Welcome to Bayesian Statistics, Simulation and Software – with a View to Application Examples
Description: During the last decades, Bayesian statistics has gained enormous popularity as an elegant and powerful computational tool to perform statistical analysis in complex stochastic models as applied in engineering, science and medicine. Bayesian statistics offers an alternative approach to traditional data analysis by including prior knowledge about the model parameters in form of a prior distribution. Using Bayes formula the prior distribution is updated from the posterior distribution by incorporating the observed data by means of the likelihood. Subsequently statistical inference about the unknown model parameters is derived from the posterior distribution. However, the posterior distribution is often intractable due to high-dimensional complex integrals implying that approximate stochastic simulation techniques such as Markov Chain Monte Carlo (MCMC) methods become crucial. This course reviews the basics ideas behind Bayesian statistics and Markov chain Monte Carlo (MCMC) methods. Background on Markov chains will be provided and subjects such as Metropolis and Metropolis-Hastings algorithms, Gibbs sampling and output analysis will be discussed. Furthermore, graphical models will be introduced as a convenient tool to model complex dependency structures within a stochastic model. The theory will be demonstrated through different examples of applications and exercises, partly based on the software package R.
Prerequisites: The course is accessible to those new to these subjects; however, a basic knowledge of statistics and probability theory as obtained through engineering studies at Aalborg University is expected.
Additional information and assessment: All course material and additional information is available at the course website https://asta.math.aau.dk/course/bayes/2018/. In particular note the assessment of the course through active participation and a hand-in exercise.
Frequently asked questions:
Q: If I participate in the course, can you then help me analyze a dataset that I work with as part of my ph.d. project.
A: No, I am afraid that this is not possible
Q: I would like to participate in the course, but during a part of the course period I can not be present. Is it possible to follow to course via Skype or similar?
A: No, I am afraid that this is not possible
Q: I am not a ph.d. student, but I would like to participate in the course anyway. Is that possible?
A: You will have to ask the doctoral school: aauphd@adm.aau.dk
Q: I realize that I am late for enrollment, but I would really like to participate. Is it possible.
A: You will have to ask the doctoral school: aauphd@adm.aau.dk
Organizer: Professor Jesper Møller, e-mail: jm@math.aau.dk
Lecturers: Professor Jesper Møller (e-mail: jm@math.aau.dk) and Associate Professor Ege Rubak (e-mail: rubak@math.aau.dk).
ECTS: 4
Time: 4, 5, 6, 9, 10 and 11 December 2019
Place: Fredrik Bajers Vej 7A, room 4-106
Zip code: 9220
City: Aalborg Øst
Number of seats: 40
Deadline: 13 November 2019
Important information concerning PhD courses: We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.
Description: During the last decades, Bayesian statistics has gained enormous popularity as an elegant and powerful computational tool to perform statistical analysis in complex stochastic models as applied in engineering, science and medicine. Bayesian statistics offers an alternative approach to traditional data analysis by including prior knowledge about the model parameters in form of a prior distribution. Using Bayes formula the prior distribution is updated from the posterior distribution by incorporating the observed data by means of the likelihood. Subsequently statistical inference about the unknown model parameters is derived from the posterior distribution. However, the posterior distribution is often intractable due to high-dimensional complex integrals implying that approximate stochastic simulation techniques such as Markov Chain Monte Carlo (MCMC) methods become crucial. This course reviews the basics ideas behind Bayesian statistics and Markov chain Monte Carlo (MCMC) methods. Background on Markov chains will be provided and subjects such as Metropolis and Metropolis-Hastings algorithms, Gibbs sampling and output analysis will be discussed. Furthermore, graphical models will be introduced as a convenient tool to model complex dependency structures within a stochastic model. The theory will be demonstrated through different examples of applications and exercises, partly based on the software package R.
Prerequisites: The course is accessible to those new to these subjects; however, a basic knowledge of statistics and probability theory as obtained through engineering studies at Aalborg University is expected.
Additional information and assessment: All course material and additional information is available at the course website https://asta.math.aau.dk/course/bayes/2018/. In particular note the assessment of the course through active participation and a hand-in exercise.
Frequently asked questions:
Q: If I participate in the course, can you then help me analyze a dataset that I work with as part of my ph.d. project.
A: No, I am afraid that this is not possible
Q: I would like to participate in the course, but during a part of the course period I can not be present. Is it possible to follow to course via Skype or similar?
A: No, I am afraid that this is not possible
Q: I am not a ph.d. student, but I would like to participate in the course anyway. Is that possible?
A: You will have to ask the doctoral school: aauphd@adm.aau.dk
Q: I realize that I am late for enrollment, but I would really like to participate. Is it possible.
A: You will have to ask the doctoral school: aauphd@adm.aau.dk
Organizer: Professor Jesper Møller, e-mail: jm@math.aau.dk
Lecturers: Professor Jesper Møller (e-mail: jm@math.aau.dk) and Associate Professor Ege Rubak (e-mail: rubak@math.aau.dk).
ECTS: 4
Time: 4, 5, 6, 9, 10 and 11 December 2019
Place: Fredrik Bajers Vej 7A, room 4-106
Zip code: 9220
City: Aalborg Øst
Number of seats: 40
Deadline: 13 November 2019
Important information concerning PhD courses: We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.
- Teacher: Jesper Møller
- Teacher: Ege Rubak