Tommy wants to estimate Ontario’s annual unemployment rate in 2019 and he will repeat this again in 2020, 2021, and so on. Tommy thinks the Bayesian approach is a good idea because he can use his posterior from the previous year as the prior for the current year, but he is unsure what prior to use in 2019 and worried how it might influence his unemployment rate estimates.

Which of the following best addresses Tommy’s concerns with the Bayesian approach? Assume the data is modeled by a Bernoulli distribution.

1. Tommy could obtain a maximum-likelihood estimate of the unemployment rate from the 2019 data and then use this estimate as a suitable 2019 prior.
2. Tommy can confidently use a Beta distribution as 2019 prior because it is a conjugate prior for the Bernoulli distribution.
3. 2019 prior might have a negligible impact on future unemployment rate estimates, so Tommy can confidently proceed with the Bayesian approach.
4. If Tommy has no initial information about the unemployment rate, he can use a flat prior for 2019 and still obtain a Bayesian estimate that is similar to the maximum-likelihood estimate