Safety First: Stochastic Decision Problems

Vladimir Norkin of the Glushkov Institute of Cybertronics in Kiev gave a very interesting (and very equation based) seminar on mixed integer approaches in stochastic optimisation on Friday afternoon. Norkin has been a visitor in IME for the last week. Titled "Safety First Class of Stochastic Decision Problems: Mixed Integer Approach" he explored examples of portfolios with critical thresholds.

Portfolio selection is a relatively new area for me, something I have learnt since arriving at IIASA. Its interesting to see how the idea is used in a variety of sectors and the philosophy of risk minimisation by selecting a diverse portfolio. Safety first means the minimisation of the probability of bad events.

Norkin started the seminar with a quote from Ulrich Beck (1986) that "society starts to realise its exposure to changes including those that appear due to its own development..." and then moved on to AD Roy's (1952) paper on "Safety first and the holding of assets". Its interesting to note that while mathematical techniques and computational capabilities have increased since then, the idea and fundamental theory still holds true.

Norkin also discussed techniques associated with a finite scenario set that relates directly to my YSSP project. He intimated that all finite scenario set probability optimisation problems can be reduced to a mixed Boolean programming problem building on Korbut and Finkelstein (1969).

Wine country

When I think of Austria wine farming doesn't really spring to mind, meat and beer and anything deep-fried yes but not wine. There is in fact a large winelands area near to Laxenburg dotted with Heurigers (wine taverns), most of which produce young wines as their house wine that isn't Sauvignon Blanc or Riesling. I can't place it.

Last night the IME group (we're rather colourful for a bunch of scientists) frequented a proper (read not touristy) heuriger, you can tell because it only opens at specific times of the year unlike the touristy ones.

Nestled into the side of the hill and almost completely obscured by plants, the heuriger Rotes Mauerl is an ideal place to relax and enjoy the view of the valley below.

The menu is meant to be fairly simple but I don't think anyone told the owners. There is a lot of meat and bread, like a large tower available to choose from.

We drank the house white and red, delivered in large carafes, while catching the last rays of sun. Oh what a charmed life we lead :)

The dessert here is interesting, they seem to leave out the sugar from many a thing, namely cheesecake. The cheesecake here, otherwise known as topfenstrudel, is almost savoury in my opinion. I think the next step is to try make a little slice of home for comparison.
Our evening ended after the last bus back from Laxenburg so we were dropped at the Modling train station and caught the train back to Vienna.

Overall a wonderful way to end a working day.

IME: Coping with Uncertainty: Spatio-temporal heterogeneities

The second uncertainty seminar dealt with spatio-temporal problems. This seminar series is not meant to teach us new techniques but to create an awareness that one shouldn't automatically use the stock standard stochastic tools available like averaging, regression etc.

When analysing spatio-temporal problems they often have multiple scales, high dimensionality and multimodal dimensions. There are methods available to deal with this, most notably discounting and Fast Monte Carlo simulations. Consider the scatter plot above, its multimodal. How do you describe the multi-dimensional density function?
The Adaptive Monte Carlo STO procedure can be used for optimization module (structural and non-structural decision, production allocation).

All these techniques are all of interest to me currently. I'm currently designing a decision framework and to cope with the uncertainty one needs to implement some sort of robust solution. Note the some sort, I haven't got there yet.

IME: Modeling Primer

Yesterday afternoon saw the second seminar of the day, 'Modeling Primer' by the IME group. This lecture delved into the world of rational decision making: making the right decision at the right time. The right decision takes experience, intuition and knowledge (facts and rules).

It is a myth that it is easy to find a solution to a complex problem, for simple cases the decision is correct but you are taking a chance for complex problems.

A model is an adequate (for a purpose) representation of a part of (interdisciplinary) knowledge. I reiterate a quote from the beginning of June: All models are wrong but some are useful. They provide a tool to HELP find the best decision. BEST is merely a suggestion of decisions for reaching certain goals which can be done through analysis of trade-offs between conflicting goals or an evaluation of the consequences of various decisions.

A model requires consistency, transparency, replicability and documentation. Something to remember is that RARE events do happen, the low probability mean it won't happen.

Some parting words of wisdom from A. Einstein - "Everything should be made as simple as possible, but not one bit simpler." Words to live by.

IME: Coping with Uncertainty: Concept of Robust Solutions

Tatiana Ermolieva (IME/LUC) presented what will probably be one of the most useful lectures of the YSSP for my research. Uncertainty is inherent in every decision one takes, how do you design a system that copes with it?

There are two types of systems (processes), one is the traditional natural system like physics that is governed by fixed relations, the other is human-related systems governed by old and new policies dependent on decisions of various agents/actors. From this we can distinguish knowable and unknowable (inherent: natural systems) uncertainties.

Human-related systems require a new approaches to stability (security) analysis. There are multiple reasons, the lack of observations, the expense of experimentation, observations contaminated by old policies and observations of results/impacts may come with a delay or cause irreversible change (climate change for instance)

Although its impossible to predict human-driven systems, it is possible to find robust solutions good against all uncertainties. These robust policies assist in the long-term stability of systems performance.

Popular security analysis includes aggregate analysis, least-squares analysis etc but these are not robust solutions, all are sensitive to outliers. I've appropriated the image above because it is one of the best examples I've ever seen of a mean/median/mode argument. The mean is in red, the median in green and the mode in maroon. Notice how most of the information is lost in the case of the mean. Remember: the mean is MEANINGLES! The median is more robust.
A common feature of most systems is a range of possible outcomes resulting from different scenarios or the variability (eg weather). The uncertainty is which scenario comes next?

I'm currently making my way through 'Coping with Uncertainty: Robust Solutions'. Its written by the IME group at IIASA and works through various techniques for robust systems mostly through real-world applications. The UCT library is in the process of buying a copy, it should arrive sometime in the next year :P

IME: Multiple Criteria Analysis

Marek Makowski gave a seminar today on Multiple Criteria Analysis for the Integrated Modeling Environment (IME) group.

Integrated model analysis helps one analyse a manageable number of solutions having different trade-offs between (conflicting) criteria. There are two different types available. Descriptive (simulations) which is alternative-focused. The input is the decisions and the outcomes the goals. The other is Prescriptive (optimisation) is goal-orientated. The inputs are the goals (preferences) and the outcomes are the decisions. Where there are goals, one needs multiple criteria analysis.

IME IIASA developed a Multi-criteria Analysis tool for an energy project a few years ago. The tool is fairly easy to use and available to the public (along with some introductory and advanced papers). Our next session is a hands on workshop for using the tool.

In other news I skipped Adaptive Dynamics this morning, the PHD Comic below seems rather apt, the lecture venue is literally just down the hall.

Structured Modeling Technology

"Structured Modeling Technology (SMT) is based on the paradigm of separating the model specification from its data. Model specification contains the semantic descriptions of the model entities (variables or parameters) and the relationships between them. Based on the model specification it is possible to generate the data structures in the data-warehouse (DW) to store the model data".

SMT was designed to support model-based analysis of complex decision problems. There are many advantages to divide, conquer and integrate (see computer science theory) such as one data repository, reuse of specifications etc.

The Integrated Modeling Environment (IME) group at IIASA developed SMT in 2004. I am hoping to learn how to use the same fundamental modeling techniques (divide, conquer, integrate, document) while developing my thesis methodology.