How to handle risky experiments producing uncertain phenomenon like cold fusion?

Some experiments are risky in that they cannot repeatedly produce certain phenomenon at will for study because the scientific knowledge of the process generating the uncertain phenomenon is poorly understood or may directly contradict with existing scientific knowledge. These experiments may have great impact not just to the scientific community but to mankind in general. Banning them from study may incur societies a great opportunity cost but accepting them runs the risk that scientists are doing junk science. How to make an informed decision to accept/reject such study scientifically for the mainstream scientific community is of great importance to mankind. Here, we propose a statistical methodology to handle the situation. Specifically, we consider the likelihood of not observing the phenomenon after n trails so that it is statistically significant to have nil result. Consequently, we reject the hypothesis that there is some probability that we observe the phenomenon.