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The conventional approach to detecting and attributing climate change impacts on extreme weather events is generally based on frequentist statistical inference wherein a null hypothesis of no influence is assumed, and the alternative hypothesis of an influence is accepted only when the null hypothesis can be rejected at a sufficiently high (e.g., 95% or "p = 0.05") level of confidence. Using a simple conceptual model for the occurrence of extreme weather events, we show that if the objective is to minimize forecast error, an alternative approach wherein likelihoods of impact are continually updated as data become available is preferable. Using a simple "proof-of-concept," we show that such an approach will, under rather general assumptions, yield more accurate forecasts. We also argue that such an approach will better serve society, in providing a more effective means to alert decision-makers to potential and unfolding harms and avoid opportunity costs. In short, a Bayesian approach is preferable, both empirically and ethically.