1. Chapter 10
Using Data

2. 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

3. 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

4. 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

5. 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

6. 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)

7. 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

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

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

10. 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)