# Frequentist vs. Bayesian Interpretations

There are two prominent and sometimes conflicting schools of statistics: Bayesian and
frequentist. Their approaches are rooted in differing interpretations of the meaning of
probability.
Frequentists say that probability measures the frequency of various outcomes of an ex
periment. For example, saying a fair coin has a 50% probability of heads means that if we
toss it many times then we expect about half the tosses to land heads.
Bayesians say that probability is an abstract concept that measures a state of knowledge
or a degree of belief in a given proposition. In practice Bayesians do not assign a single
value for the probability of a coin coming up heads. Rather they consider a range of values
each with its own probability of being true.
The frequentist approach has long been dominant in fields like biology, medicine, public health and social sciences. The Bayesian approach has enjoyed a resurgence in the era of powerful computers and big data. It is especially useful when incorporating new data into an existing statistical model, for example, when training a speech or face recognition system. Today, statisticians are creating powerful tools by using both approaches in complementary ways.

## Frequentist Reasoning

I can hear the phone beeping. I also have a mental model which helps me identify the area from which the sound is coming. Therefore, upon hearing the beep, I infer the area of my home I must search to locate the phone.

## Bayesian Reasoning

I can hear the phone beeping. Now, apart from a mental model which helps me identify the area from which the sound is coming from, I also know the locations where I have misplaced the phone in the past. So, I combine my inferences using the beeps and my prior information about the locations I have misplaced the phone in the past to identify an area I must search to locate the phone.
Frequentist: Sampling is infinite and decision rules can be sharp. Data are a repeatable random sample - there is a frequency. Underlying parameters are fixed i.e. they remain constant during this repeatable sampling process.
Bayesian: Unknown quantities are treated probabilistically and the state of the world can always be updated. Data are observed from the realised sample. Parameters are unknown and described probabilistically. It is the data which are fixed.