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 degreeofbelief interpretation of probability, as opposed to a relativefrequency 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[edit]
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