Bayesian Learning & Monte Carlo Simulation — Final Project 2026

Yacht Hydrodynamic Resistance

A Bayesian study of the residuary resistance of sailing yachts as a function of hull geometry and speed (Froude number).

Dataset

Source. UCI Machine Learning Repository, https://archive.ics.uci.edu/dataset/243/yacht+hydrodynamics. Original record: Gerritsma, Onnink and Versluis, Geometry, resistance and stability of the Delft Systematic Yacht Hull Series, 1981.

Data. The dataset describes 22 different hull forms (sailing yachts), each tested at multiple Froude numbers in a towing tank, producing 308 hull-form × Froude-number rows (data/yacht_hydro.csv).

Variables.

Variable	Description
LCB	Longitudinal position of the center of buoyancy (% length)
prismatic	Prismatic coefficient (dimensionless)
L_disp	Length–displacement ratio
beam_draught	Beam–draught ratio
L_beam	Length–beam ratio
Froude	Froude number (dimensionless, Fn = v/√(gL)), in [0.125, 0.45]
resistance	Residuary resistance per unit weight of displacement (target)

The first five covariates are geometric form factors that are constant within a given hull. Froude is a dimensionless measure of speed and is the dominant predictor: for sailing yachts the residuary resistance scales approximately as a power law of the Froude number, with an exponent close to 4 in the bulk regime.

Task

The physics of the problem says that for sailing yachts the residuary resistance follows a power law of the Froude number with exponent close to 4 in the bulk regime. The project explores this with a Bayesian analysis:

1. Log–log regression. Fit

   $$\log(\mathrm{resistance}) = \beta_0 + \beta_F,\log(\mathrm{Froude}) + \sum_k \beta_k,\mathrm{hull}_k + \varepsilon,.$$

   Verify that $\hat\beta_F \approx 4$.

2. BAS / BMA. Use bas.lm to enumerate the $2^5$ submodels over the five hull-geometry covariates and identify which of them (LCB, prismatic, L/disp, B/draught, L/beam) carry signal once Froude is in the model.

3. Correct for heteroscedasticity. Train the nonlinear model

   $$\mathrm{resistance} = k,\mathrm{Froude}^{\gamma_F},\exp\left\lbrace\sum_k \beta_k,\mathrm{hull}_k\right\rbrace + \varepsilon$$

   where only the form factors that appear relevant in the model-selection phase are kept. Compare the results with the log–log regression and discuss the impact of the heteroscedasticity correction on the inference on $\gamma_F$ and on the hull-geometry covariates.

4. Posterior predictive. Plot the posterior predictive curves and compare the curves with and without the treatment of the heteroscedasticity, and compare the curves with the data.

Repository layout

Path	Contents
data/yacht_hydro.csv	The yacht hydrodynamics dataset (UCI #243)
yacht_resistance.Rmd	Analysis notebook (R Markdown)
report.tex / report.pdf	Project report (LaTeX source and compiled PDF)
figures/	Figures used in the report
Project2026_INFO.pdf	Official final-project instructions