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Petteri Piiroinen's picture

Petteri Piiroinen

Published, 6.3.2020 at 8:23

Hi, and good luck for the exam today.

I added yesterday the suggestions to prob 4 from Spring 2020. I also added the chapter 8 with something about Bayes factor (from last year notes, don't know why it was taken out) and modified the slides to include more of the things we discussed during the lectures on Bayes factor and information criteria and corrected the few typos noted during the lecture that were there.

So at least take a look at the modified lecture slides (I only modified first 15 pages of slides of the 25.2. lecture slides) and the suggestions to the last year course exam for last preparation :). All the distributions needed are attached to the exam sheet,.

Thank you all for participating so actively on the course. I will soon post the point list from exercises to the course page. I might increase the points you can get from those, since they were sometimes overly difficult.

With best,

Petteri

Petteri Piiroinen's picture

Petteri Piiroinen

Published, 25.2.2020 at 12:22

Hi,

I would like to remind you that you need to do separate registration to the course exam (on Friday, March 6th) on Weboodi. The registration ends *today* Tuesday Feb 25th at 23:59.

Hei,

muistuttaisin, että ilmoittautuminen perjantain 6.3. kurssikokeeseen tehdään erikseen Weboodissa. Ilmoittautuminen päättyy *tänään* tiistaina 25.2. klo 23:59.

Petteri Piiroinen's picture

Petteri Piiroinen

Published, 20.1.2020 at 6:50

Hi, the lectures are today in Physicum E204 at 12:15 - 14:00. You will find this information always up-to-date in the My Studies (Opintoni) pages https://student.helsinki.fi (behind login) or from this Course webpage under Timetable.

Hei, luennot ovat tänään salissa E204 Physicum klo 12:15 - 14:00. Löydät tiedon aina joko Opintoni (My Studies) -sivulta https://student.helsinki.fi (kirjautumisen takaa) tai tältä Courses-sivulta Aikataulu -osiosta.

Petteri Piiroinen's picture

Petteri Piiroinen

Published, 13.1.2020 at 8:36

Hi, there are no exercise session on the first week.

Hei, tällä viikolla ei ole vielä harjoituksia.

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Timetable

Preliminary schedule (this will be updated to match the actual content :)

• Week 1, Lecture 1: Preliminaries, basic philosophy, review of probability, parametric models
• Week 1, Lecture 2: Prior, likelihood, posteriori, prediction
• Week 2, Lecture 3: Conjugate pairs: one parameter models, Priors and selection of priors
• Week 2, Lecture 4: Priors and selection of priors, Summarizing the posteriori, credible sets, HPD
• Week 3, Lecture 5: Credible sets, HPD, Approximate inference, Rejection sampling, Grid approximation
• Week 3, Lecture 6: Posteriori sampling and prediction, Approximate inference for d = 1
• Week 4, Lecture 7: MCMC methods, Multiparameter models d > 1.
• Week 4, Lecture 8: Approximate inference, examples and Using RStan and Stan (video)
• Week 5, Lecture 9: Multiparameter models, Hierarchical models
• Week 5, Lecture 10: Hierarchical models - with RStan
• Week 6, Lecture 11: Hierarchical models, Model selection, Bayesian hypothesis testing (Decision theory, Bayes estimators)
• Week 6, Lecture 12: Decision theory, Bayes estimators, Model selection, Bayesian linear regression
• Week 7, Lecture 13: Bayesian linear regression, Review of course topics
• Week 7, Lecture 14: Review of course topics

/

Alustava luentopäiväkirja tätä päivitetetään vastaamaan luennoilla oikeasti käytyjä asioita :)

• Viikko 1, Luento 1: Alustavat asiat, filosofia, todennäköisyyden kertausta, parametriset mallit
• Viikko 1, Luento 2: Priori, uskottavuus, posteriori, ennustaminen
• Viikko 2, Luento 3: Konjugaattiparit: yhden parametrin mallit, Priorit ja priorin valinta
• Viikko 2, Luento 4: Priorit ja priorin valinta, Posterioriyhteenvedot, bayesiläiset luottamusjoukot, HPD
• Viikko 3, Luento 5: Approksimatiivinen päättely, MCMC-mentelmät
• Viikko 3, Luento 6: Approksimatiivinen päättely, otanta posteriorista ja ennustaminen
• Viikko 4, Luento 7: Moniparametriset mallit
• Viikko 4, Luento 8: Moniparametriset mallit, Hierarkiset mallit
• Viikko 5, Luento 9: Hierarkiset mallit
• Viikko 5, Luento 10: Hierarkiset mallitPäätösteoria, Bayes-estimaattorit
• Viikko 6, Luento 11: bayesiläinen hypoteesin testaus, mallin valinta
• Viikko 6, Luento 12: Mallin valinta, bayesiläinen lineearinen regressio
• Viikko 7, Luento 13: bayesiläinen lineearinen regressio, kertausta
• Viikko 7, Luento 14: kertausta

DateTimeLocation
Tue 14.1.2020
10:15 - 12:00
Thu 16.1.2020
14:15 - 16:00
Mon 20.1.2020
12:15 - 14:00
Thu 23.1.2020
14:15 - 16:00
Mon 27.1.2020
12:15 - 14:00
Thu 30.1.2020
14:15 - 16:00
Mon 3.2.2020
12:15 - 14:00
Mon 3.2.2020
16:15 - 18:00
Thu 6.2.2020
14:15 - 16:00
Tue 11.2.2020
10:15 - 12:00
Thu 13.2.2020
14:15 - 16:00
Tue 18.2.2020
10:15 - 12:00
Thu 20.2.2020
14:15 - 16:00
Tue 25.2.2020
10:15 - 12:00
Thu 27.2.2020
14:15 - 16:00

Other teaching

23.01. - 27.02.2020 Thu 12.15-14.00
Teaching language: Finnish
22.01. - 26.02.2020 Wed 12.15-14.00
Teaching language: English
13.01. - 24.02.2020 Mon 10.15-12.00
Teaching language: English

Material

Video

Tasks

Exercises 1 / Suggested solutions

Week 1 exercises was added on Monday 13.1, but make sure they are not updated later. Exercises 1 will be covered in exercises classes during 20.-23.1.

The suggested solutions will be added on Friday 24.1.

Added 13.1.2020
Added 24.1.2020. Modified 28.1.2020

Exercises 2 / Suggested solutions

Week 2 exercises was added on Tuesday 21.1, but make sure they are not updated later. Exercises 2 will be covered in exercises classes during 27.1.-30.1.

Suggested solutions were added on Friday 31.1. but make sure they are not updated later.

Exercises 3 / Suggested solutions

Week 3 exercises were added on Tuesday 28.1, but make sure they are not updated later. Exercises 3 will be covered in exercises classes during 3.2.-7.2.

Last modified: 2.2.2020 (based on the discussion Presemo)

Exercises 4 / Suggested solutions

Week 4 exercises will be added on Monday 3.2, but make sure they are not updated later. Exercises 4 will be covered in exercises classes during 10.2.-14.2.

Exercises 5 / Presuggested solutions

Week 5 exercises will be added on Tuesday 11.2 (in two parts, first 3 exercises in the morning and the latter 3 after the lectures in the afternoon, sorry for this), but make sure they are not updated later. Exercises 5 will be covered in exercises classes during 17.2.-21.2.

Added 11.2.2020
Added 11.2.2020
Added 22.2.2020: Modified 23.2.2020

Exercises 6 / Suggested solutions

Week 6 exercises was added partially on Tuesday 18.2 and modified couple of times, but make sure they are not updated later. Exercises 6 will be covered in exercises classes during 24.2.-28.2.

Added 18.2.2020. Last modified: 21.2.2020
Added 28.2.2020. Modifies 29.2.2020

Conduct of the course

There are two lectures per week. There is one exercise set per week (and three exercise groups).

The course is graded with a course exam, which is applied for **separately** via Weboodi.. In the course exam (unless arranged for the general exam), the permissible accessories are 1) a calculator and 2) a cheat sheet. The cheat sheet must be self-made and _handwritten_ (that is, not printed on a computer) and has no limitations other than its size: one A4 sheet (both sides allowed).

Alternatively, you can take the course with a general exam, which is applied for separately via Weboodi. In the general exam you cannot use your own cheat sheet so I have a "sheet cheat" that I have added to the assignment paper. The next general exams are 18.3.2020 (note that this is mean as the replacement for the course exam, if you cannot make to the actual course exam), and then 10.6.2020 and 5.8.2020.

In addition to the exam points, you can get extra points by solving exercises. It is possible to get 3.5 points in total from exercises. If you can not attend to the course exam, the exercise points are valid for half a year after the end of the course.

The maximum points from exercises is 3.5 points and these are determine with the following way: 20% = 0.5p; 30% = 1p; 40% = 1.5p; ...; 70% = 3p; 80% = 3.5p.

The course exam is organized during the exam week (more precisely on)

• 6.3.2020 from 12:00 to 14:30 in one of Exactum's auditoriums.

You MUST REGISTER for the course exam in Weboodi **separately** (the registration period closes 10 days before).

The exam score is probably 4 * 6 = 24 points. In order to complete the course, the sum of the exam points and the extra points must be at least 12 points.

Updating course page is still ongoing...

Kurssilla on luennot kahdesti viikossa. Laskuharjoituksia on yhdet viikossa (ryhmiä on kolme).

Kurssi suoritetetaan kurssikokeella, johon ilmoittaudutaan **erikseen** Weboodissa. Kurssikokeessa (ellei se ole järjestetty yleisen tentin aikaan) sallitut apuvälineet ovat 1) laskin sekä 2) lunttilappu. Lunttilapun pitää olla itse laadittu ja _käsinkirijoitettu_ (eli ei tietokoneella tulostettu), eikä sillä ole muita rajoituksia kuin sen koko: yksi A4-kokoinen arkki (molemmat puolet saa käyttää).

Kurssin voi vaihtoehtoisesti suorittaa erilliskokeella, joihin ilmoittaudutaan erikseen Weboodin kautta. Erilliskokeissa (tai yleisen tentin aikana järjestetyssä kurssikokeessa) omaa lunttia ei voi käyttää, joten erilliskokeessa tehtäväpaperin yhteydessä on laatimani "luntti". Seuraavat erilliskokeet ovat 18.2.2020 (huomaa, että tämä on tarkoitettu korvaamaan kurssikoe, jos kyseinen ajankohta ei ole sopiva), ja sitten 10.6.2020 ja 5.8.2020.

Kurssikokeeseen voi saada laskuharjoitustehtävien ratkaisuista lisäpisteitä koepisteiden lisäksi. Näitä on mahdollista saada 3,5 pistettä. Jos et pääse kurssikokeeseen, niin laskuharjoituspisteet ovat mukana puolen vuoden ajan kurssin päättymisestä.

Laskuharjoituksista saa lisäpisteitä (max 3.5 pistettä.) Laskuharjoituksista saa pisteitä seuraavasti: 20% = 0.5p; 30% = 1p; 40% = 1.5p; ...; 70% = 3p; 80% = 3.5p.

Kurssikoe järjestetään tenttiviikolla

• pe 06.03. klo 12.00-14.30 jossakin Exactumin auditorioista.

HUOM! Kurssikokeeseen *tulee ERIKSEEN ILMOITTAUTUA* Weboodissa (ilmoittautuminen sulkeutuu 10 päivää ennen koetta).

Kokeen pistemäärä on luultavasti 4*6 = 24 pistettä. Jotta saisit suoritettua kurssikokeen pisteiden sekä lisäpisteiden summan pitää yhteen laskettuna olla tällöin vähintään 12 pistettä.

Kurssisivun päivittäminen on kesken...

Description

Bachelors's program of mathematical sciences.

Mandatory course in Intermediate studies in Statistics (MAT221). Also mandatory in MAT221, and optional in MAT020.

Basic studies in statistics (MAT120), basic studies in mathematics (MAT110). From the subject studies of statistics the courses MAT22001 and MAT22002 (Probability IIa and IIb) and their background requirements, or the equivalent background knowledge (basics in likelihood and bayesian inference, R programming, usual one- and multidimensional probability distributions, analysis of discrete one- and multidimensional distributions with (joint) probability mass functions, analysis of continuous one- and multidimensional distributions with (joint) probability density functions, change of variables formula for one- and multidimensional (joint) density functions, usual statistics of distributions and estimation based on these statistics, expectation, (co)variance and covariance matrix, and the basic properties of these, conditional distribution and conditional expectation, hierarchical definition of multidimensional distributions with marginal and conditional distributions, multinormal distribution and its properties, law of large numbers, central limit theorem and some approximations based on these limit results.)

Recommended studies (optional): Statistical inference II (MAT22003), Linear models I (MAT22004), Linear algebra and matrix computations III (MAT22011)

After the course the student should be able to do Bayesian inference both analytically, and using simulations, and to be able to use R and Stan to perform these simulations.

For students of statistics the recommended time for the course is the autumn of the third year of the studies.

The course is held on period II (second period of the autumn).

  • Topics of the course:
    • Basics of the Bayesian inference: likelihood, priori and posteriori
    • Bayesian inference for models with one parameter
    • Bayesian for multiparameter models
    • Predicting new observations using the posterior predictive distribution
    • Simulating from the posterior distribution using R and Stan
    • Quantifying the uncertainty of the parameter estimates using posterior intervals, statistics, and plots
    • Hierarchical models
    • Linear regression in the Bayesian framework
    • Model selection

Recommended (optional) background material : Gelman et al.: Bayesian data analysis, 3:rd edition (2013).

Stan- and R exercises in the exercise session.

Grading is mainly determined by the final exam, but you can also gain some points from doing the home exercises.

Lectures and exercise sessions