Talk:Expected value of including uncertainty

Non-notable, mathematically invalid spam
This is not a noteworthy topic. It seems to be a summary of a key point in someone's dissertation, and as far as I can see no citation is given that uses this measure other than a book by the dissertation author himself.

Moreover, the article appears to be partly spam. Five times -- count them, five! -- it links to the article on the software package Analytica. A google search shows that the dissertation author is the CEO of a company that markets Analytica (see http://www.lumina.com/company/the-lumina-team/max-henrion/ ).

Further, there is a basic problem with the measure discussed in this article: the way of measuring gain that is used here has long been known in the literature to be meaningless. The measure of the expected value of the gain from including uncertainty is given as



EVIU = \int_{X} \left[ U(d^*,x) - U(d_{iu},x) \right] f(x) dx $$

This is simply the difference in the expected values of utility from the optimal and sub-optimal policies. But it is well-known that this difference is not invariant to arbitrary scale changes. Specifically, if the utility function U(.) is replaced by the utility function W(.) = b×U(.) (with b>0), then the policies chosen in each case (including and ignoring uncertainty) are unaffected; so there is no substantive difference between the two utility functions -- they contain identical information about preferences. Yet the expected utility difference EVIU in the case of using W(.) differs from that in the case of using U(.) by the multiplicative factor b. Since b can be chosen arbitrarily, it can be chosen to achieve any positive value of EVIU that one wants. (Note that this can't be rectified by using, say, the percentage difference in expected utility -- any desired outcome for the percentage difference can be achieved by using the substantively identical utility function V(.) = W(.) + c, and choosing the arbitrary parameter c accordingly.)

Since the literature has long since rejected the use of such expected utility differences, this reinforces my perception that the article here is not noteworthy. Duoduoduo (talk) 21:17, 9 December 2010 (UTC)

Noteworthiness
Unfortunately, I cannot claim any credit for the invention of EVIU. It was almost 15 years after the introduction of EVIU that my own Ph.D. thesis was completed. I do know Dr. Henrion well and work for the company that he founded. My only public contribution to the development of EVIU is my authorship of the EVIU article on Wikipedia. I also provided technical assistance to a group (at a company not affiliated with Lumina or Dr. Henrion) in 2010 who were implementing EVIU and EVSI calculations in an environmental modeling application, who had contacted me for assistance due to my expertise with Analytica, and in statistics and decision analysis. It was that experience that inspired me to contribute this article to Wikipedia.

EVIU does appear in many articles in published literature by authors unassociated with its creator. Some of these should be worked into the primary article eventually. I tried to focus citations on the articles I felt did a good job at explaining and defining EVIU, or that deserved the historic credit for its introduction, rather than articles that give it a more cursory treatment. Here are some such articles (this is a very small sampling):


 * Hadi Dowlatabadi, Milind Kandlikar, and Charles Linville (1995), "Climate Change Decision-making: Model & Parameter Uncertainties Explored", International Society for Bayesian Analysis conference, Oaxaca, Mexico Sep 28-30.
 * Maxine E. Dakins, John E. Toll, and Mitchell J. Small (1994), "Risk-Based Environmental Remediation: Decision Framework and Role of Uncertainty", Environmental Technology and Chemistry 13(12):1907-1915.
 * Shane W. Frederick and Randall M. Peterman (1995), "Choosing Fisheries Harvest Policies: when does uncertainty matter?", Can. J. of Fish. Aquat. Sci. 52:291-306
 * David A. Bennet, et al (2001) "Risk Assessment Guidance for Superfund (RAGS): Advanced Modeling Approaches for Characterizing Variability and Uncertainty", RAGS Vol 3. Part A., Process for Conducting Probabilistic Risk Assessment, US Environmental Protection Agency report. See especially Appendix D.
 * Integrated Environmental Health Impact Assessment System, web page.
 * F. Yokota and K. M. Thompson (2004a), "Value of Information literature analysis: a review of applications in health risk management", Medical Decision Making 24(3):287-298.
 * F. Yokota and K. M. Thompson (2004b), "Value of information analysis in environmental health risk management decisions: past, present and future", Risk Analysis 24(3):635-650.
 * K. Loague and Dennis L. Corwin (1996), "Uncertainty in Regional-Scale Assessments of Non-Point Source Pollutants", Soil Science Society of America, Application of GIS to the Modeling of Non-Point Source Pollutants in the Vadose Zone, SSSA Special Publication 48.
 * Jeffrey A. Grout (1993), An evaluation of the management implications of depensatory predation mortality in Pacific salmon using Bayesian decision analysis, Masters Thesis, University of British Columbia.

Use of Analytica
I felt my article made three primary contributions:
 * A clear description of the concept of EVIU
 * A mathematically precise description of the concept
 * A fully worked out, open-source, functional, transparent and understandable example that readers can actually run themselves.

Analytica was the perfect framework and programming language for this example, and I think the example is a valuable contribution that readers should find extremely helpful. When I was working on the EVIU project, I had wished such an example was available when I was refreshing my own knowledge of this concept. Yes, Analytica is "my baby", but it is also one of (if not the) most widely used framework for this type of modeling.

Mathematics Concerns
I believe my mathematical characterization to be a correct and precise characterization of EVIU. My purpose here is to describe the concept as it exists. Your mathematical concerns don't despute this, but are instead intended to be a criticism of the metric itself.

However, I disagree with your criticism. You say that if we scale our utility by a constant factor, $$b$$, as might be done with a change of units of measurement, then the EVIU also changes by a factor of $$b$$. Let's hope so! That is precisely what we want, given that EVIU is expressed in the same units as the utility. This is one of the positive attributes of all Value of Information metrics -- EVPI, EVSI and EVIU -- that because they are expressed in the same units of measurement as the utility, the resulting value has an intuitive interpretation.

— Preceding unsigned comment added by Ldc (talk • contribs) 15:37, 8 July 2011 (UTC)