Hello,

I’m a beginner data science student and for a course we need to replicate a paper which models multi-party elections in a Bayesian framework. Basically, we understand the model: poll respondents y are modeled by a multinomial distribution and the linear predictor includes a pollster parameter \beta _{d} and, more importantly here, a **time parameter \beta _{t}** which is modeled after a random walk.

y_{i} \sim multinomial(\pi_{i})

\pi_{i,p} = \frac{exp(\eta _{i,p})}{1 +\sum_{j=1}^{P-1}exp(\eta _{i,j})}

\eta _{i,p} = x_{i,d} *\beta _{d, p} + x_{i,t} *\beta _{t, p}

\beta _{t,p} \sim N(\beta _{t-1,p}, \sigma_{p}^{2})

What we don’t understand is the following sentence from the paper: “For the starting values \beta_{1,p} we use normal distributions with variance 1 and the **maximum likelihood estimated for t = 1 as the mean**.” How do you compute the MLE of the time parameter for t=1 from the data? I hope it’s not too dumb of a question, but can anyone help? Thanks in advance!