Ron Clutz’s introduction, based on a Scientific American article by John Horgan on January 4, 2016, starts to grapple with the issues involved.

The take home quote from Horgan is on the subject of false positives.

“Here is my more general statement of that principle: The plausibility of your belief depends on the degree to which your belief–and only your belief–explains the evidence for it. The more alternative explanations there are for the evidence, the less plausible your belief is. That, to me, is the essence of Bayes’ theorem.

“Alternative explanations” can encompass many things. Your evidence might be erroneous, skewed by a malfunctioning instrument, faulty analysis, confirmation bias, even fraud. Your evidence might be sound but explicable by many beliefs, or hypotheses, other than yours.

In other words, there’s nothing magical about Bayes’ theorem. It boils down to the truism that your belief is only as valid as its evidence. If you have good evidence, Bayes’ theorem can yield good results. If your evidence is flimsy, Bayes’ theorem won’t be of much use. Garbage in, garbage out.”
With respect to the question of whether global warming is human caused, there is basically a combination of three elements – (i) Human caused (ii) Naturally caused (iii) Random chaotic variation. There may be a number of sub-elements and an infinite number of combinations including some elements counteracting others, such as El Nino events counteracting underlying warming. Evaluation of new evidence is in the context of explanations being arrived at within a community of climatologists with strong shared beliefs that at least 100% of recent warming is due to human GHG emissions. It is that same community who also decide the measurement techniques for assessing the temperature data; the relevant time frames; and the categorization of the new data. With complex decisions the only clear decision criteria is conformity to the existing consensus conclusions. As a result, the original Bayesian estimates become virtually impervious to new perspectives or evidence that contradicts those original estimates.