Experiment sample sizes on influence diagrams
Abstract/Contents
- Abstract
- In many decision situations there are opportunities to gather additional information before making some of the decisions, but the choice of which experiments to conduct with limited resources of time and money can be even less intuitive than the original decision problem. For example, a pharmaceutical company can conduct trials to observe the risks and benefits of new treatments, an oil company can perform seismic studies before drilling wells, or a manufacturer can operate a pilot plant before investing in a new production process. This dissertation explores the available experiments in a decision context and how many of each should be acquired, weighing the costs of the experiments against their potential benefits. The solution methodology developed to answer these research questions is inspired by the preposterior analysis from Raiffa and Schlaifer's seminal "Applied Statistical Decision Theory". They use a Gaussian model to approximate both the decision maker's prior beliefs and likelihood of experimental observations about a single binary uncertainty. This work extends their method to multiple multinomial uncertainties, represented by an influence diagram, for which there can be many different possible experiments. The methodology first considers a general decision problem with finite alternatives and states, a decision maker with constant absolute risk aversion, and a linear sampling cost. Computing the value of experimentation of one uncertain variable in such a problem is at least exponential in the number of states of that variable. Therefore, an approximate expression is derived for the value of experimentation as a function of the number of samples acquired based on a Gaussian approximation to the sample information. Determining an optimal sample size for the approximate value of experimentation is shown to be tractable with numerical methods. The methodology is extended to general finite-prospect influence diagrams containing multiple uncertainties where the decision maker chooses sample sizes for several experiments simultaneously. The resulting approximation for the value of experimentation has similar properties to the single uncertainty case which makes analysis tractable for many practical problems. Policies can be derived for both parallel and sequential experimentation, and they are shown to be close to the exact optimal policies in problems where the exact solutions can be determined.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Lacy, Ahren J |
|---|---|
| Associated with | Stanford University, Department of Management Science and Engineering. |
| Primary advisor | Shachter, Ross D |
| Thesis advisor | Shachter, Ross D |
| Thesis advisor | Howard, Ronald A. (Ronald Arthur), 1934- |
| Thesis advisor | Van Roy, Benjamin |
| Advisor | Howard, Ronald A. (Ronald Arthur), 1934- |
| Advisor | Van Roy, Benjamin |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Ahren J. Lacy. |
|---|---|
| Note | Submitted to the Department of Management Science and Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Ahren Joseph Lacy
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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