Logisall, our customer requested for the model to be fitted in one second(learning only, excluding the data retreiving). We searched for ways to gain independence from Stan, which had following shortcomings:

– program is heavy (a few MB)

– compling is slow, though we use our cache model

– sampling, even MAP estimation exceeded the limit offered by Logisall

Trend, seasonality, and other regression components exist in our model; regression include weather, holiday, economic indicators etc.

Two viable options existed

1. Bayesian linear regression using conjugate prior

2. Laplace approximation

For the first approach, response variable(demand) and features should be reformulated as (1) to (2).

$ latex y \sim X \beta+\epsilon$

\alpha

$\alpha$