Introduction to Markov Chains. Definition. Irreducible, recurrent and aperiodic chains. Main limit theorems for finite, countable and uncountable state spaces.| www.statlect.com
Learn how the variance inflation factor (VIF) is defined, and how it is derived and calculated. Understand under what assumptions the VIF provides reliable indications.| www.statlect.com
Run your regression with SimpleR, an easy to use calculator for multiple linear regression. SimpleR is a free regression analysis tool.| www.statlect.com
Learn how information criteria such as AIC and BIC are used to perform model selection and choose the best compromise between the fit of a linear regression model and its parsimony.| www.statlect.com
Learn how Jeffreys' scale is used to subdivide the values of the Bayes factor into categories (or grades of evidence).| www.statlect.com
Learn how the posterior odds ratio is used in Bayesian statistics to compare two different models or hypotheses.| www.statlect.com
Learn how the Discrete Fourier Transform (DFT) and its inverse are defined. Discover how they can be written in matrix form.| www.statlect.com
The Dirichlet distribution explained, with detailed derivations of the mean vector and the covariance matrix, and proofs of other important results.| www.statlect.com
Learn how minors and cofactors are defined and how they are used in the Laplace expansion to compute the determinant of a matrix.| www.statlect.com
Discover criteria used to select statistical models that have been estimated by maximum likelihood, such as the Akaike Information Criterion and the Bayesian Information Criterion.| www.statlect.com
Learn how unconditional and conditional heteroskedasticity (or heteroscedasticity) are defined in linear regression models. Discover their consequences and how to find remedies, such as heteroskedasticity-robust standard errors.| www.statlect.com
Ridge estimation of linear regression models. Bias, variance and mean squared error of the ridge estimator. How to choose the penalty parameter and scale the variables.| www.statlect.com
Understand the problem of multicollinearity in linear regressions, how to detect it with variance inflation factors and condition numbers, and how to solve it.| www.statlect.com
Bayesian estimation of the mean and the variance of a normal distribution. How to derive the posterior. Formulae, derivations, proofs.| www.statlect.com
Introduction to Bayesian statistics with explained examples. Learn about the prior, the likelihood, the posterior, the predictive distributions. Discover how to make Bayesian inferences about quantities of interest.| www.statlect.com
The Gauss Markov theorem: under what conditions the OLS estimator of the coefficients of a linear regression is BLUE (best linear unbiased estimator). With proofs and detailed explanations.| www.statlect.com
Discover the mathematics of probability and how probability is defined. Learn about the properties of probability through examples and solved exercises.| www.statlect.com
The probit classification model (aka probit regression). Definition. Interpretation. Maximum likelihood estimation.| www.statlect.com
The logistic classification model (aka logit or logistic regression). Definition. Interpretation. Maximum likelihood estimation.| www.statlect.com
Learn how to formulate and test a null hypothesis without incurring in common mistakes and misconceptions.| www.statlect.com
The beta distribution explained, with examples, solved exercises and detailed proofs of important results.| www.statlect.com