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Course Catalog 2012-2013
MAT-33317 Statistics 1, 4 cr |
Person responsible
Keijo Ruohonen, Robert Piche
Lessons
| Study type | P1 | P2 | P3 | P4 | Summer | Implementations | Lecture times and places |
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Requirements
exam and exercise points
Completion parts must belong to the same implementation
Learning outcomes
Upon completing the course, the student can carry out statistical inference for numerical and boolean data. The student can recognise situations where standard data models (normal, binomial, linear regression) can be applied. The student can compute, interpret and explain statistical summaries, including posterior probabilities and credibility intervals.
Content
| Content | Core content | Complementary knowledge | Specialist knowledge |
| 1. | descriptive statistics: graphics (dot plot, histogram, box plot) and summary measures (sample mean, median, variance, standard deviation). | empirical cdf, QQ plot, sample range, interquartile range, alternative definitions for median and quantile, percentile | variational characterisation of mean and median, Chebyshev's inequality, Samuelson's inequality, Jensen's inequality |
| 2. | Inference on a discrete parameter: Bayes' law, the elements of statistical inference (sampling model, likelihood, prior, posterior) | false detection rate & missed detection rate, binary symmetric transmission channel, medical testing | base rate fallacy; randomized response, Monty Hall |
| 3. | Inference for proportions: single proportion (beta prior, posterior, 95% credibility interval, predictive distribution), comparing two proportions (normal approximation); Bernoulli & binomial distributions | simulation, recursive update, equivalent number of observations | Laplace's law of succession, decision theory, mathematical derivation of formulas |
| 4. | Inference for means and variances: one population (marginal of mean, predictive distribution), two populations with equal variance, with unequal variance (normal approximation); distributions (normal, t, gamma) | MAP estimate, simulation, paired observations, marginal precision, model checking using predictive distribution, scale invariance of reference precision prior | recursive update, mathematical derivation of formulas |
| 5. | Simple linear regression: normal sampling model, posterior distribution of regression coefficients, posterior predictive distribution; regression with transformed variables | least squares fitting, coefficient of determination, regression through the origin | physical analogy of least squares line; proof of 0<= r^2 <=1 |
| 6. | Inference for correlation: bivariate normal sampling model, posterior distribution of r based on atanh approximation | correlation coefficient and width of standardized variable ellipse, model checking using simulation, correlation does not imply causation | mathematical derivation of formulas |
| 7. | Doing statistical analysis using Matlab or Octave |
Study material
| Type | Name | Author | ISBN | URL | Edition, availability, ... | Examination material | Language |
| Other literature | Sample exam | Robert Piche | Exam of 13.5.2013 with solutions. There are more sample exam questions in the last pages of the textbook. | English | |||
| Online book | Introduction to Statistical Data Analysis for Scientists and Engineers | Robert Piche | The course textbook. | English |
Prerequisite relations (Requires logging in to POP)
Correspondence of content
| Course | Corresponds course | Description |
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More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |
| There are no lectures; students need to self-study the material before coming to the exercise sessions. Exercises are mandatory. |