Question

What is the posterior distribution for θ in the Normal-Cauchy model when X follows a normal distribution with mean θ and variance 1, and θ follows a Cauchy distribution with mean 0 and scale parameter 1?

Answer 1

The posterior distribution for θ in the Normal-Cauchy model can be derived using Bayes' theorem.Using the properties of these distributions, we can plug in the values and calculate the posterior distribution for θ.

Step-by-step explanation:

The posterior distribution for θ in the Normal-Cauchy model can be derived using Bayes' theorem.

The posterior distribution is given by:

p(θ|X) ∝ p(X|θ) * p(θ)

In this case, X follows a normal distribution with mean θ and variance 1, and θ follows a Cauchy distribution with mean 0 and scale parameter 1.

Using the properties of these distributions, we can plug in the values and calculate the posterior distribution for θ.