Statistical inference I

Prerequisites for the course are the upper secondary education advanced

syllabus in mathematics and the courses MAT12001 Basics of statistics

and R I, MAT12002 Basics of statistics and R II, MAT12003 Probability I.

Basic concepts of mathematical statistics, statistical inference and
their interpretations.

Topics covered: statistical inference objectives, (parametric)
statistical model, likelihood function and maximum likelihood method,
confidence intervals and sets, background of statistical testing,
hypotheses, test statistics and p-value, t-test and z-test for the
expectation of the normal distribution, linear regression and the linear
model, basics of Bayesian inference.

Learning objectives

* Student can form a simple statistical model and understands the
purpose of statistical inference and the possibility of erroneous
conclusions
* Student can form a likelihood function and interpret it, and is able
to find the global maximum of the likelihood for basic models
* Student can define and interpret confidence sets and is able to form
confidence intervals for models with normal distribution
* Student can determine the least squares line, and knows about the
linear model and the assumptions on which it is based on
* Student is able to use Bayes formula to find the posterior, knows the
concepts of a prior and posterior distribution, and understands the
concept of a conjugate prior distribution

Literature is given on the course's home page.

Target group

The course MAT12004 Statistical inference I is a mandatory basic level course in statistics in Bachelor’s programme in Mathematical Sciences and belongs to the study package MAT120 (Basics studies in statistics).

The course is available to students in other degree programs and Open University students can complete the course within the agreed quota.

Timing

The course is recommended in the spring of the first study year.

Completion methods

Lectures for which there is no obligation to participate, as well as
exercises. The guidance, submission and evaluation of the exercises are
carried out digitally, but it is possible to participate in voluntary
local guidance to support the exercises. Completion of the course
completely digitally is possible, with the exception of the course exam.
The course can also be completed in a separate general examination.

Contents

The basic concepts of statistical inference and their interpretations
are mainly from the point of view of frequentist inference.
Topics covered: statistical inference objectives, (parametric)
statistical model, likelihood function and maximum likelihood method,
confidence intervals and sets, background of statistical testing,
hypotheses, test statistics and p-value, t-test and z-test for the
expectation of the normal distribution, linear model, basics of
Bayesian inference.

Activities and teaching methods in support of learning

Students peer- and self-evaluate weekly exercises. Students are

encouraged to guide each other, and when this happens digitally,

the discussions and guidance is accessible to all the students

simultaneously.

Assessment practices and criteria

The exercises contribute at least 30% of the final grade.

If the course is completed with a separate exam, grade is based

exclusively on the separate exam. The course is assessed on a scale of

1-5.