RUŌOD Lab

Stage F · Mastery and Research

Mastery course: Advanced Mathematics and Statistics for Perfumers

Formulas as linear systems, constrained optimization, mixture designs, Thurstonian d′, measurement uncertainty and PCA.

Mastery 7 lessons After Level 5 and the Research and Innovation track About 6.5 hours of study, plus practice

0 of 7 lessons completed
By the end you will have: A statistical study of one accord, from a mixture design through panel data to a model, with its uncertainty budget and its limitations stated.

Lessons

The algebra of a formula

  1. A Formula as a Linear System

    Write a formula built from stock dilutions and premixes as a matrix equation, solve it for the weights that hit a target, and see when no solution exists.

    55 min · Exercise: Solve a premix formula three ways

  2. Optimization Under Constraints: Cost and Composition

    Set up cost reduction as a linear program, solve a three-material case by hand, read shadow prices, and see how a model drops what it was not told to keep.

    55 min · Exercise: Optimize one accord, then smell the optimum

  3. Mixture Designs for Accords

    Use simplex-lattice and simplex-centroid designs to map how an accord responds to its proportions, fit a Scheffé model, and check it at the centroid.

    55 min · Exercise: Run a seven-point simplex-centroid on one accord

Measurement and inference

  1. Discrimination Tests and Thurstonian d′

    Derive the binomial test behind a triangle test, convert a proportion correct into d′, and see why d′ compares methods where proportion correct cannot.

    60 min · Exercise: Plan and analyze a reformulation test with d′

  2. Measurement Uncertainty in Weighing and Dilution

    Propagate a balance's resolution through a dilution and a formula line with the GUM method, and see why small weighings dominate a formula's uncertainty.

    55 min · Exercise: Write an uncertainty budget for your own batch

  3. Regression and Principal Component Analysis of Panel Data

    Fit and judge a regression between two descriptors, compute a principal component analysis by hand, and learn when a tidy sensory map is an artifact.

    60 min · Exercise: Map six fragrances from your own panel

  4. Mastery Project: A Statistical Study of One Accord

    The mathematics course project: design, run and analyze a study of one accord, from mixture design and uncertainty budget to panel statistics and a model.

    40 min · Exercise: The mathematics course project