# Measurements, uncertainties, and statistics

The physical meetings of this course will be held in Luleå, April 9-10, 2019 and in Uppsala May 15-16, 2019.

# Course Syllabus

## Basic course information

**Education level: **Third cycle

**Grade:** Fail/Pass; U/G

**Subject: **Urban Water Engineering

**Swedish name:** Mätningar, osäkerheter och statistik.

**Entry requirements: **This course is open for PhD students with in the urban water area. For external course participants, a Master Exam within Environmental Engineering or similar is needed.

**Course examiner: **Associated professor Annelie Hedström

## Measurements and chemical analysis

### Course aims:

At the end of the first part of the course you should be able to:

• Understand how the choice of chemical analytical methods and sampling containers influence the sampling plan and interpretation of the results.

• Understand and explain concepts related to analysis such as detection/quantification/reporting limit, accreditation, and standard method.

• Understand the importance of representative samples/sampling/measurements and explain how different sampling strategies will influence the interpretation of the results.

• Explain the importance of blank/blind and control samples, and how these can be chosen for specific applications.

• Make an experimental and sampling plan considering the above mentioned concepts.

• Describe challenges with continuous measurements such as flow measurements, and be able to systematically estimate associated uncertainties.

### Course content:

This part of the course gives the fundamental knowledge of how to choose analytical methods and data collection and basic concepts in measurements and chemical analysis. The course also provides knowledge about continuous measurements and uncertainties.

### Realization

This first part of the course is carried out as a distance course with one physical meeting. Prior to the physical meeting three tasks should be carried out. 1) preparation and submission of a PM describing a sampling plan which will be distributed to the other participants. 2) read the PM’s from 3-4 other participants. 3) read an article regarding the application of the Law of Propagation of Uncertainties. During the physical meeting lectures, workshops and calculation exercises will be carried out. After the physical meeting the PM should be updated based on the new knowledge and insights gained on the meeting. Four weeks prior to the physical meeting, course information, instructions and article will be sent out.

### Examination

This part of the course is examined by a PM submitted after the first physical meeting and calculation exercises solved during the lectures at the first physical meeting.

### Course Teacher

Helene Österlund and Günther Leonhardt och Ico Broekhuizen

## Uncertainties and Statistics

### Course aims:

At the end of the course you should be able to:

• Describe the basic concepts of probability and statistics. (Probabilities, random variables, expected value, variance, Baye’s theorem and so on)

• Understand the Law of large numbers and the central limit theorem.

• Understand the notion of confidence intervals and construct them in some cases

• Perform hypothesis testing for different models using p-values and confidence intervals. (Categorical models using Chi2-tests)

• Perform linear regression and using different methods for model selection and shrinkage. (Ridge, Lasso and so on)

• Do some non-linear regressions, for instance logistic regression.

• Use the bootstrap method to perform statistical tests.

### Course content:

This part of the course gives the foundation in probability and statistics with the aim of performing statistical modelling and tests (hypothesis testing) for different types of data and models.

We will start with a brief summary of basic probability theory and statistics (what could be included in a basic course in an engineering program). This includes stochastic variables, some basic probability theory and the Central Limit Theorem and Law of Large Numbers.

We will then go over the basis of statistical modelling and hypothesis testing in some cases. This includes testing the probability in the binomial distribution, the mean in a Gaussian distribution, the variance in a Gaussian distribution and test for distributions and independence using the chi2-tests. Briefly talk about the difference between correlation and causality.

The second big focus of the course will be on regression, where we will go over the basic linear regression, we will talk about model selection in different ways and shrinkage methods, this includes Ridge and Lasso. We will also discuss different ways of tackling non-linear regression with focus on logistic regression.

Finally we will discuss bootstrap statistical methods for hypothesis testing in different models. Standard bootstrap, parametric bootstrap, residual bootstrap and permutation tests.

Illustrations of the above methods will be done in R with code provided to the students.

### Realization

The part of the course is carried out as a distance course with 1 physical meeting.

The meeting (2 days) is a series of lectures on the subject and an introduction to the examination task.

### Examination

This part of the course is examined by an examination task which consists of two parts. One part where the students are given problems by the teacher that they should solve individually, the second part consists of a larger problem where the students should find an interesting data set (preferably one that they are working on in their PhD studies) and set up an hypothesis and use the available statistical methods to test the hypothesis. For the second part, every student will have the opportunity to have a supervision meeting with the teacher to discuss the proposed problem.

### Course Teacher

Johan Alenlöv