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Jun 1, 2000 · The uncertainty that remains after the best possible analysis has been undertaken is what we call residual uncertainty—for example, the outcome of an ongoing regulatory debate or the performance attributes of a technology still in development.
- Clear Enough/Predictable Future. This would apply to situations where sufficiently precise predictions can be made about key variables affecting a company’s markets and businesses (e.g.
- Alternative Futures. Sometimes firms are faced with discrete scenarios, e.g. regulatory changes, significant actions of competitors, etc. It’s hard to predict which outcome will actually happen, although one can assign probabilities to various alternatives.
- Range of Futures. Unlike level two (where the outcome is either-or), in level three, a small number of variables define a broad range out outcomes, but the actual result may lie anywhere in between.
- True Uncertainity/Ambiguity. This type of uncertainty is actually quite rare. It may happen in cases of entirely new technologies where technology adoption, platform prevalence, competitive landscape and revenue models are all up in the air.
The value xi –x is the deviation of a particular trial from the mean (also called a residual). We can’t sum the residuals, because the construction of the definition of x causes the residuals to always sum to zero.
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What makes for a good strategy in highly uncertain business environments? Some executives seek to shape the future with high-stakes bets. Eastman Kodak Company, for example, is spending $500...
- 9 Model Sensitivity and Uncertainty Analysis
- 1. Introduction
- 2. Issues, Concerns and Terminology
- 3. Variability and Uncertainty in Model Output
- 3.1. Natural Variability
- 3.2.1. Parameter Value Uncertainty
- 3.3. Decision Uncertainty
- Surprises
- 4. Sensitivity and Uncertainty Analyses
- 4.1. Uncertainty Analyses
- 4.1.1. Model and Model Parameter Uncertainties
- 4.1.2. What Uncertainty Analysis Can Provide
- 4.2. Sensitivity Analyses
- 4.2.1. Sensitivity Coefficients
- 4.2.2. A Simple Deterministic Sensitivity Analysis Procedure
- Groups of factors
- Latin Hypercube Sampling
- 6. Communicating Model Output Uncertainty
- 7. Conclusions
The usefulness of any model depends in part on the accuracy and reliability of its output. Yet, because all models are imperfect abstractions of reality, and because precise input data are rarely if ever available, all output values are subject to imprecision. Input data errors and modelling uncertainties are not independent of each other – they ca...
Models are the primary way we have to estimate the multi-ple effects of alternative water resources system design and operating policies. Models predict the values of various system performance indicators. Their outputs are based on model structure, hydrological and other time-series inputs, and a host of parameters whose values describe the system...
Outcomes or events that cannot be predicted with certainty are often called risky or uncertain. Some indi-viduals draw a special and interesting distinction between risk and uncertainty. In particular, the term risk is often reserved to describe situations for which probabilities are available to describe the likelihood of various events or outcome...
Differences between model output and observed values can result from either natural variability, such as is caused by unpredictable rainfall, evapotranspiration, water consumption and the like, and/or by both known and unknown errors in the input data, the model param-eters or the model itself. The later is sometimes called knowledge uncertainty, b...
The main source of hydrological model output value variability is the natural variability in hydrological and meteorological input series. Periods of normal precipita-tion and temperature can be interrupted by periods of extended drought and intense meteorological events such as hurricanes and tornadoes. There is no reason to believe that such even...
A possible source of uncertainty in model output results from uncertain estimates of various model parameter values. If the model calibration procedure were repeated using different data sets, different parameter values would result. Those values would yield different simulated sys-tem behaviour and, thus, different predictions. We can call this pa...
Uncertainty in model predictions can result from unanticipated changes in what is being modelled. These can include changes in nature, human goals, interests, activities, demands and impacts. An example of this is the deviation from standard or published operating policies by operators of infrastructure such as canal gates, pumps and reservoirs in ...
Water resources managers may also want to consider how vulnerable a system is to undesirable environmental surprises. What havoc might an introduced species like the zebra mussel invading the Great Lakes of North America have in a particular watershed? Might some introduced disease suddenly threaten key plant or animal species? Might management pla...
An uncertainty analysis is not the same as a sensitivity analysis. An uncertainty analysis attempts to describe the entire set of possible outcomes, together with their associated probabilities of occurrence. A sensitivity analysis attempts to determine the change in model output values that results from modest changes in model input values. A sens...
Recall that uncertainty involves the notion of random-ness. If a value of a performance indicator or performance measure, like the phosphorus concentration or the depth of water at a particular location, varies, and this variation over space and time cannot be predicted with certainty, it is called a random variable. One cannot say with certainty w...
Consider a situation as shown in Figure 9.8, in which, for a specific set of model inputs, the model outputs differ from the observed values, and for those model inputs, the observed values are always the same. Here, nothing occurs randomly. The model parameter values or model structure need to be changed. This is typically done in a model calibrat...
An uncertainty analysis takes a set of randomly chosen input values (which can include parameter values), passes them through a model (or transfer function) to obtain the distributions (or statistical measures of the distributions) of the resulting outputs. As illustrated in Figure 9.11, the output distributions can be used to describe the range of...
‘Sensitivity analysis’ aims to describe how much model output values are affected by changes in model input values. It is the investigation of the importance of impreci-sion or uncertainty in model inputs in a decision-making or modelling process. The exact character of a sensitivity analysis depends upon the particular context and the questions of...
One measure of sensitivity is the sensitivity coefficient. This is the derivative of a model output variable with respect to an input variable or parameter. A number of sensitivity analysis methods use these coefficients. First-order and approximate first-order sensitivity analyses are two such methods that will be discussed later. Analytical metho...
This deterministic sensitivity analysis approach is very similar to those most often employed in the engineering economics literature. It is based on the idea of varying one uncertain parameter value, or set of parameter values, at a time. The ideas are applied to a water quality example to illustrate their use. The output variable of interest can ...
It is often the case that reasonable error scenarios would have several parameters changing together. For this reason, the alternatives have been called parameter sets. For example, possible errors in water depth would be accompanied by corresponding variations in aquatic vege-tation and chemical parameters. Likewise, alternatives related to change...
For the simple Monte Carlo simulations described in Chapters 7 and 8, with independent errors, a proba-bility distribution is assumed for each input parameter or variable. In each simulation run, values of all input data are obtained from sampling those individual and independent distributions. The value generated for an input parameter or variable...
Spending money on reducing uncertainty would seem preferable to spending it on ways of calculating and describing it better. Yet attention to uncertainty commu-nication is critically important if uncertainty analyses and characterizations are to be of value in a decision-making process. In spite of considerable efforts by those involved in risk ass...
This chapter has provided an overview of uncertainty and sensitivity analyses in the context of hydrological or water resources systems simulation modelling. A broad range of tools are available to explore, display and quantify the sensitivity and uncertainty in predictions of key output variables and system performance indices with respect to impr...
A residual (or fitting deviation), on the other hand, is an observable estimate of the unobservable statistical error. Consider the previous example with men's heights and suppose we have a random sample of n people.
Nov 2, 2020 · In normal times organizations face numerous uncertainties of varying consequence. Managers deal with challenges by relying on established structures and processes. These are designed to reduce uncertainty and support calculated bets to manage the residual risks.
