Measurement model

A critical component for performing inference (either from a frequentist or Bayesian perspective) is the definition of the measurement model. This component connects the System Dynamics model (X) with data (y). Let's denote the measurement model by $\pi(y | X(\theta))$, where $\pi$ is a probabilistic function & $\theta$ represents a vector of model parameters. If we fix $\theta$, we refer to the measurement model as the sampling distribution. From this distribution, we can obtain simulated measurements. If we fix y, we refer to the measurement model as the likelihood function which acts as a device to determine whether a measurement is close to its expected value.

Since the parameterisation of the measurement model is not unique given the various choices of probabilistic distributions, users are required to input the appropriate probabilistic function for the System Dynamics model. The challenge from the developers' point of view is how to make this process as seamlessly as possible. The purpose of this issue is to identify & discuss user-friendly approaches to get the specification of measurement models, & further default choices. For instance, the specification of the negative binomial distribution entails an additional parameter (phi).

A proposal for this specification is the requirement for users to employ Stan language:
"y ~ neg_binomial_2(stock_name, phi)"