Chapter 10 Using Data

Using Data We have discussed subjective judgments and theoretical distributions as sources for probabilities when modeling uncertainty in a decision problem In this chapter we consider an obvious source for information about probabilities-historical data

Using Data Use data alone to develop probability distributions Use of data to understand and model relationships among variables Use data in conjunction with theoretical probability models

Using data to construct Probability Distributions Using data when it is available is a straightforward idea Example: planning picnic at the Los Angeles zoo on an as-yet undetermined day during February The weather is a concern in this case, and you want to assess the probability of rain

Using data to construct Probability Distributions National Weather Service report that the probability of rain on any given day in February is approximation 0.25 This estimate is based on analysis of weather during past year On 25% of the days in February over the past several years rain has fallen in Los Angeles

Using data to construct Probability Distributions We can develop both discrete and continuous probability distribution on the basis of empirical data In discrete situation, the problem really becomes one of creating a relative frequency histogram from data In the case of a continuous situation, use data to draw an empirical based CDF (cumulative distribution function)

Histogram Relative frequency histogram Example: You are in charge of a manufacturing plant and you are in charge of developing a maintenance policy for your machines Examination of the frequency of machine failures

Histogram You might collect the following data over 260 days: No failures 217 days One failure 32 days Two failures 11 days

Histogram These data could be used as estimates of probabilities of machine failures No failures 0.835 = 217/260 One failure 0.123 = 32/260 Two failures 0.042 = 11/260

Empirical CDFs Continuous probability distribution are common in decision-making situations Example: yearly bed-rental costs for 35 halfway houses Table 10.1 Use of cumulative probability (figure 10.3)