Ismaël Castillo studied mathematics at the École Normale Supérieure de Lyon and obtained a PhD in statistics from the Université Paris-Sud at Orsay in 2006. After a postdoc at the Vrije Universiteit in Amsterdam, in 2009 he became CNRS researcher in Paris, France. Since 2015 he has been full professor of Statistics at Sorbonne Université in Paris. He has taught statistics courses worldwide, especially in Bayesian inference, including invited lectures at Cambridge, Columbia, Berlin, Lunteren and St-Flour. He is an IMS fellow and an honorary fellow of the Institut Universitaire de France.

• -1. Introduction, rates I.-2. Rates II and first examples.-3. Adaptation I: smoothness.-4. Adaptation II: high-dimensions and deep neural networks.- 5. Bernstein-von Mises I: functionals.- 6. Bernstein-von Mises II: multiscale and applications.- 7. classification and multiple testing.- 8. Variational approximations.

Ismaël Castillo studied mathematics at the École Normale Supérieure de Lyon and obtained a PhD in statistics from the Université Paris-Sud at Orsay in 2006. After a postdoc at the Vrije Universiteit in Amsterdam, in 2009 he became CNRS researcher in Paris, France. Since 2015 he has been full professor of Statistics at Sorbonne Université in Paris. He has taught statistics courses worldwide, especially in Bayesian inference, including invited lectures at Cambridge, Columbia, Berlin, Lunteren and St-Flour. He is an IMS fellow and an honorary fellow of the Institut Universitaire de France.

• -1. Introduction, rates I.-2. Rates II and first examples.-3. Adaptation I: smoothness.-4. Adaptation II: high-dimensions and deep neural networks.- 5. Bernstein-von Mises I: functionals.- 6. Bernstein-von Mises II: multiscale and applications.- 7. classification and multiple testing.- 8. Variational approximations.

Ismaël Castillo studied mathematics at the École Normale Supérieure de Lyon and obtained a PhD in statistics from the Université Paris-Sud at Orsay in 2006. After a postdoc at the Vrije Universiteit in Amsterdam, in 2009 he became CNRS researcher in Paris, France. Since 2015 he has been full professor of Statistics at Sorbonne Université in Paris. He has taught statistics courses worldwide, especially in Bayesian inference, including invited lectures at Cambridge, Columbia, Berlin, Lunteren and St-Flour. He is an IMS fellow and an honorary fellow of the Institut Universitaire de France.

• -1. Introduction, rates I.-2. Rates II and first examples.-3. Adaptation I: smoothness.-4. Adaptation II: high-dimensions and deep neural networks.- 5. Bernstein-von Mises I: functionals.- 6. Bernstein-von Mises II: multiscale and applications.- 7. classification and multiple testing.- 8. Variational approximations.