Abstract
Recently, we proposed “measurement theory”, i.e., the foundation of measurements. This is a general measurement theory for both classical and quantum systems. The purpose of this paper is to give a foundation to statistics in terms of measurements, that is, to characterize or understand statistics as one of the aspects of measurement theory. Studying several statistical examples in the light of measurement theory, we show that Fisher's and Bayes's methods are described in terms of measurements. Also, we characterize “estimation under loss function in statistics” in measurement theory. Therefore, we may conclude that statistics is a certain aspect of measurements. This viewpoint is important since it clarifies the relation between statistics and the other aspects of measurements.
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