Techniques are studied in decision analysis. It’s also hard to make sure you’ve hired the *right* people, and that they have the right incentives. We need to decide, every month, how much electricity to buy 1, 2, 3, 4, …, up to say 12 months in advance, at each facility. I think you’re right about the 5% (or so) and what you’re paying for is a group of energy analysts sitting at someone else’s desk. In insurance problems, it is well known that the worst case are when there is aggregate risk: when the bad things that can happen, happen to many agents at the same time. TY - JOUR. I have clearly done a bad job explaining what I am trying to accomplish. Write a review. For instance the function to be minimized could be Z = E + a*c95, where E is the expected cost, c95 is the estimated 95th percentile cost, and a is a parameter that represents the risk tolerance. title = "Ordinal utility models of decision making under uncertainty", abstract = "This paper studies two models of rational behavior under uncertainty whose predictions are invariant under ordinal transformations of utility. Similarly, we have a forecast for the amount of electricity the facility will use next August (also based on fitting a model to historical data), and we have a model for the distribution of actual consumption around the forecast. I agree with this somewhat, but suppose this is a company that owns and rents 100 large office buildings. We are looking for a method of making these decisions. It happens. Although I’m pretty sure it would not be worthwhile to try to build a model to answer the question posed above, there are plenty of other cases in which making a model is well worth the trouble. that all of these geographically dispersed facilities are going to face exceptionally high energy costs at the same time. * do they trade futures cap contract with an exchange or with an investment bank over-the-counter Quiggin (1990, 1994) shows that violations of stochastic dominance are pervasive in regret theory, in the sense that for any prospect with more than two distinct outcomes, there exists a preferred prospect which is first-order stochastically dominated by the initial one. How much of public health work “involves not technology but methodicalness and record keeping”? We really have no idea: if you go back twenty or thirty years, the markets and the electricity industry were so different that they don’t seem all that relevant. Thus, many consumers will anchor on an initial value, such as a monthly PITI payment, and then devote less effort to processing additional charges. The sources of uncertainty in decision making are discussed, emphasizing the distinction between uncertainty and risk, and the characterization of uncertainty and risk. In the prototypical formulation of decision making under uncertainty, an individual decision maker (DM) must choose one among a set of actions, whose consequences depend on some unknown state of the world. The other kind of hedge is a “block hedge”, in which you buy a fixed amount at a fixed price, e.g. remain decisions that humans must make. Actually I have skipped a detail, in the stuff above: you can’t just calculate the cost of electricity by multiplying (average monthly cost) x (electricity used in the month) because the cost varies from day to day, indeed from hour to hour, within the month. Electricity markets are geographically separate but electricity prices are correlated across markets, and we care very much about that correlation — …not necessarily the correlation coefficient, but the probability that multiple geographies will experience extremely high prices in the same month. The 'quantile utility' model assumes that the agent maximizes some quantile of the distribution of utility. It’s sort of like Andrew’s example that when you’re building a presidential elections model you really only have fifteen or twenty elections to use for calibration, because it’s not like the election of Martin Van Buren in 1836 tells you anything useful about today. Mendel, A Survey of Knowledge-based Sequential Decision Making under Uncertainty. We started by considering a single facility, i.e. uncertainty that the DM can encounter: upper/lower probability intervals, pos- sibilities/necessities, complete ignorance, small samples, etc. That suggests to me that even if you can put together a reasonable multi facility and month model, it might have a limited useful life. One implication of loss aversion is a bias toward the status quo (also known as consumer inertia). Obviously one way to attain this goal is to apply it to each individual facility: if no facility exceeds 20% over-budget then obviously the sum over all of them will also be acceptable. If the goal is to avoid exceeding their electricity budget by more than 20% in a given quarter year at a specific facility, with 95% certainty, that’s standard, we know how to buy hedges to handle that. Basically complex models can lull us into being more confident than is justified, especially considering the likelihood for tail events. Yes to everything you say above, pretty much. We can create a model that generates synthetic data that look like the last few years of real data, but that is not nearly enough years to know what the tail probabilities are. But if you view the challenge as partly dealing with correlations between extreme events then copula modeling might be useful. The unique value function that is consistent with homogeneous preferences is a power function (see Tversky and Kahneman, 1992, p. 309). I guess the suggestion is to think about what it would take to break the simple model or the complicated model. buy 2200 MWh at $43 per MWh. Several people on this thread have suggested this sort of scenario-based approach and it does make sense to me. You ask “How encompassing can you make your set of correlation models that will spit out synthetic data that “looks like” the realworld data that you have and expect?” That’s the right question, and the answer is that I have no faith that we can do this, largely because we don’t really know what we expect. when advising the Bank of England on risk assessment, they don’t create complicated models; rather, they create simple rules (e.g. It draws on developments in other fields, especially probability theory, to bring some structure to the challenging task of making decisions under conditions of uncertainty. Given a suitably convex regret function, the first of these effects will dominate, so decision makers will prefer the lower-probability high-payoff bet. If the company as a whole wants to avoid spending far more than expected for energy, they are already partially covered simply by being spatially diverse. “The goal is to find the optimal set of ‘hedges’ “. So, yeah, I don’t really think we can build a model that will have the right statistical properties. We draw thousands of simulations from this distribution and calculate the 95th percentile cost of electricity. Following an introduction to probabilistic models and decision theory, the course will cover computational methods for solving decision problems with stochastic dynamics, model uncertainty, and imperfect state information. *FREE* shipping on qualifying offers. Here’s a cool new book of stories about the collection of social data. I suspect you can do better with block hedges, at the cost of having a group of qualified people to continually rebalance the hedges. I, too, am worried about whether using something like lognormal distributions with a specified variance-covariance structure will capture the events the company really needs to be protected from. one year from now. I’m not really sure, actually, but that’s my impression. fast and frugal trees). This leads Tversky and Kahneman to suggest that the value function is a power function. Maybe you need to repeat this message about once a week to help keep us all in touch with reality. T1 - Ordinal utility models of decision making under uncertainty. In my experience, models with such variance-covariance matrices tend to make money here and lose money there. We also assume that the errors are correlated, so if the price is higher than the forecast price then the consumption (the ‘load’) is more likely to be higher than lower than the forecast load. Abdelrahman marked it as to-read Apr 03, 2013. Rahul, Whether or not this makes sense depends on the profitability of the facility and the price of power, but there are lots of situations in which a low profit per unit of electricity consumed (aluminum mills are a classic example) industry can make more money when electricity prices are high by not consuming than they can at average prices. I think that if they’re hedged adequately against a 95th percentile fiscal quarter, whatever they mean by that exactly, and they experience a 99th percentile fiscal quarter, that will hurt but won’t be crushing. The model that is useful to an options issuer will be quite different to the one required for an options user ( as a hedge). This involves both the problem of modeling our initial uncertainty about the world, and that of draw-ing conclusions from evidence and our initial belief. Decision Making Under Uncertainty: Models and Choices Conditions of uncertainty exist when the future environment is unpredictable and everything is in a state of flux. We can check the market price per MWh for buying electricity in that month. These biases may explain borrowers who fail to refinance higher-rate mortgages, despite favorable interest rates, credit quality, or equity advantages. The models used in cost-benefit analyses, unlike … Putting this stuff together, we have a joint distribution of (price, load) next August. You can model the demand stochastically with historical data. Filipe rated it liked it Apr 10, 2020. This approach is based on the notion that individual attitudes towards risk vary. An introduction to decision making under uncertainty from a computational perspective, covering both theory and applications ranging from speech recognition to airborne collision avoidance. Some individuals are willing to take only smaller risks (“risk averters”), while others are willing to take greater risks (“gamblers”). Decision under Uncertainty: Further, as everybody knows that now-a-days a business manager is unable to have a complete idea about the future conditions as well as various alternatives which will come across in near future. 2013). An action's consequences depend on the unknown state of the world, however, and each action yields a certain consequence corresponding to each state of the world. The model leverages recent advances in three different fields: (1) neural models of Bayesian inference, (2) the theory of optimal decision making under uncertainty based on partially observable Markov decision processes (POMDPs), and (3) algorithms for temporal difference (TD) learning in … Making decisions in conditions of uncertainty involves judgment, values, and balance in appraising the different options available (including the option of deciding not to act). A Dynamic Dual-Process Model of Decision-making Under Uncertainty. It’s these hourly numbers that we use for the actual calculation. probably not helpful to understand those. New textbook, “Statistics for Health Data Science,” by Etzioni, Mandel, and Gulati, Hey! This axiom has been challenged by many researchers, starting with Allais (1953b) who presented a now-classic example that violates linearity in probabilities (and thus the independence axiom). First, how do we learn about the world? Sorry about the late response. With this problem It is not clear to me in either direction. There is evidence that mortgage borrowers focus on the monthly payment and pay less attention to additional points and fees (ICF Macro 2009). The classical expected utility model remains, however, the most useful model for insurance analysis. Mostly no problem, but a tail event leads to catastrophe. What if it happened again, with even higher prices and for an even longer duration? An introduction to decision making under uncertainty from a computational perspective, covering both theory and applications ranging from speech recognition to airborne collision avoidance. Thanks much Many important problems involve decision making under uncertainty—that is, choosing actions based on often imperfect observations, with unknown outcomes. John Quiggin, in Handbook of the Economics of Risk and Uncertainty, 2014. In the end, I’d want to compare the complex models with the simpler ones – if the complex model does not provide more useful or different results, then why use it? This chapter reviews developments in the theory of decision making under risk and uncertainty, focusing on models that, over the last 40 years, dominated the theoretical discussions. There was so much to read here for a two minute coffee break. The Hurwicz criterion computes a weighted value from the minimum and the maximum payoff of the strategies and is therefore a combination of maximin and maximax. On the Foundations of Decision Making Under Partial Information; D. Rios Insua. Similarly, how predictable is a facility’s electric load, and what does the distribution p(load | predicted load) look like? It’s pretty clear that the optimal decision for the company, as far as the amount of electricity to buy in advance, is going to be less than the amount that would be obtained by trying to make sure they don’t go over 15% at any facility, in any month. Some quarters they won’t be of any use (and you lose premium), other quarters they will do exactly what they were meant to do. Each model is different, of course, but in the ones I’ve done, the false-positives and false-negatives (opportunity costs etc.) Sometimes it’s worth creating a complicated statistical model that can help you make a decision; other times it isn’t. The basic approach proposed by Loomes and Sugden may be traced back to Savage’s (1951) work on statistical decision theory. The basic idea is that you are worried that the price of electricity next June might be exceptionally high, but some electricity producer somewhere is worried that the price might be exceptionally low, so you’re both willing to make a deal. Sl.No Chapter Name MP4 Download; 1: Tutorial - How to Install Octave and using Octave: Download: 2: Background and relevance: Download: 3: Examples of managing uncertainty and making decisions Regret theory (Loomes and Sugden, 1982, see also Bell, 1982) was based on the same intuition that later gave rise to Gul’s disappointment theory. Yes, some of the facilities have the capability of on-site generation, or at least I think so; normally only for emergency use, but if the price of electricity spiked prohibitively then I suppose that could qualify, maybe. This value function satisfies V′(x) > 0 for all x ≠ 0, V″(x) > 0 for x < 0, and V”(x) < 0 for (x) > 0, and is therefore S-shaped (see Figure 9.1) The convexity of the value function for negative x, and its concavity for positive x, is in accordance with the findings of risk seeking for negative prospects (x < 0), and risk aversion for positive prospects (x < 0). Why are we not framing the problem this way? The price for a given month for a given facility can be thought of as a forecast for what the price will be when the time comes. I just don’t know how much there is to gain from such a model, compared to just using some rules of thumb to make the decisions, and I think that even figuring this out will take a lot of work. As I mentioned in an earlier comment, one thing the ‘specified amount of protection’ can mean is: That’s why I’m a fan of scenario analysis, at least as a first step. If they budget $x and the expense is $1.2*x, well, they’re out $0.2*x but that’s it. In statistical analyses, loss functions are often stated directly, without reference to underlying consequences or utility functions. Since 1997 he has taught courses in applied probability, stochastic systems, queuing models, decision-making, operations research, and statistics while being on the faculty at Pennsylvania State University and Texas A&M University. Whereas if we don’t have a model at all, what are we gonna do? In our case we are assuming the distribution is lognormal. Interesting problem! Consider the expected-utility representation, where p and q are simple probability distributions on X=X1× … ×Xn and u on X is unique up to a positive affine transformation au+b, a>0. I am part of a three-person consulting team that is advising the company. See also Elicitation of Probabilities and Probability Distributions. Wow. However, this model has been criticized as inadequate … But coding it up and getting it to converge is a much bigger task. A company say in India exporting products to the USA is exposed to the risks of dollar to rupee price fluctuations. First, it is often possible to identify clear trends, such as market demographics, that can help define potential demand for a company's future products or services. The wide adoption of Convolutional Neural Networks (CNNs) in applications where decision-making under uncertainty is fundamental, has brought a great deal of attention to the ability of these models to accurately quantify the uncertainty in their predictions. Presumably Phil’s group has some mechanism to account for out of sample events because there have been several in the last few decades and it would be crazy to overlook those, so I’m sure they haven’t. But I don’t think that will really do what we want: in the abstraction of our model, there’s this energy market and you buy and sell energy, and pay these prices, yada yada, but if the ‘black swan events’ are not of the type that we’re modeling then the whole modeling paradigm breaks down. I always start with a simple model and then add complexities (e.g., correlations between uncertain factors are added to a model without these; multiple types of sectors/agents are added after modeling a generic one, etc.). Such “black swans” pose a real challenge. Is there viability in having on site generators with perhaps on site gas storage? If your company is big enough to have a well-staffed energy trading group, you probably don’t have to pay more than few million to save $10-$20 million. In this case, with prize probabilities of 0.05 and 0.04, the likelihood that both bets will pay off in a given state is 0.002. We assume the actual price will be distributed around the forecast price. But do you have to? Policies that are optimal under an expected utility over a given time horizon, are often not optimal when you are concerned about the properties of sample paths, most importantly if there is some return that would act as an “absorbing state” which is basically what Herman refers to. 1, 07.1988, p. 79-104. And consumption may correlate highly with price and demand spikes in the region. G. Parmigiani, in International Encyclopedia of the Social & Behavioral Sciences, 2001. Electricity prices are correlated across the country, but they are not perfectly correlated (coal, hydro, wind, solar, nuclear, and natural gas prices don’t vary in lockstep, and there are transmission losses and transmission bottlenecks that stop electricity from flowing freely all across the country.) As the model becomes more complex (hence, more realistic), the danger of tunnel vision increases. 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