Make a class which runs Bayesian inference (in the simple case)

[rccreswell]

• [x] Make a new class BranchProPosterior. It should accept some data in the form of a dataframe on the number of cases, a serial interval in days as a list, and prior hyperparameters upon instantiation. Allow the user to specify the column names in the dataframe. Alternatively, make another method to set the serial interval in the form of a dataframe.
• [x] Make clear in the class docstring that this is not a general solution for inference, but rather applies to certain assumptions and priors (see the handout). Explain the forward model that is assumed by this class. Explain the time window and the conjugate prior.
• [x] Write a method run_inference which calculates the posterior distribution for R at the time points, and accepts the time window from the user
• [x] Write a method get_interval (must be called after run_inference) which returns a dataframe containing the times and the lower and upper bounds and median of the Bayesian credible interval for R for a user specified central probability. Explain the purpose of the method in detail in the docstring.