before we discuss few other models in the following sectionswe would like to emphasize number of points about modeling any model for data is likely to be wrong for examplereal data (as opposed to computer-generated dataare often assumed to come from normal distributionwhich is never exactly true howeveran important advantage of using normal distribution is that it has many nice mathematical propertiesas we will see in section most data models depend on number of unknown parameterswhich need to be estimated from the observed data any model for real-life data needs to be checked for suitability an important criterion is that data simulated from the model should resemble the observed dataat least for certain choice of model parameters here are some guidelines for choosing model think of the data as spreadsheet or data frameas in where rows represent the data units and the columns the data features (variablesgroupsfirst establish the type of the features (quantitativequalitativediscretecontinuousetc assess whether the data can be assumed to be independent across rows or columns decide on the level of generality of the model for exampleshould we use simple model with few unknown parameters or more generic model that has large number of parameterssimple specific models are easier to fit to the data (low estimation errorthan more general modelsbut the fit itself may not be accurate (high approximation errorthe tradeoffs discussed in section play an important role here decide on using classical (frequentistor bayesian model section gives short introduction to bayesian learning multivariate normal models standard model for numerical observations xn (forminge column in spreadsheet or data frameis that they are the outcomes of iid normal random variables iid xn (us it is helpful to view normally distributed random variable as simple transformation of standard normal random variable to witif has standard normal distributionthen sz has (us distribution the generalization to dimensions is discussed iid in appendix we summarize the main pointslet zn ( the pdf of [ zn ](that isthe joint pdf of zn is given by fz (ze zi ( ) = rn (