## Key concepts and terminology

Definitions associated with conducting an uncertainty analysis include uncertainty, accuracy, precision and variability. These terms are sometimes used loosely and may be misunderstood. They have in fact clear statistical definitions that should be used in order to be clear about what is being quantified and reported. Several definitions are given here, in alphabetical order:

Accuracy: Agreement between the true value and the average of repeated measured observations or estimates of a variable. An accurate measurement or prediction lacks bias or, equivalently, systematic error.

Bias: Lack of accuracy. Bias (systematic error), can occur because of failure to capture all relevant processes involved or because the available data are not representative of all real-world situations, or because of instrument error.

Confidence Interval: The true value of the quantity for which the interval is to be estimated is a fixed but unknown constant, such as the annual total emissions in a given year for a given country. The confidence interval is a range that encloses the true value of this unknown fixed quantity with a specified confidence (probability). Typically, a 95 percent confidence interval is used in greenhouse gas inventories. From a traditional statistical perspective, the 95 percent confidence interval has a 95 percent probability of enclosing the true but unknown value of the quantity. An alternative interpretation is that the confidence interval is a range that may safely be declared to be consistent with observed data or information. The 95 percent confidence interval is enclosed by the 2.5th and 97.5th percentiles of the PDF.

Precision: Agreement among repeated measurements of the same variable. Better precision means less random error. Precision is independent of accuracy.

Probability density function (PDF): The PDF describes the range and relative likelihood of possible values. The PDF can be used to describe uncertainty in the estimate of a quantity that is a fixed constant whose value is not exactly known, or it can be used to describe inherent variability. The purpose of the uncertainty analysis for the emission inventory is to quantify uncertainty in the unknown fixed value of total emissions as well as emissions and activity pertaining to specific categories. Thus, throughout this chapter it is presumed that the PDF is used to estimate uncertainty, and not variability, unless otherwise stated.

Random errors: Random variation above or below a mean value. Random error is inversely proportional to precision. Usually, the random error is quantified with respect to a mean value, but the mean could be biased or unbiased. Thus, random error is a distinct concept compared to systematic error.

Systematic error: Another term for bias, which refers to lack of accuracy.

Uncertainty: Lack of knowledge of the true value of a variable that can be described as a probability density function (PDF) characterising the range and likelihood of possible values. Uncertainty depends on the analyst's state of knowledge, which in turn depends on the quality and quantity of applicable data as well as knowledge of underlying processes and inference methods.

Variability: Heterogeneity of a variable over time, space or members of a population (Morgan and Henrion, 1990; Cullen and Frey, 1999). Variability may arise, for example, due to differences in design from one emitter to another (inter-plant or spatial variability) and in operating conditions from one time to another at a given emitter (intra-plant variability). Variability is an inherent property of the system or of nature, and not of the analyst.

Figure 3.2 Illustration of accuracy and precision

(a) inaccurate but precise; (b) inaccurate and imprecise; (c) accurate but imprecise; and (d) precise and accurate

Figure 3.2 Illustration of accuracy and precision

Inventories should be accurate in the sense that they are neither over- nor underestimated as far as can be judged, and precise in the sense that uncertainties are reduced as far as practicable. Figure 3.2 provides a conceptual comparison of accuracy and precision. An accurate inventory is one that is free of bias but that could be precise or imprecise. A precise inventory may appear to have low uncertainty but if the inventory is inaccurate, then the inventory systematically over- or under-estimates the true emissions or removals. Inaccuracy, or bias, can occur because of failure to capture all relevant emissions or removal processes or because the available data are not representative of real-world situations. There is no predetermined level of precision, in part because of the inherent variability of some categories.