This chapter develops the notion introduced in Chapter 6 on how one defines a statistical error and extends this to look at one- and two-sided intervals (see Sections 7.1 and 7.2). One-sided intervals fall into the categories of upper or lower limits, which we can place on a hypothesised effect or process that has not been observed (see Section 7.2). Each of these concepts can be interpreted in terms of a frequentist or Bayesian approach. Section 9.7.3 discusses the concept of Bayesian upper limits in the context of a fit to data, and Appendix E contains tables of integrals of several common PDFs that can be used to determine confidence intervals and limits.

Two-sided intervals

The relevance of two-sided confidence intervals is discussed in the context of useful distributions used to represent PDFs. In particular the following sections highlight the use of Gaussian, Poisson, and binomial distributions as particular use cases of such intervals.

In general, for a distribution f(x) given by some variable x, we can define some region of interest in x called a two-sided interval such that x1 < x < x2.