I need help transforming a rich set of horse-racing variables into a clear, end-to-end mathematical engine written in Python. The core of the job is to translate domain knowledge into rigorous formulas and then implement them so that I can feed race data in one side and obtain actionable probabilities on the other, all framed within Bayesian statistics. Variables to be modelled • Horse speed • Jockey performance • Track condition • Weight • Distance • Bias • Prep cycle • Class • Horse’s historical record Scope of work 1. Formalise each variable above as part of a coherent Bayesian model, explaining assumptions and priors. 2. Code the full workflow in Python (NumPy/Pandas for data handling and a Bayesian library such as PyMC or Stan via CmdStanPy). 3. Expose clean functions or a notebook that lets me update priors with fresh data and returns posterior win probabilities, place/show probabilities, and confidence intervals. 4. Document the mathematics and the code so another analyst can follow the logic line by line. Acceptance criteria • All formulas and priors are explicitly stated in comments or a short PDF. • The Python script/notebook runs on my machine with a sample CSV and produces posterior distributions without errors. • Results make intuitive sense when I sanity-check edge cases (e.g., extreme speed or poor track conditions). This is an analytical task first, a coding task second—solid math must drive clean, transparent code. If that sounds like your wheelhouse, let’s talk through the dataset and schedule milestones for formula approval, prototype code, and final delivery.