FANDOM


Probability

This page contains resources about Probability Theory and Statistics in general.

More specific information is included in each subfield.

Subfields and ConceptsEdit

See Category:Probability and Statistics for all its subfields.

  • Statistical Inference / Inferential Statistics
    • Frequentist Inference
      • Statistical Hypothesis Testing / Statistical Tests
        • Fisher's Null Hypothesis Testing
        • Neyman-Pearson Theory
        • Analysis of Variance (ANOVA)
        • Analysis of Covariance (ANCOVA)
        • Multivariate Analysis of Variance (MANOVA)
        • T-test
        • F-test
        • Tests of Goodness-of-Fit
      • Confidence Intervals
      • Bootstrapping
    • Bayesian Inference
    • Inductive inference
    • Causal Inference
    • Interval Estimation
    • Estimation Theory / Point Estimation
    • Decision Theory
      • Neyman-Pearson Theory
      • The Expected Loss Principle
      • Optimal decision rules
      • Bayesian Decision Theory / Bayesian Estimator
      • Cost function / Loss function
      • Risk function
      • Admissibility
      • Unbiasedness
      • Minimaxity
    • Algorithmic Information Theory
      • Minimum Description Length (MDL)
      • Minimum Message Length (MML)
      • Occam's Razor
      • Kolmogorov Complexity
    • Model Selection and Evaluation
      • Akaike Information Criterion (AIC)
      • Bayesian Information Criterion (BIC)
      • Deviance Information Criterion (DIC)
      • Bayesian Predictive Information Criterion (BPIC)
      • Focused Information Criterion (FIC)
      • Bayesian Model Selection / Bayesian Model Comparison
        • Bayesian Model Averaging
      • Bayesian Parameter Estimation
      • Minimum Description Length (MDL)
      • Minimum Message Length (MML)
      • Akaike Final Prediction Error (FPE)
      • Parzen's Criterion Autoregressive Transfer Function (CAT)
      • Cross-Validation
      • Statistical Hypothesis Testing (for Multilevel Models / Nested Models only)
        • Lagrange multiplier test / Score test / Score Method
        • Likelihood-ratio test
        • Wald test
  • Statistical Models
    • Regression Analysis
      • Linear Regression Model
      • Simple Linear Regression
      • Multiple Linear Regression (not to be confused with Multivariate Linear Regression)
      • General Linear Model / Multivariate Linear Regression
      • Generalized Linear Model (GLM or GLIM)
      • Poisson Regression
      • Least Squares Methods
        • Ordinary Least Squares / Linear Least Squares
        • Weighted Least Squares
        • Nonlinear Least Squares
      • Logistic Regression Model / Logit Model
      • Probit Model
      • Fixed Effects Model
      • Hierarchical Linear Models / Multilevel Models / Nested Data Models
        • Random Effects Model / Variance Components Model
        • Mixed Effects Models (not to be confused with Mixture Models)
      • Nonparametric Regression Models
      • Nonlinear Regression Models
      • Robust Regression Models
      • Random sample consensus (RANSAC)
      • Regularization
        • Ridge regression / Tikhonov regularization
        • Least absolute shrinkage and selection operator (LASSO)
        • Elastic Nets
    • Probabilistic Models
    • State Space Models
      • Time Series Models
  • Probability Theory
    • Random Variables
      • Continuous Random Variables
        • Probability Density Function
      • Discrete Random Variables
        • Probability Mass Function
      • Jointly Distributed Random Variables
        • Joint Density Function
      • Independent Random Variables
      • Uncorrelated Random Variables
    • Moments of a distribution
      • First Moment / Mean
      • Second Moment / Variance
      • Third Moment / Skewness
      • Fourth Moment / Kurtosis
    • Probabilistic Models
    • Stochastic Convergence
    • Probability Space
    • Measure Space
    • State Space
    • Theorem of Total Probability
    • Central Limit Theorem
    • Queueing Theory
    • Martingale Theory
    • Ergodic Theory
    • Decision Theory
    • Measure Theory
    • Utility Theory

Online CoursesEdit

Video LecturesEdit


Lecture NotesEdit

BooksEdit

Statistical Inference and Theory of Statistics Edit

  • Bruce, P., & Bruce, A. (2017). Practical Statistics for Data Scientists: 50 Essential Concepts. O'Reilly Media.
  • Imbens, G. W., & Rubin D. B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction.
  • Ross, S. M. (2014). Introduction to probability models. 11th Ed. Academic Press.
  • Smith, R. C. (2013). Uncertainty quantification: theory, implementation, and applications. SIAM.
  • Gentle, J. E. (2013). Theory of statistics. (link)
  • DeGroot, M. H., & Schervish, M. J. (2012). Probability and statistics. 4th Ed. Pearson.
  • Abu-Mostafa, Y. S., Magdon-Ismail, M., & Lin, H. T. (2012). Learning From Data. AMLBook.
  • Diez, D. M., Barr, C. D., & Cetinkaya-Rundel, M. (2012). OpenIntro Statistics. CreateSpace.
  • Ramachandran, K. M., & Tsokos, C. P. (2012). Mathematical Statistics with Applications in R. Elsevier.
  • Gentle, J. E. (2007). Matrix algebra: theory, computations, and applications in statistics. Springer Science & Business Media.
  • Rice, J. (2006). Mathematical statistics and data analysis. 3rd Ed. Duxbury Press.
  • Cox, D. R. (2006). Principles of statistical inference. Cambridge University Press.
  • Lavine, M. (2005). Introduction to Statistical Thought. Michael Lavine.
  • Young, G. A., & Smith, R. L. (2005). Essentials of statistical inference. Cambridge University Press.
  • Lehmann, E. L., & Casella, G. (2003). Theory of point estimation. Springer.
  • Bertsekas, D. P., & Tsitsiklis, J. N. (2002). Introduction to Probability. Athena scientific.
  • Casella, G., & Berger, R. L. (2002). Statistical inference. Cengage Learning.
  • Garthwaite, P. H., Jolliffe, I. T., & Jones, B. (2002). Statistical inference. Oxford University Press.
  • Shao, J. (2000). Mathematical Statistics. Springer.
  • Mukhopadhyay, N. (2000). Probability and statistical inference. CRC Press.
  • Schervish, M. J. (1995). Theory of statistics. Springer Science & Business Media.

Regression Analysis and Generalized Linear Models Edit

  • Harrell, F. (2015). Regression modeling strategies. 2nd Ed. Springer.
  • Chatterjee, S., & Hadi, A. S. (2012). Regression analysis by example. 5th Ed. John Wiley & Sons.
  • Goldstein, H. (2010). Multilevel statistical models. 4th Ed. John Wiley & Sons.
  • Dobson, A. J., & Barnett, A. (2008). An introduction to generalized linear models. 3rd Ed. CRC press.
  • Fox, J. (2008). Applied regression analysis and generalized linear models. 2nd Ed. Sage Publications.
  • Gelman, A., & Hill, J. (2006). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.
  • Ruppert, D., Wand, M. P., & Carroll, R. J. (2003). Semiparametric regression. Cambridge University Press.
  • Faraway, J. J. (2002). Practical regression and ANOVA using R. (link)
  • Draper, N. R., & Smith, H. (1998). Applied regression analysis. 3rd Ed. John Wiley & Sons.
  • Long, J. S., & Freese, J. (1997). Regression models for categorical dependent variables. Sage Publications.
  • McCullagh, P., & Nelder, J. A. (1989). Generalized linear models. CRC press.

Counting and Probability Edit

  • Shu, Z. (2016). Probability and Expectation (Volume 14). World Scientific.
  • Zhou, X. (2015). Counting: Math for Gifted Students. CreateSpace. 
  • Hollos, S. & Hollos, J. R. (2013). Probability Problems and Solutions. Abrazol Publishing.
  • Patrick, D. (2007). Introduction to Counting and Probability. 2nd Ed. AoPS Incorporated.
  • Patrick, D. (2007). Intermediate Counting and Probability. AoPS Incorporated.

SoftwareEdit

See List of Statistical packages for a complete list.

See alsoEdit

Other ResourcesEdit