In what follows, we assume that the outbreak is in its initial phase and that there is an unlimited supply of susceptible individuals. This implies that all contacts that an infected individual has are with susceptible individuals. Additionally, we follow standard methods and assume homogenous mixing among individuals in the system being studied. Following [5] , we assume that N t = {N 1 , ..., N T } are the number of new cases each day of the epidemic, with T being the total number of days of data analyzed, and that the serial interval is given by p = {p 1 , ..., p k } where k is the maximal length of the serial interval and p j is the probability of an infectee presenting with symptoms j days after the infector. In practice we can model the p j with a multinomial distribution or a truncated continuous distribution, such as the Gamma or Weibull, and estimate the parameters of that distribution so that the dimensionality of the estimation is independent of k. Then, we show in [5] that the likelihood of the case counts N t = {N 1 , ..., N T } is given by a thinned Poisson: