This course set is coordinated by Dr. Raazesh Sainudiin, a Researcher in Applied Mathematics and Statistics at the Department of Mathematics, Uppsala University and a Data Science Consultant at Combient AB in Stockholm.

# OFFICIAL CONTENT

Critical review of how statistics are presented and interpreted. General about statistical studies. Basic theory of point and interval estimations and hypothesis test. Correlation and regression. Parametric methods. Statistical software.

See 1MS035: Inferensteori I for more details.

# Style

The approach will use formal mathematical communication of concepts with concomitant development of computer programs to cover the syllabus for 1MS035: Inferensteori I.

Lectures will build on: Sets, Maps, Functions, Modular Arithmetic, Axiomatic Probability, Conditional probability, constructive understanding of random variables and structures including graphs, Statistics, Likelihood Principle, Bayes Rule, Decisions (parametric and non-parametric) including hypothesis testing and estimation.

# Course Materials

**Download**the SageMath`.ipynb`

notebooks as well as`images`

and`data`

directories in the following`.zip`

file:**Unzip**it into the directory you launched the sage jupyter notebook server from.- You should be able to see all the jupyter
`.ipynb`

notebooks by navigating from your jupyter notebook server.

**Individual SageMath Jupyter .ipynb Notebooks**

*- replace with these possibly updated notebooks, as newer content is added*to cover target topics including correlation, linear regression and parametric hypothesis testing, as well as typeset black-board notes.

- 00. Introduction
- 01. BASH Crash
- 02. Numbers, Strings, Booleans and Sets
- 03. Map, Function, Collection and Probability
- 04. Conditional Probability, Random Variable, Loop and Conditional
- 05. Random Variables, Expectations, Data, Statistics, Arrays and Tuples, Iterators and Generators
- 06. Statistics and List Comprehensions with New Zealand Earth Quakes
- 07. Modular Arithmetic, Linear Congruential Generators, and Pseudo-Random Numbers
- 08. Pseudo-Random Numbers, Simulating from Some Discrete and Continuous Random Variables
- 09. Estimation, Likelihood, Maximum Likelihood Estimators and Symbolic Expressions
- 10. Markov Chains and Random Structures
- 11. Limits, Convergence, and Estimation
- 12. Non-parametric Estimation and Testing

This is the GitHub directory containing the SageMath contents for the course:

## Course Structure

I would like to customize the course for you! So would prefer to do the content week-by-week dynamically based on interactions and feedback.

However, if you want to have *some idea* of the structure for the course and complete some assigned exercises then take a look at Chapters 1-9, 11-14, 17-18 in *CSEBook.pdf*, one of my books under progress:

- Download
*CSEBook.pdf*from https://github.com/lamastex/computational-statistical-experiments/raw/master/matlab/csebook/CSEBook.pdf

**A Global Background and Context:**

This is a mathematically more mature inference-theoretic variant of UC Berkeley’s popular freshman course in data science, http://data8.org/, with the formula:

**computational thinking + inferential thinking + real-world relevance =: data science**- as talked about from 23:18 into the Data Science Revolution talk and
- about how inference is integral to data science from 15:43 into this UC Berkeley video lecture.

This course is aimed at covering the Syllabus of 1MS035: Inferensteori I for second-year undergraduate students of mathematics at Uppsala University, Uppsala, Sweden.

## Scribed Black-Board Notes

One of your classmates has kindly agreed to allow me to make his hand-scribed notes available for the convenience of others in the class at the following link:

This course is **being** designed to help you take your mathematical steps in the inferential direction in a computationally sound manner.

# Assigned Exercises

## How to Submit Computer Exercises?

**Four Steps to Submit Computer Exercises in .ipynb SageMath Notebooks**

- Work through each cell, i.e., read the code and comments, evaluate the cell and understand the output of what you are doing, in the notebook
- Complete any
*You Try*’s in the notebook - Save the completed
`.ipynb`

notebook from your Jupyter notebook server - Send an Email to your instructor’s
`math.uu.se`

email address from your`uu.se`

email address as follows:- attach the completed and saved
`.ipynb`

notebook(s) as attachment to the email - In the
`Subject`

field of the email write`1MS035:Assignment#x`

, where`x`

is the`number`

of the assignment

- attach the completed and saved

**NOTE:**

- Assignments will be considered unsubmitted if you do NOT
*strictly adhere*to the above four Steps. For example, do NOT send me emails from your non-`uu.se`

addresses or have the wrong string in the`Subject`

field. - Late submissions will be noted to ensure fairness for the timeliness of all students.

## Computer Exercises

- Weeks 1–3:
**Assignment#1**- Due Date is Monday November 19, 2018 at 1159 hours CET (announced in class on November 09, 2018)

- Weeks 4–5:
**Assignment#2**- Due Date is Wednesday December 05, 2018 at 1159 hours CET (announced in class on November 28, 2018)

- Weeks 6–7:
**Assignment#3**- Due Date is January 06, 2019 at 2359 hours CET (announced in class on December 11, 2018)

## Hand-written Exercises

Generally, such exercises should be tried by yourself or with your mates. They need not be submitted. You can ask about them in class if you are stuck interpreting or solving them. These exercises are invaluable to pass the final exam of the course.

- Weeks 1–3: Review of Probability and Introduction to Point Estimators
- Do Exercises in
*CSEBook.pdf*: Ex. 6.11, 6.12, 6.14, 6.16, 6.17, 6.18, 6.19 in Chapter 6, pages 129-130. - Give a
*proof of the LLN*that was required in the complete proof of the claim that*(asymptotic) consistency of the estimator given by the sample mean of the product Bernoulli experiment “follows” from the (Weak) Law of Large Numbers or LLN*. - Four problems were assigned during black-board lecture (see page 16 and 15 of scribed/arch/soFar.pdf). (NOTE: Problem 1 of 4 is the same as that in previous item.)

- Do Exercises in

# Software

We will use SageMath locally during face-to-face interactions. You may also collaborate in COCALC remotely. All needed programming basics will be introduced as needed.

**Supplementary Book:**

### Prepare your laptop

- Follow the download and installation instructions for your Operating System from the following URL:
- To test that you have installed correctly do the following:

- On a Mac OS X or Unix/Linux system, say you installed sage in a directory inside your home directory called
`~/all/software/sage/`

, then you can see if the following command launches a Jupyter notebook server successfully:

$ ~/all/software/sage/SageMath/sage -n jupyter

- Those with Windows should follow the instructions in the following URL and test that the jupyter notebook server launches successfully:

# Sample Exam

Prepare with this sample exam.

Go over the notes scribed on the black-board and work through examples done and homework assigned in class.