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By F. Thomas Bruss, Lucien L. Cam

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Extra info for Game theory, optimal stopping, probability and statistics: Paper in honor of T.S. Ferguson

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Where condition is a logical value or an expression that leads to a single logical value. ) will be executed; otherwise R will run the expressions in the second block. Note that the else statement can be omitted if it is not required. As an example, we modify the code used previously to illustrate the for loop. In particular, if the sample average is positive we compute and save its square root (rounded to two decimals), otherwise we return a NA value. 6 Basic statistical analysis with R In this section, we illustrate some basic statistical analysis that can be carried out on a dataframe.

Residual" "model" In R, there are also functions for regression diagnostics that are used to evaluate the model assumptions and investigate whether or not there are observations with a large influence on the regression output. We do not cover this or other advanced regression issues here and we refer the reader to more specialized book such as Faraway (2004), Dalgaard (2008), Sheather (2008) and Fox and Weisberg (2011). , a factor object in R) as a predictor. In this case, R represents the factor as a set of dummy (or indicator) variables.

Having looked back at the essential steps taken by Bayesianism and how it has affirmed itself during more than three centuries, in the rest of the chapter we are INTRODUCTION TO BAYESIAN METHODS 51 going to present the fundamental principles of Bayesian methods, starting with the concept of conditional and inverse probability. We will then focus on the three components of Bayesian inference: likelihood, prior, and posterior, and how the posterior can be obtained through Bayes theorem. The families of conjugate models will follow, particular types of models which are easy to treat analytically, but that are limited in their flexibility.

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