Subjectivism

The probability of an event is not determined in a unique manner.

Bayesianism states that a probability varies depending on new information (Bayes theorem). It involves a prior probability.

The Bayesian approach can be summarized as such (source):

• Define prior distribution i.e. subjective beliefs about a parameter.
• Gather data.
• Update prior distribution to have a posterior distribution.
• Analyze the posterior distribution and summarize it.

There is today a neo-Bayesianism current of thought.

Limits: how to choose the prior probability?

Objectivism

The probability of an event is determined in a unique manner.

Frequentism assumes that results occur with a given frequency based on repeated sampling. The probabilty is defined as a frequency i.e. of the form $\frac{number~of~successes}{number~of~trials}$. It is based on the law of large numbers (the probability approaches its theoretical value).

It’s the most most taught form of statistics nowadays in college.

Limits: impossible to define the probability of a non-repeatable event.