Bayesian econometrics

Bayesian econometrics

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Bayesian econometrics is a branch of econometrics which applies Bayesian principles to economic modelling. Bayesianism is based on a degree-of-belief interpretation of probability, as opposed to a relative-frequency interpretation.
The Bayesian principle relies on Bayes’ theorem which states that the probability of B conditional on A is the ratio of joint probability of A and B divided by probability of B. Bayesian econometricians assume that coefficients in the model have prior distributions.
This approach was first propagated by Arnold Zellner.[1]

Contents

1 Basics
2 History
3 Current research topics
4 References

Basics
Main article: Bayesian inference
Subjective probabilities have to satisfy the standard axioms of probability theory if one wishes to avoid losing a bet regardless of the outcome.[2] Before the data is observed, the parameter

θ

{\displaystyle \theta }

is regarded as an unknown quantity and thus random variable, which is assigned a prior distribution

π
(
θ
)

{\displaystyle \pi (\theta )}

with

0

θ

1

{\displaystyle 0\leq \theta \leq 1}

. Bayesian analysis concentrates on the inference of the posterior distribution

π
(
θ

|

y
)

{\displaystyle \pi (\theta |y)}

, i.e. the distribution of the random variable

θ

{\displaystyle \theta }

conditional on the observation of the discrete data

y

{\displaystyle y}

. The posterior density function

π
(
θ

|

y
)

{\displaystyle \pi (\theta |y)}

can be computed based on Bayes’ Theorem:

p
(
θ

|

y
)
=

p
(
y