When applying the Bayesian framework, we have considerable freedom in specifying the family of our prior distribution. Which of the following factors must we consider in deciding on our prior? (Choose all that apply.)
Whether or not we could specify the parameters of the distribution so that its shape approximates our prior belief
Whether or not the support of the distribution is realistic based on our context
How tractable it would be to compute the posterior distribution and perform inference from it, given the form of the likelihood function
All of the following factors must be considered in deciding on our prior distribution:
- Whether or not we could specify the parameters of the distribution so that its shape approximates our prior belief: This factor is important because the shape of the prior distribution should reflect our prior beliefs or knowledge about the parameter(s) of interest. If we can specify the parameters in a way that aligns with our beliefs, it would be more suitable.
- Whether or not the support of the distribution is realistic based on our context: The support of the prior distribution refers to the range of possible values for the parameter(s). It is important that the support is realistic and makes sense in the context of the problem being studied.
- How tractable it would be to compute the posterior distribution and perform inference from it, given the form of the likelihood function: In Bayesian inference, the prior distribution combines with the likelihood function to create the posterior distribution. It is crucial to choose a prior distribution that allows for tractable computations and inference, as complex or intractable calculations can hinder the application of the Bayesian framework.
The factors to consider when deciding on a prior distribution in the Bayesian framework are:
1. Whether or not we could specify the parameters of the distribution so that its shape approximates our prior belief
2. Whether or not the support of the distribution is realistic based on our context
3. How tractable it would be to compute the posterior distribution and perform inference from it, given the form of the likelihood function
Therefore, the correct choices are:
- Whether or not we could specify the parameters of the distribution so that its shape approximates our prior belief
- Whether or not the support of the distribution is realistic based on our context
- How tractable it would be to compute the posterior distribution and perform inference from it, given the form of the likelihood function