Multivariate statistics

MULTIVARIATE STATISTICS (MATH-444)

Victor Panaretos

Assistant: Leonardo Santoro

Teaching methods:
Lectures and exercise sessions (on-site only)


Summary:
Multivariate statistics refers to to data in vector form, and focusses on inferring the joint distributional properties of several random variables, seen as random vectors. The main objective is to uncover the associations between the components of the vectors, and specifically to understand how to encapsulate, model, and infer this dependence. This course offers a broad introduction to its concepts, methods & theory.


Content:


Schedule:
Lectures: Thursday 13h15-15h00 in MA A1 10
Exercises: Thursday 15h15-17h00 in MA A1 10


Slides (v8, updated 22/5)
The slides also serve as lecture notes. They may occasionally be updated/corrected, so please check periodically - if there is a new version it will be explicitly noted (including version and date of last change). Non-trivial corrections will be listed here:

• v2: corrects slide #10 at the top, so that the base-case SVD adheres to the (n x n) (n x p) (p x p) convention, as in the statement, instead of the alternative (n x p) (p x p) (p x p) convention. Slide #14/15, eigenvector w defined to be normalised, and σ^2 replaced by σ.
• v3: corrects the block inverse in slide #47 (bottom right block), and makes various small corrections/adjustments.

Lecture Progress:

• week 1: ----
• week 2: slides 1 to 20
• week 3: slides 20 to 43
• week 4: sides 44 to 74
• week 5: slides 75 to 101
• week 6: slides 102 to 127
• week 7: slides 128 to 143
• week 8: slides 168 to 187
• week 9: ----
• week 10: slides 168 to 187
• week 11: slides 188 to 208
• week 12: slides 209 to 228
• week 13 slides 229 to 244

Exercises  and Solutions (updated on 21/05)
Exercises are uploaded and assigned weekly, in relation to the material covered in the lectures.  The corresponding solutions are made available the subsequent week.  

• week 1: ----
• week 2: exercises 1 to 6 
• week 3: exercises 7 to 13
• week 4: exercises 14 to 17
• week 5: exercises 18 to 22
• week 6: exercises 23 to 28
• week 7: exercises 29 to 33
• week 8: exercises 33 to 38
• week 9: ----
• week 10: exercises 39 to 43
• week 11: exercises 44 to 48
• week 12: exercises 49 to 53
• week 13: ----

Bonus (and non-compulsory) midterm: Thursday 17 April, 13h15-15h00 (MA 10). The bonus will apply as follows:

Unrounded final grade = 0.75*{final exam grade} + 0.25 *max {final exam grade, midterm grade}

(we will round upwards to the nearest multiple of 0.25)

Cheat-sheet: A single page (front and back) of handwritten* notes will be allowed in the midterm. Two pages (four sides) of handwritten* notes will be allowed in the final.

*handwritten really means handwritten on a piece of paper. No printouts of scaled tablet notes or scanned/photographed notes will be allowed.