Basic Statistical Analysis in Life and Environmental Sciences

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This page describes the course 'Basic Statistical Analysis in Life and Environmental Sciences', a course at PhD level under the PhD school at the Faculty of Science and Technology GSST), Aarhus University. The course is offered and maintained by the Applied Statistics Research Unit at the Department of Mathematics, Aarhus University.

The course yields 4 ECTS.

Target group: PhD students applying statistics, with emphasis on biological, agricultural and environmental sciences.

The course will be offered two times in 20156 and two times in 2017: Spring (March) and Fall (November). The courses will be in Aarhus.



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Course Description

The aim of the course is to introduce the PhD student to basic notions of statistical analyses and give an idea of a typical statistical modelling process. The course does not intend to cover systematically key statistical models nor to supply a large applicable statistical toolbox in the research area of the PhD student. Instead, the idea is to build up a solid basis on general statistical principles, which will allow the PhD student to understand and apply more complex statistical models used in their research area or in other statistical courses. The examples used are based on relatively simple real cases occurring in life and environmental sciences strategically chosen for pedagogical purposes.

It is not presupposed that the PhD student masters statistic techniques beforehand. For those who have some experience in the use of statistical tools the course could be used as an opportunity to review and re-think basic concepts of statistics from a different perspective.

The course starts with a quick review of basic probability principles including definition and basic properties of probability, independence, expectation, variance, covariance, law of large numbers and the central limit theorem. The first statistical model (a simple binomial model for binary data) is presented and the notions of statistical parametrization, parameter estimation, hypothesis test and confidence intervals are introduced using those simple models as the first examples. Two other families of statistical models are then presented: Poisson models for counting data and Normal models (t-test, regression, analysis of variance and analysis of covariance) for continuous data. The basic notions of estimation and hypotheses tests are revisited and applied in examples involving the three families of statistical models already introduced. Two techniques of model control are presented: residual analysis and model embedding.

The course ends with a supervised analysis of some key examples involving some of the techniques studied in the course where the PhD student is supposed to: 1) perform a statistical analysis of a simple practical problem, 2) write a short report on that analysis and 3) report and discuss this analysis orally.

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Learning Goals

At the end of the course, the student should be able to:
  1. Identify the key assumptions and critically analyse some chosen (simple) statistical models
  2. Perform basic inference and draw conclusions from those models
  3. Present (orally) and report (written) the results of those analyses.
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Course Prerequisites

It is not presupposed that the PhD student masters statistic techniques beforehand.
The course will use the software R as a tool, but it is NOT a course on R. It will be assumed that the PhD students have the software R installed on their computers, and that they know the basic notions of R programming. This includes knowing to: read and write data in R, perform basic operations with variables and vectors, make simple tabulations, use simple functions, use repeated and conditional calculations and draw simple graphs.

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Course Details (location, language, registration and admission, the rules of the game)

Location:
The lectures will be in Aarhus (precise location to be announced).

Language and software:
The course will be in English. We will use the free package R (
click here to go to the official R web-page)

The rules of the game:
  • The course will require relatively hard work for the teacher, but he will do that with pleasure. On the other hand, I expect serious dedication from the participants.
  • Each student will be evaluated in final examination consisting on a written report and an oral examination based on a set of analyses proposed by the instructor.

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Course Evaluation and Form of Exam

The assessment (approved or not) will be based on the final examination, which constitutes a short written report on the analysis of three datasets and an oral examination based on that report. Based on the oral examination and the written report, it will be evaluated whether the PhD student has passed the course.
Details: Six datasets and the respective descriptions will be delivered at the beginning of the course. The analysis of these datasets involve the use of the basic techniques studied during the course. There will be also codes performing some basic analyses of these datasets. The six datasets will be such that two datasets will be related to binomial models, two related to Poisson models and two related to normal distribution based models. Each of the course participants choose 3 of those data, which should be analysed (under some supervision) and the analysis should be briefly exposed in a written report.

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Software

The Software R will be used in the course. I recommend you to install the version of R and the software RStudio (both are freeware) indicated in the links below:


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2 - (cos(x + T*y) + cos(x - T*y) + cos(y + T*z) + cos(y - T*z) + cos(z - T*x) + cos(z + T*x))




Course Structure (plan of lectures and activities)

The course is organised in 5 modules: 1) Basic probability and statistics, 2) Binomial models, 3) Poisson models, 4) Normal models and 5) General statistical modelling techniques. These modules will be covered in 8 lecture days disposed as follows:
  1. Module 1 - Basic probability and statistics
    Lecture 1 - Basic probability theory
    Lecture 2 - Some morre basic probability theory, parametric statistical models and basic statistical inference techniques

  2. Module 2 - Binomial models
    Lecture 3 - Binomial models with discrete explanatory variables, binomial models with one- and two-way classification structures
    Lecture 4 - Binomial models with continuous explanatory variables

  3. Module 3 - Poisson models
    Lecture 5 - The Poisson distribution, Poisson models with discrete explanatory variables
    Lecture 6 - Poisson models with continuous and discrete explanatory variables

  4. Module 4 - Normal models
    Lecture 7 - Normal distribution, normal models with discrete and continuous explanatory variables

  5. Module 5 - Concluding
    Lecture 8 - Case studies and techniques for model control, overview and concluding remarks

  6. Examination - Two to three weeks after the lecture 9.



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Time Schedule - Fall (maximum 20 participants)

In the fall the course will be in November (with examination in the beginning of December) on Tuesdays and Thursdays.
Location:
On Tuesdays - Department of Mathematics Building 1532, room 1532-322 (Kol. D)
On Thursdays - Department of Mathematics Building 1531, room 1531-211 (Aud. G3)

  1. Module 1 - Basic probability and statistics - Week 44
    Lecture 1 - 1st November 2016 (Tuesday) - Room 1532-322 (Kol. D): Basic probability theory
    Lecture 2 - 3rd November 2016 - Room 1531-211 (Aud. G3): Some morre basic probability theory, parametric statistical models and basic statistical inference techniques

  2. Module 2 - Binomial models - Week 45
    Lecture 3 - 8th November 2016 (Tuesday) - Room 1532-322 (Kol. D): Binomial models with discrete explanatory variables, binomial models with one- and two-way classification structures
    Lecture 4 - 10th November 2016 Room 1531-211 (Aud. G3): Binomial models with continuous explanatory variables

  3. Module 3 - Poisson models - Week 46
    Lecture 5 - 15th November 2016 (Tuesday) - Room 1532-322 (Kol. D): The Poisson distribution, Poisson models with discrete explanatory variables
    Lecture 6 - 17th November 2016 Room 1531-211 (Aud. G3): Poisson models with continuous and discrete explanatory variables

  4. Module 4 - Normal models - Week 47
    Lecture 7 - 22nd November 2016 (Tuesday) - Room 1532-322 (Kol. D): Normal distribution, normal models with discrete and continuous explanatory variables

  5. Module 5 - Concluding - Week 48
    Lecture 8 - 24th November 2016 Room 1531-211 (Aud. G3): Case studies and techniques for model control

  6. Examination - Week 50
    12th and 13th December.



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Course Responsible:

Rodrigo Labouriau
Senior Scientist (with special qualifications)
Department of Mathematics
Faculty of Science and Technology
Aarhus University.

Rodrigo works in development of quantitative methods directed to biological applications involving models of high complexity such as multivariate generalized linear mixed models and models for survival and event-history analysis. He has recently applied that in quantitative genetics, molecular biology, register-based epidemiologic research, agricultural experimental and observational studies (among other applications). Rodrigo has more than 20 years experience in applied statistics, statistical consulting in life and environmental sciences and teaching statistics to non-statisticians. He likes also to study mathematical foundations of statistics and computer symbolic manipulation applied to theoretical statistics (generating the drawings in this page, among other things ...), likes mountain bike, swim, classic music, modern jazz and likes to play bossa-nova, cello and to play with his three kids.

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2 - (cos(x + T*y) + cos(x - T*y) + cos(y + T*z) + cos(y - T*z) + cos(z - T*x) + cos(z + T*x))


This page was written by Rodrigo Labouriau (click here to send a mail to Rodrigo)
Last modified: 09 October 2016 .

Total number of accesses: 96454

Last access at Sat, 19 Jan 2019 14:39:31 +0100



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