We present a new Bayesian approach to object identification: variants. By object identification, we mean the detection of the member (regular variant) of a given statistical population (model) among a group of observations (variants). We present estimators for selecting the regular variant, which (i) depend on the knowledge of this population and on a suitable reference measure, only, (ii) are simple to evaluate, and (iii) are optimal, i. e. Bayesian, under certain conditions. Moreover, we combine variant selection with Bayesian classification considering the situation where we observe m _ n objects belonging to n classes and each object i is observed by way of bi variants, including the regular one. We present classifier-selectors based on the distributions of the regular variants of all classes and on suitable reference measures. We thus simultaneously estimate the regular variants and the classes using efficient algorithms.