parameter Estimation
  • Iterative proportional fitting (IPF)
  • Density Estimation (i.e. the unknown parameter is probability density itself)
    • Risk Function / Expected Loss (i.e. Expectation Value of Loss Function)
      • Mean integrated squared error (MISE)
    • Parametric Density Estimation
      • Maximum likelihood estimator (MLE)
      • Bayes estimator / Bayesian Density Estimation (i.e. a distribution over distributions)
    • Nonparametric Density Estimation
      • Rescaled Histogram (i.e. the oldest and most naive approach)
      • Parzen window / Kernel Density Estimation (KDE) / Parzen-Rosenblatt estimator
      • k-Nearest Neighbors Density Estimation
      • Bayesian Nonparametric Density Estimation

Books and Book Chapters[edit]

  • 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[edit]

  • 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 E70(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.

See also[edit]

Other resources[edit]