Precipitation in Snoqualmie Falls revisited. Fitting a two-component Gaussian mixture; examining the fitted distribution; checking calibration. Using cross-validation to select the number of components to use. Examination of the selected mixture model. Suspicious patterns in the parameters of the selected model. Approximating complicated distributions vs. revealing hidden structure. Using bootstrap hypothesis testing to select the number of mixture components. The multivariate Gaussian distribution: definition, relation to the univariate or scalar Gaussian distribution; effect of linear transformations on the parameters; plotting probability density contours in two dimensions; using eigenvalues and eigenvectors to understand the geometry of multivariate Gaussians; estimation by maximum likelihood; computational aspects, specifically in R.
Posted at April 09, 2011 23:51 | permanent link