Consider Bayes' formula as discussed from the lecture. Which of the following pieces of information are definitely necessary in order to use Bayes' formula to compute the posterior? (Choose all that apply.)
The mean of the n observations
The Fisher information of the prior distribution \pi (\lambda )
The likelihood function L(X_1, X_2, \ldots , X_ n | \lambda ) of the observations
The value of the prior distribution \pi (\lambda ) at every point where it is defined.
The likelihood function L(X_1, X_2, \ldots , X_ n | \lambda ) of the observations
The value of the prior distribution \pi (\lambda ) at every point where it is defined.
In order to use Bayes' formula to compute the posterior, the following pieces of information are definitely necessary:
- The likelihood function L(X_1, X_2, ..., X_n | λ) of the observations: The likelihood function represents the probability of observing the data given different values of the parameter λ, which is required to calculate the posterior.
- The value of the prior distribution π(λ) at every point where it is defined: The prior distribution represents our belief about the parameter before observing the data. The values of the prior at different points are needed to calculate the posterior.
Therefore, the necessary pieces of information are the likelihood function and the value of the prior distribution at every point where it is defined.