If you want to know: do Higgs Bosons exist, you can go frequentist or bayesian:

Wasserman: p-value is fine for Higgs experiment:

https://normaldeviate.wordpress.com/2012/07/11/the-higgs-bos...

Tom Campbell-Ricketts: Bayes is better even for Higgs experiment

https://maximum-entropy-blog.blogspot.com/2012/07/higgs-boso...

My take: frequentist p-value is simpler but Bayes is what you really want.