Data-set description and bias (Review)

The qualities of astronomical observations - ranging from good measurements with a definite result and negligible error to upper limits or even no result at all - and their relevance to data sets are considered, as well as the contraction of data sets to their essential contents and the evaluation of intrinsic data. Maximum likelihood methods are illustrated, using deconvolution methods. Parameters and parameter spaces, incompleteness, bias, selection, and the role of data quality on biases are considered. Principal component analysis and its role in detecting biases, and a method to statistically remove biases, in particular the observational magnitude cut-off bias, are discussed recipes for avoiding undetected biases are outlined.