(Created 2009-08-11.)
 STATISTICS WITH DECISION THEORY TNX071

Higher education credits: 9. Grading scale: TH. Level: G1 (First level). Language of instruction: The course will be given in Swedish. Compulsory for: BI2. Course coordinator: Per-Erik Isberg, per-erik.isberg@stat.lu.se, Statistiska inst. Recommended prerequisits: FMA415 Calculus in one Variable. Assessment: Written examination and approved computer exercises. Further information: For retake of examination, contact the course coordinator. Home page: http://www.stat.lu.se/dk/tnx071.htm.

Aim
The aim of the course is to give a basic knowledge of statistical concepts in technology, science and economics and to give training in the use of computers for statistical calculations and in the evaluation of the quality of statistical investigations.

The course will give the student knowledge in how to describe random variation and understanding of the principles behind statistical analysis. It will also give the student a tool-box with the most common models and methods and the ability to use these in different practical situations.

The aim is both to give a general knowledge in statistics and to give a foundation for further studies.

The general knowledge is required for those who in their professional activities perhaps will not need to perform statistical analyses regularly, but who will have to interpret results from various investigations, present results and perform simple statistical analyses.

The course will also give a foundation for further studies, foremost by defining and using the basic concepts within probability theory, risk-analysis, decision theory, statistical modelling etc.

Knowledge and understanding
For a passing grade the student must

• be able to relate questions on random variation and observed data, to both applied and theoretical concepts: variables/random variables, distributions and association between variables

• be able to explain the concepts: independence, probability, conditional probability, distribution, expected value, variance, covariance and correlation,

• be able to calculate the probability of an event and expected value and variance in a theoretical distribution,

• be able to explain a statistical decision model and concepts as decision, uncertainty and values,

• be able to describe basic techniques for statistical inference and be able to use them in simple statistical models.

Skills and abilities
For a passing grade the student must

• be able to describe a dataset with the aid of different descriptive techniques,

• be able to choose and use an appropriate statistical method to answer a specific statistical question,

• be able to describe a problem with the help of a decision-tree and also be able to find the optimal decision,

• be able to use a statistical computer program for data analysis and simulations,

• be able to use statistical concepts in writing.

Judgement and approach
For a passing grade the student must

• be able to evaluate the presentation of a statistical study,

• be able to evaluate a statistical model and its description of reality.

Contents
The course presents the theoretical and practical foundations for statistical analysis of data. Concepts as event, probability (risk), independence and expected value are defined. Further, different discrete and continuous probability models are studied, e.g. binomial, poisson and normal models. The structure and basic concepts of decision analysis are studied, e. g. Bayes theorem, decision-trees and sensitivity analysis. The foundations of descriptive statistics: Principles of tabulation and graphs, measures of location, variation and association, standardization, and index-theory. The meaning of concepts as statistical precision and statistical significance are discussed. The course will also give an introduction to Monte Carlo simulation.

Literature
Körner S., Wahlgren L.: Praktisk statistik, 3rd ed, chapters 16. Studentlitteratur 2002. ISBN 91-44-01915-7
Körner, S., Wahlgren L.: Statistisk Dataanalys, 4th ed, chapters 18, 10. Studentlitteratur 2006. ISBN 91-44-01573-9.
Decision of Analysis, chapter 11 from Tools for Making Acute Risk Decisions. The Centre for Chemical Process Safety, American Institute of Chemical Engineers, New York 1995.
Körner, S., Tabeller och formler för statistiska beräkningar 2nd ed. Studentlitteratur 2000. ISBN 91-44-01485-6
Study material (Introductions to computer programs).