Bayesian statistics has gained some popularity among applied researchers. Andrew Gelman explained the basics here. One fascinating episode in Bayesian's history: "Alan Turing used Bayesian probability methods to crack the Enigma code in the second world war."
I am a geographer who studies the relationship between human society and the environment. I apply both quantitative (i.e., statistics and geospatial models) and qualitative (i.e., in-person interviews and policy analysis) methods in my research.