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Triggered on . . . mouse being released mouse being depressed and released mouse being clicked twice keyboard key being depressed and released keyboard key being depressed keyboard key being released form field being highlighted either by tabbing, by an access key, or by clicking in the field form field losing the focus by tabbing out of the field, by an access key, or by clicking another form field submit button being clicked or pressed reset button being clicked the value of any field being changed and then that field losing focus

To set the tab order of your controls, choose View Tab Order. You can also rightclick the dialog box and choose Tab Order from the shortcut menu. In either case, Excel displays the Tab Order dialog box shown in Figure 13-6. The Tab Order dialog box lists all the controls, the sequence of which corresponds to the order in which controls pass the focus between each other in the UserForm. To move a control, select it and click the arrow keys up or down. You can choose more than one control (click while pressing Shift or Ctrl) and move them all at once.

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Since this in nite sum is nite and the terms are nonnegative, the terms must tend to 0; that is, lim I (X1 ; Yn |Yn 1 , . . . , Y1 ) = 0, which proves the lemma. Combining Lemmas 4.5.1 and 4.5.2, we have the following theorem. Theorem 4.5.1 If X1 , X2 , . . . , Xn form a stationary Markov chain, and Yi = (Xi ), then H (Yn |Yn 1 , . . . , Y1 , X1 ) H (Y) H (Yn |Yn 1 , . . . , Y1 ) and lim H (Yn |Yn 1 , . . . , Y1 , X1 ) = H (Y) = lim H (Yn |Yn 1 , . . . , Y1 ). (4.74) In general, we could also consider the case where Yi is a stochastic function (as opposed to a deterministic function) of Xi . Consider a Markov (4.73) (4.72)

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The Bayesian approach to probability turns these assumptions around In Bayesian statistics, the parameters are considered to be random variables, and the data are considered to be known The parameters are regarded as coming from a distribution of possible values, and Bayesians look to the observed data to provide information on likely parameter values Let represent the parameters of the unknown distribution Bayesian analysis requires elicitation of a prior distribution for , called the prior distribution, p( ) This prior distribution can model extant expert knowledge, if any, regarding the distribution of For example, churn1 modeling experts may be aware that a customer exceeding a certain threshold number of calls to customer service may indicate a likelihood to churn This knowledge can be distilled into prior assumptions about the distribution of customer service calls, including its mean and standard deviation.

If expert knowledge regarding the prior distribution is not available, Bayesian analysts may posit a noninformative prior, which assigns equal probability to all values of the parameter For example, the prior probability of both churners and nonchurners could be set at 05 using a noninformative prior (Note that if this assumption does not seem reasonable, you must be applying your expert knowledge about churn modeling!) Regardless, because the eld of data mining often encounters huge data sets, the prior distribution should be dominated by the overwhelming amount of information to be found in the observed data Once the data have been observed, prior information about the distribution of can be updated, by factoring in the information about contained in the observed data This modi cation leads to the posterior distribution, p( |X), where X represents the entire array of data.

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This updating of our knowledge about from prior distribution to posterior distribution was rst performed by the Reverend Thomas Bayes (Figure 51), in his Essay Towards Solving a Problem in the Doctrine of Chances [1], published posthumously in 1763..

Alstead, M., Campsmith, M., Halley, C. S., Hart eld, K., Goldbaum, G., & Wood, R. W. (1999). Developing, implementing, and evaluating a condom promotion program targeting sexu-

Sub CloseInActive() Dim Book as Workbook For Each Book In Workbooks If Book.Name <> ActiveWorkbook.Name Then Book.Close Next Book End Sub