Introduction

It is difficult and expensive to collect the field observations that an environmental engineer or hydrogeologist needs to answer an engineering or scientific question. Therefore, one must make the best use of available data to estimate the needed parameters. For example, a large number of measurements are collected in the characterization of a hazardous-waste site: water-surface level in wells, transmissivity and storativity (from well tests), conductivity from permeameter tests or borehole flowmeters, chemical concentrations measured from water and soil samples, soil gas surveys, and others. However, because most subsurface environments are complex, even a plethora of data is not sufficient to resolve with accuracy the distribution of the properties that govern the rates of flow, the rates of transport and transformation of chemicals, or the distribution of concentrations in the water and the soil. The professionals who analyze the data must fill in the gaps using their understanding of the geologic environment and of the flow, transport, or fate mechanisms that govern the distribution of chemicals.

However, process understanding is itself incomplete and cannot produce a unique or precise answer. Statistical estimation methods complement process understanding and can bring one closer to an answer that is useful in making rational decisions. Their main contribution is that they suggest how to weigh the data to compute best estimates and error bounds on these estimates. Statistics has been aptly described as a guide to the unknown; it is an approach for utilizing observations to make inferences about an unmeasured quantity.