**Identifiability Problems in Statistics and Biology**

**Speaker: **Seth Sullivant

These lectures are for my short course as part of the conference Current Trends on GrÃ¶bner Bases, Mathematical Society of Japan, Seasonal Institute, Osaka, Japan, July 1-10, 2015.

**Abstract: **A parametric model is identifiable if the mapping from parameters to probability distributions (or density functions or trajectories) is one-to-one. Since many widely used models are algebraic in nature, deciding identifiability of a model is a fundamentally algebraic problem, often of a computational nature. This lecture series will introduce the audience to these identifiability problems and methods from computational algebra for addressing them.

Lecture 1: Introduction to Identifiability
Parametric statistical models; Definition of identifiability; Methods to test identifiability and find identifiable functions using Grobner bases; Illustration with examples from linear structural equation models or other graphical models.

Lecture 2: Phylogenetic Models Introduction to phylogenetic models; Identifiability of tree parameters and mumerical parameters; Phylogenetic invariants; Using invariants to identify tree parameters, Kruskals theorem and application to identifiability of numerical parameters.

Lecture 3: Linear Compartment Models ODE models, Using differential algebra to compute input/output equations, Linear compartment models, Identifiability and reparametrizations of linear compartment models.

**Slides:**

Identifiability Problems in Statistics and Biology I (July 1, 2015)

Identifiability Problems in Statistics and Biology II (July 2, 2015)

Identifiability Problems in Statistics and Biology III (July 3, 2015)

Exercises (July 3, 2015)