The difference between Bayesian and frequentist inference in a nutshell:
With Bayes you start with a prior distribution for θ and given your data make an inference about the θ-driven process generating your data (whatever that process happened to be), to quantify evidence for every possible value of θ. With frequentism, you make assumptions about the process that generated your data and infinitely many replications of them, and try to build evidence for what θ is not.
There are many principles involved in the theory and practice of statistics, but here are the ones that guide my practice the most.
Use methods grounded in theory or extensive simulation Understand uncertainty Design experiments to maximize information Understand the measurements you are analyzing and don’t hesitate to question how the underlying information was captured Be more interested in questions than in null hypotheses, and be more interested in estimation than in answering narrow questions Use all information in data during analysis Use discovery and estimation procedures not likely to claim that noise is signal Strive for optimal quantification of evidence about effects Give decision makers the inputs (other than the utility function) that optimize decisions Present information in ways that are intuitive, maximize information content, and are correctly perceived Give the client what she needs, not what she wants Teach the client to want what she needs .