Modeling with Decision Theory

Probability and Expected Value

$$\text{probability of an event = }\frac{\text{favorable outcomes}}{\text{total outcomes}}$$

Weighted Average

The formula of expected value is:

$$E=w_1{p}_1+w_2{p}_2+\cdots +w_n{p}_n$$

or

$$E=\sum _{i=1}^n{w}_i{p}_i$$

where $w_i$ is the payoff of each outcome, $p_i(0\le p_i\le 1)$ is the corresponding probability. Note that weightes must sum to 1.

Sensitivity Analysis

A typical decision model depends on many assumptions. We use sensitivity analysis to determine how the probabilities are likely to change.

Decision Trees

A terminal node with a consequence branchshowing the payoff for that outcome.

Sequential Decisions and Conditional Probabilities

Sequential Decision: Decision is made step by step, where each decision depends on the previous outcome. Conditional Probability: The probability of one event when another event has already occurred.