Testing distributed parameter hypotheses for the detection of climate change

A general statistical methodology, based on testing alternative distributed parameter hypotheses, is proposed as a method for deciding whether or not anthropogenic influences are causing climate change. This methodology provi des a framework for including known uncertainties in the definition of the hypotheses by allowing model parameters to be specified by probability dist ributions and thereby allowing the definition of more realistic hypotheses. The method can be used to derive the unique statistical test that minimize s errors in test conclusions. The method is applied to illustrative detecti on problems by first defining alternative hypotheses for global mean temper ature; second, deriving the most powerful test and calculating its statisti cs; third, applying the test to observed temperature records; and finally, illustrating the test statistics and results on a receiver or relative oper ating characteristic curve showing the relation between false positive and false negative test errors. It is demonstrated, with an illustrative exampl e, that proper accounting for the uncertainty in all the parameters can pro duce very different statistical conclusions than the conclusions that would be obtained by simply fixing some parameters at nominal values.