Dealing with Uncertainty

In general, there are two uncertainty types, namely, random uncertainty and nonrandom (inherent) uncertainty. For random uncertainty, the classical example is the question of What is the probability of observing a dry year from a sequence of say, 12-year record It is assumed that the probability of wet and dry year occurrences is equally likely, mutually exclusive and completely random (independent). Given the information that there are 4 dry and 8 wet years in sequence, the probabilities of random wet and dry year occurrences are 4/12 = 0.32 and 8/12 = 0.78, respectively. Hence, random uncertainty deals with events. Once the event occnrs, the uncertainty goes away for that particular event. 

On the other hand, nonrandom (inherent) uncertainty deals with characteristics of the objects themselves, and arises from our att pt to classify or categorize than. The classical question is to ask which years are dry (black) and which are wet (white) If thae are gray years of different tones then the answer to such a question becomes fuzzy, i.e. vague, ambiguous and incomplete. 

The third kind of uncertainty deals with potential hazards and exploring the unknown. It is often a subjective, rather than an objective, exercise, and our perceptions are an integral part of our assessment. The second type, we will use to classify all the problems where uncertainly occurs as a result of an essential difficulty in calculating the results of a deterministic process. This includes chaotic systems (ones in which the outcome is deterministically dependent on initial conditions, but is also extremely sensitive to their change, making it practically impossible to predict it) and problems in which computing a solution is probably unfeasible. 

How to extract from E(qj,t) knowledge about momenta is treated below in Sec. III. A, where the structure of quantum mechanics, the use of operators and wavefunctions to make predictions and interpretations about experimental measurements, and the origin of uncertainty relations such as the well known Heisenberg uncertainty condition dealing with measurements of coordinates and momenta are also treated. 

In dealing with future uncertainties. Royal Dutch/SheU pioneered Scenario planning (54,55). Alternative assumptions for future developments can be combined under this approach in various ways to give a number of consistent possible outcomes (56) and provide a basis for both actions and reactions. The approach has rewarded Shell handsomely. 

Rules may represent either guidelines based on experience, or compact descriptions of events, processes, and behaviors with the details and assumptions omitted. In either case, there is a degree of uncertainty associated with the appHcation of the rule to a given situation. Rule-based systems allow for expHcit ways of representing and dealing with uncertainty. This includes the representation of the uncertainty of individual rules, as weU as the computation of the uncertainty of a final conclusion based on the uncertainty of individual rules, and uncertainty in the data. There are numerous approaches to uncertainty within the rule-based paradigm (2,35,36). One of these approaches is based on what are called certainty factors. In this approach, a certainty factor (CF) can be associated with variable—value pairs, and with individual rules. The certainty of conclusions is then computed based on the CF of the preconditions and the CF for the rule. For example, consider the foUowing example. 

Statistics represents a body of knowledge which enables one to deal with quantitative data reflecting any degree of uncertainty. There are six basic aspects of apphed statistics. These are ... 

Six isotopes of element 106 are now known (see Table 31.8) of which the most recent has a half-life in the range 10-30 s, encouraging the hope that some chemistry of this fugitive species might someday be revealed. This heaviest isotope was synthsised by the reaction Cm( Ne,4n) 106 and the present uncertainty in the half-life is due to the very few atoms which have so far been observed. Indeed, one of the fascinating aspects of work in this area is the development of philosophical and mathematical techniques to define and deal with the statistics of a small number of random events or even of a single event. 

In LC both quantitative and qualitative accuracy depends heavily on the components of the sample being adequately resolved from one another. The subject of resolution has already been discussed, but it is necessary to consider those areas where uncertainty can still arise. Unfortunately, unless the analyst is aware of the pitfalls and how to deal with them, false assumptions of resolution can be made very easily. 

All these methods pretend to represent the intuitive way an expert deals with uncertainty. Whether this is true remains an open question. No method has yet been evaluated thoroughly. Modelling uncertainty to obtain a reasonable reliability measure for the conclusions remains one of the major unsolved issues in expert system technology. Therefore, it is important that in the expert system a mechanism is provided to define its boundaries, within which it is reasonably safe to accept the conclusions of the expert system. 

There are a number of other problems relating to the manipulation and interpretation of data that cause difficulty. The most common are (i) uncertainty about the number of replicate results required for proper comparison of the certified reference value, and (2) the actual analytical result and how gross outlier results should be handled. These issues and how to deal with data that falls outside the confidence limit are reviewed in detail by Walker and Lumley (1999), who conclude that whilst customer requirements may provide answers the judgement of the analyst must always be the final arbiter in any decision ... 

Fuzzy logic is often referred to as a way of "reasoning with uncertainty." It provides a well-defined mechanism to deal with uncertain and incompletely defined data, so that one can make precise deductions from imprecise data. The incorporation of fuzzy ideas into expert systems allows the development of software that can reason in roughly the same way that people think when confronted with information that is ragged around the edges. Fuzzy logic is also convenient in that it can operate on not just imprecise data, but inaccurate data, or data about which we have doubts. It does not require that some underlying mathematical model be constructed before we start to assess the data. 

Within a fuzzy system, an inference engine works with fuzzy rules it takes input, part of which may be fuzzy, and generates output, some or all of which may be fuzzy. Although the role of a fuzzy system is to deal with uncertain data, the input is itself not necessarily fuzzy. For example, the data fed into the system might consist of the pH of a solution or the molecular weight of a compound, both of which can be specified with minimal uncertainty. In addition, the output that the system is required to produce is of more value if it is provided in a form that is crisp "Set the thermostat to 78°C" is more helpful to a scientist than "raise the temperature of the oven." Consequently, the fuzzy core of the inference engine is bracketed by one step that can turn crisp data into fuzzy data, and another that does the reverse. 

Accuracy is often used to describe the overall doubt about a measurement result. It is made up of contributions from both bias and precision. There are a number of definitions in the Standards dealing with quality of measurements [3-5]. They are only different in the detail. The definition of accuracy in ISO 5725-1 1994, is The closeness of agreement between a test result and the accepted reference value . This means it is only appropriate to use this term when discussing a single result. The term accuracy , when applied to a set of observed values, describes the consequence of a combination of random variations and a common systematic error or bias component. It is preferable to express the quality of a result as its uncertainty, which is an estimate of the range of values within which, with a specified degree of confidence, the true value is estimated to lie. For example, the concentration of cadmium in river water is quoted as 83.2 2.2 nmol l-1 this indicates the interval bracketing the best estimate of the true value. Measurement uncertainty is discussed in detail in Chapter 6. 

This chapter deals with handling the data generated by analytical methods. The first section describes the key statistical parameters used to summarize and describe data sets. These parameters are important, as they are essential for many of the quality assurance activities described in this book. It is impossible to carry out effective method validation, evaluate measurement uncertainty, construct and interpret control charts or evaluate the data from proficiency testing schemes without some knowledge of basic statistics. This chapter also describes the use of control charts in monitoring the performance of measurements over a period of time. Finally, the concept of measurement uncertainty is introduced. The importance of evaluating uncertainty is explained and a systematic approach to evaluating uncertainty is described. 

Related to the hydromorphological key issue, one of the main uncertainties is the feasibility (technical but mainly economic) of the restoration measures. As already mentioned, the lack of policy (guidelines, guidance) on how to restore hydromorphology is identified. Guidelines on the percentage of the basin to restore are desirable but also recommendations how to deal with, for instance existing dams in the basin and potentially the need to build new ones. 

---