Random Processes | Institute of Mathematics and Statistics of University of Tartu

Contacts of UT units

Faculty of Arts and Humanities
Faculty phone: 
+372 737 5341
Faculty address: 
Jakobi 2, rooms 116–121, 51005 Tartu
  • Dean's Office
    Faculty phone: 
    + 372 737 5341
    Faculty address: 
    Jakobi 2, rooms 116–121, 51005 Tartu
  • Institute of History and Archaeology
    Faculty phone: 
    +372 737 5651
    Faculty address: 
    Jakobi 2, 51005 Tartu
  • Institute of Estonian and General Linguistics
    Faculty phone: 
    +372 737 5221
    Faculty address: 
    Jakobi 2, 51005 Tartu
  • Institute of Philosophy and Semiotics
    Faculty phone: 
    +372 737 5314
    Faculty address: 
    Jakobi 2, rooms 309–352, 51005 Tartu
  • Institute of Cultural Research
    Faculty phone: 
    (+372) 737 5223
    Faculty address: 
    Ülikooli 16, 51003 Tartu
  • School of Theology and Religious Studies
    Faculty phone: 
    +372 737 5301
    Faculty address: 
    Ülikooli 18–310, 50090 Tartu
  • College of Foreign Languages and Cultures
    Faculty address: 
    J. Liivi 4, 50409, Tartu
  • Viljandi Culture Academy
    Faculty phone: 
    +372 435 5232
    Faculty address: 
    Posti 1, 71004 Viljandi
Faculty of Social Sciences
Faculty phone: 
+372 737 5957
Faculty address: 
Lossi 36, 51003 Tartu
  • Dean's Office
    Faculty phone: 
    + 372 737 5900
    Faculty address: 
    Lossi 36, 51003 Tartu
  • Institute of Education
    Faculty phone: 
    +372 737 6440
    Faculty address: 
    Salme 1a–29, 50103 Tartu
  • Johan Skytte Institute of Political Studies
    Faculty phone: 
    +372 737 5582
    Faculty address: 
    Lossi 36–301, 51003 Tartu
  • School of Economics and Business Administration
    Faculty phone: 
    +372 737 6310
    Faculty address: 
    Narva mnt 18, 51009 Tartu
  • Institute of Psychology
    Faculty phone: 
    +372 737 5902
    Faculty address: 
    Näituse 2, 50409 Tartu
  • School of Law
    Faculty phone: 
    +372 737 5390
    Faculty address: 
    Näituse 20–324, 50409 Tartu
  • Institute of Social Studies
    Faculty phone: 
    +372 737 5188
    Faculty address: 
    Lossi 36, 51003 Tartu
  • Narva College
    Faculty phone: 
    +372 740 1900
    Faculty address: 
    Raekoja plats 2, 20307 Narva
  • Pärnu College
    Faculty phone: 
    +372 445 0520
    Faculty address: 
    Ringi 35, 80012 Pärnu
Faculty of Medicine
Faculty phone: 
+372 737 5326
Faculty address: 
Ravila 19, 50411 Tartu
  • Dean's Office
    Faculty phone: 
    +372 737 5326
    Faculty address: 
    Ravila 19, 50411 Tartu
  • Institute of Biomedicine and Translational Medicine
    Faculty phone: 
    +372 737 4210
    Faculty address: 
    Biomeedikum, Ravila 19, 50411 Tartu
  • Institute of Pharmacy
    Faculty phone: 
    +372 737 5286
    Faculty address: 
    Nooruse 1, 50411 Tartu
  • Institute of Dentistry
    Faculty phone: 
    +372 731 9856
    Faculty address: 
    Puusepa 1a, 50406 Tartu
  • Institute of Clinical Medicine
    Faculty phone: 
    +372 737 5323
    Faculty address: 
    L. Puusepa 8, 50406 Tartu
  • Institute of Family Medicine and Public Health
    Faculty phone: 
    +372 737 4190
    Faculty address: 
    Ravila 19, 50411 Tartu
  • Institute of Sport Sciences and Physiotherapy
    Faculty phone: 
    +372 737 5360
    Faculty address: 
    Ujula 4, 51008 Tartu
Faculty of Science and Technology
Faculty phone: 
+372 737 5820
Faculty address: 
Vanemuise 46–208, 51014 Tartu
  • Dean's Office
    Faculty phone: 
    +372 737 5820
    Faculty address: 
    Vanemuise 46–208, 51003 Tartu
  • Institute of Computer Science
    Faculty phone: 
    +372 737 5445
    Faculty address: 
    Narva mnt 18, 51009 Tartu
  • Estonian Marine Institute
    Faculty phone: 
    +372 671 8902
    Faculty address: 
    Mäealuse 14, 12618 Tallinn
  • Institute of Physics
    Faculty address: 
    W. Ostwaldi 1, 50411 Tartu
  • Institute of Chemistry
    Faculty phone: 
    +372 737 5261
    Faculty address: 
    Ravila 14a, 50411 Tartu
  • Institute of Genomics
    Faculty phone: 
    +372 737 4000
    Faculty address: 
    Riia 23b, 51010 Tartu
  • Institute of Mathematics and Statistics
    Faculty phone: 
    +372 737 5860
    Faculty address: 
    Narva mnt 18, 51009 Tartu
  • Institute of Molecular and Cell Biology
    Faculty phone: 
    +372 737 5027
    Faculty address: 
    Riia 23, 23b–134, 51010 Tartu
  • Tartu Observatory
    Faculty phone: 
    +372 737 4510
    Faculty address: 
    Observatooriumi 1, Tõravere, 61602 Tartumaa
  • Institute of Technology
    Faculty phone: 
    +372 737 4800
    Faculty address: 
    Nooruse 1, 50411 Tartu
  • Institute of Ecology and Earth Sciences
    Faculty phone: 
    +372 737 5835
    Faculty address: 
    Vanemuise 46, 51003 Tartu
Institutions
  • Library
    Faculty phone: 
    +372 737 5702
    Faculty address: 
    W. Struve 1, 50091 Tartu
  • Youth Academy
    Faculty phone: 
    +372 737 5581
    Faculty address: 
    Uppsala 10, 51003 Tartu
  • Museum
    Faculty phone: 
    +372 737 5674
    Faculty address: 
    Lossi 25, 51003 Tartu
  • University of Tartu Natural History Museum and Botanical Garden
    Faculty phone: 
    +372 737 6076
    Faculty address: 
    Vanemuise 46, 51003 Tartu
Support Units
  • Administrative Office
    Faculty phone: 
    +372 737 5606
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Centre for Entrepreneurship and Innovation
    Faculty phone: 
    +372 737 4809
    Faculty address: 
    Narva mnt 18, 51009, Tartu
  • University Office in Tallinn
    Faculty phone: 
    +372 737 6600
    Faculty address: 
    Teatri väljak 3, 10143 Tallinn
  • Estates Office
    Faculty phone: 
    +372 737 5137
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Finance Office
    Faculty phone: 
    +372 737 5125
    Faculty address: 
    Jakobi 4, 51005 Tartu
  • Grant Office
    Faculty phone: 
    +372 737 6215
    Faculty address: 
    Raekoja plats 9, 51004 Tartu
  • Information Technology Office
    Faculty phone: 
    +372 737 6000, IT-help: +372 737 5500
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Human Resources Office
    Faculty phone: 
    +372 737 5145
    Faculty address: 
    Ülikooli 18, rooms 302 and 304, 50090 Tartu
  • Internal Audit Office
    Faculty address: 
    Ülikooli 18-244, 51005 Tartu
  • International Cooperation and Protocol Office
    Faculty phone: 
    +372 737 6123
    Faculty address: 
    Ülikooli 18, rooms 104, 301, 305, 50090 Tartu
  • Marketing and Communication Office
    Faculty phone: 
    +372 737 5687
    Faculty address: 
    Ülikooli 18, rooms 102, 104, 209, 210, 50090 Tartu
  • Office of Academic Affairs
    Faculty phone: 
    +372 737 5620
    Faculty address: 
    Ülikooli 18, 50090 Tartu
  • Procurement Office
    Faculty phone: 
    +372 737 6632
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Rector's Strategy Office
    Faculty phone: 
    +372 737 5600
    Faculty address: 
    Ülikooli 18, 50090 Tartu
  • Student Council
    Faculty address: 
    Ülikooli 18b, 51005 Tartu
  • University of Tartu Press
    Faculty phone: 
    +372 737 5945
    Faculty address: 
    W. Struve 1, 50091 Tartu
Other Units
  • University of Tartu Academic Sports Club
    Faculty phone: 
    +372 737 5371
    Faculty address: 
    Ujula 4, 51008 Tartu
  • Tartu Student Village
    Faculty phone: 
    +372 740 9959
    Faculty address: 
    Narva mnt 25, 51013 Tartu
  • Tartu Students’ Club
    Faculty phone: 
    +372 730 2400
    Faculty address: 
    Kalevi 24, 51010 Tartu
  • Tartu University Hospital
    Faculty address: 
    L. Puusepa 1a, 50406 Tartu
  • University of Tartu Foundation
    Faculty phone: 
    +372 737 5852
    Faculty address: 
    Ülikooli 18, 50090 Tartu
  • View all other units

Contacts of UT units

Faculty of Arts and Humanities
Faculty phone: 
+372 737 5341
Faculty address: 
Jakobi 2, rooms 116–121, 51005 Tartu
  • Dean's Office
    Faculty phone: 
    + 372 737 5341
    Faculty address: 
    Jakobi 2, rooms 116–121, 51005 Tartu
  • Institute of History and Archaeology
    Faculty phone: 
    +372 737 5651
    Faculty address: 
    Jakobi 2, 51005 Tartu
  • Institute of Estonian and General Linguistics
    Faculty phone: 
    +372 737 5221
    Faculty address: 
    Jakobi 2, 51005 Tartu
  • Institute of Philosophy and Semiotics
    Faculty phone: 
    +372 737 5314
    Faculty address: 
    Jakobi 2, rooms 309–352, 51005 Tartu
  • Institute of Cultural Research
    Faculty phone: 
    (+372) 737 5223
    Faculty address: 
    Ülikooli 16, 51003 Tartu
  • School of Theology and Religious Studies
    Faculty phone: 
    +372 737 5301
    Faculty address: 
    Ülikooli 18–310, 50090 Tartu
  • College of Foreign Languages and Cultures
    Faculty address: 
    J. Liivi 4, 50409, Tartu
  • Viljandi Culture Academy
    Faculty phone: 
    +372 435 5232
    Faculty address: 
    Posti 1, 71004 Viljandi
Faculty of Social Sciences
Faculty phone: 
+372 737 5957
Faculty address: 
Lossi 36, 51003 Tartu
  • Dean's Office
    Faculty phone: 
    + 372 737 5900
    Faculty address: 
    Lossi 36, 51003 Tartu
  • Institute of Education
    Faculty phone: 
    +372 737 6440
    Faculty address: 
    Salme 1a–29, 50103 Tartu
  • Johan Skytte Institute of Political Studies
    Faculty phone: 
    +372 737 5582
    Faculty address: 
    Lossi 36–301, 51003 Tartu
  • School of Economics and Business Administration
    Faculty phone: 
    +372 737 6310
    Faculty address: 
    Narva mnt 18, 51009 Tartu
  • Institute of Psychology
    Faculty phone: 
    +372 737 5902
    Faculty address: 
    Näituse 2, 50409 Tartu
  • School of Law
    Faculty phone: 
    +372 737 5390
    Faculty address: 
    Näituse 20–324, 50409 Tartu
  • Institute of Social Studies
    Faculty phone: 
    +372 737 5188
    Faculty address: 
    Lossi 36, 51003 Tartu
  • Narva College
    Faculty phone: 
    +372 740 1900
    Faculty address: 
    Raekoja plats 2, 20307 Narva
  • Pärnu College
    Faculty phone: 
    +372 445 0520
    Faculty address: 
    Ringi 35, 80012 Pärnu
Faculty of Medicine
Faculty phone: 
+372 737 5326
Faculty address: 
Ravila 19, 50411 Tartu
  • Dean's Office
    Faculty phone: 
    +372 737 5326
    Faculty address: 
    Ravila 19, 50411 Tartu
  • Institute of Biomedicine and Translational Medicine
    Faculty phone: 
    +372 737 4210
    Faculty address: 
    Biomeedikum, Ravila 19, 50411 Tartu
  • Institute of Pharmacy
    Faculty phone: 
    +372 737 5286
    Faculty address: 
    Nooruse 1, 50411 Tartu
  • Institute of Dentistry
    Faculty phone: 
    +372 731 9856
    Faculty address: 
    Puusepa 1a, 50406 Tartu
  • Institute of Clinical Medicine
    Faculty phone: 
    +372 737 5323
    Faculty address: 
    L. Puusepa 8, 50406 Tartu
  • Institute of Family Medicine and Public Health
    Faculty phone: 
    +372 737 4190
    Faculty address: 
    Ravila 19, 50411 Tartu
  • Institute of Sport Sciences and Physiotherapy
    Faculty phone: 
    +372 737 5360
    Faculty address: 
    Ujula 4, 51008 Tartu
Faculty of Science and Technology
Faculty phone: 
+372 737 5820
Faculty address: 
Vanemuise 46–208, 51014 Tartu
  • Dean's Office
    Faculty phone: 
    +372 737 5820
    Faculty address: 
    Vanemuise 46–208, 51003 Tartu
  • Institute of Computer Science
    Faculty phone: 
    +372 737 5445
    Faculty address: 
    Narva mnt 18, 51009 Tartu
  • Estonian Marine Institute
    Faculty phone: 
    +372 671 8902
    Faculty address: 
    Mäealuse 14, 12618 Tallinn
  • Institute of Physics
    Faculty address: 
    W. Ostwaldi 1, 50411 Tartu
  • Institute of Chemistry
    Faculty phone: 
    +372 737 5261
    Faculty address: 
    Ravila 14a, 50411 Tartu
  • Institute of Genomics
    Faculty phone: 
    +372 737 4000
    Faculty address: 
    Riia 23b, 51010 Tartu
  • Institute of Mathematics and Statistics
    Faculty phone: 
    +372 737 5860
    Faculty address: 
    Narva mnt 18, 51009 Tartu
  • Institute of Molecular and Cell Biology
    Faculty phone: 
    +372 737 5027
    Faculty address: 
    Riia 23, 23b–134, 51010 Tartu
  • Tartu Observatory
    Faculty phone: 
    +372 737 4510
    Faculty address: 
    Observatooriumi 1, Tõravere, 61602 Tartumaa
  • Institute of Technology
    Faculty phone: 
    +372 737 4800
    Faculty address: 
    Nooruse 1, 50411 Tartu
  • Institute of Ecology and Earth Sciences
    Faculty phone: 
    +372 737 5835
    Faculty address: 
    Vanemuise 46, 51003 Tartu
Institutions
  • Library
    Faculty phone: 
    +372 737 5702
    Faculty address: 
    W. Struve 1, 50091 Tartu
  • Youth Academy
    Faculty phone: 
    +372 737 5581
    Faculty address: 
    Uppsala 10, 51003 Tartu
  • Museum
    Faculty phone: 
    +372 737 5674
    Faculty address: 
    Lossi 25, 51003 Tartu
  • University of Tartu Natural History Museum and Botanical Garden
    Faculty phone: 
    +372 737 6076
    Faculty address: 
    Vanemuise 46, 51003 Tartu
Support Units
  • Administrative Office
    Faculty phone: 
    +372 737 5606
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Centre for Entrepreneurship and Innovation
    Faculty phone: 
    +372 737 4809
    Faculty address: 
    Narva mnt 18, 51009, Tartu
  • University Office in Tallinn
    Faculty phone: 
    +372 737 6600
    Faculty address: 
    Teatri väljak 3, 10143 Tallinn
  • Estates Office
    Faculty phone: 
    +372 737 5137
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Finance Office
    Faculty phone: 
    +372 737 5125
    Faculty address: 
    Jakobi 4, 51005 Tartu
  • Grant Office
    Faculty phone: 
    +372 737 6215
    Faculty address: 
    Raekoja plats 9, 51004 Tartu
  • Information Technology Office
    Faculty phone: 
    +372 737 6000, IT-help: +372 737 5500
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Human Resources Office
    Faculty phone: 
    +372 737 5145
    Faculty address: 
    Ülikooli 18, rooms 302 and 304, 50090 Tartu
  • Internal Audit Office
    Faculty address: 
    Ülikooli 18-244, 51005 Tartu
  • International Cooperation and Protocol Office
    Faculty phone: 
    +372 737 6123
    Faculty address: 
    Ülikooli 18, rooms 104, 301, 305, 50090 Tartu
  • Marketing and Communication Office
    Faculty phone: 
    +372 737 5687
    Faculty address: 
    Ülikooli 18, rooms 102, 104, 209, 210, 50090 Tartu
  • Office of Academic Affairs
    Faculty phone: 
    +372 737 5620
    Faculty address: 
    Ülikooli 18, 50090 Tartu
  • Procurement Office
    Faculty phone: 
    +372 737 6632
    Faculty address: 
    Ülikooli 18a, 51005 Tartu
  • Rector's Strategy Office
    Faculty phone: 
    +372 737 5600
    Faculty address: 
    Ülikooli 18, 50090 Tartu
  • Student Council
    Faculty address: 
    Ülikooli 18b, 51005 Tartu
  • University of Tartu Press
    Faculty phone: 
    +372 737 5945
    Faculty address: 
    W. Struve 1, 50091 Tartu
Other Units
  • University of Tartu Academic Sports Club
    Faculty phone: 
    +372 737 5371
    Faculty address: 
    Ujula 4, 51008 Tartu
  • Tartu Student Village
    Faculty phone: 
    +372 740 9959
    Faculty address: 
    Narva mnt 25, 51013 Tartu
  • Tartu Students’ Club
    Faculty phone: 
    +372 730 2400
    Faculty address: 
    Kalevi 24, 51010 Tartu
  • Tartu University Hospital
    Faculty address: 
    L. Puusepa 1a, 50406 Tartu
  • University of Tartu Foundation
    Faculty phone: 
    +372 737 5852
    Faculty address: 
    Ülikooli 18, 50090 Tartu
  • View all other units

Random Processes

Hidden Markov models (HMMs) and related fields. HMM is a subclass of latent variable models, where it is assumed that observed data exhibit unobserved patterns or structures that can be described by latent variables. For example, magnetic resonance tomography measurements for a human body depend on tissue classes that cannot be directly observed. HMMs are widely used for modeling for example in genetics, bioinformatics, signal processing, and image analysis. The aim is to study different theoretical problems related to HMMs and their generalizations as well as applications in real data. One of the main topics of the research group is segmentation – predicting or estimating the latent variable path based on observations. Besides classical segmentation algorithms such as Viterbi or forward-backward ones, the group also studies the alternative approaches (so-called hybrid algorithms). Theoretical research is largely focused on the asymptotic properties of the Viterbi path and several limit theorems. The research is partially international, the main foreign partner is A. Koloydenko (RHUL). Besides classical HMMs, the group also studies several modern generalizations as pairwise and triplet Markov models. Motivated largely by applications, an important research topic of the group is the segmentation in the Bayesian setup. In the Bayesian context, the classical segmentation algorithms are not applicable anymore and so the new methods and algorithms specific for the Bayesian setup need to be worked out.

Random sequence comparison. In many research areas, the central object of study is long (but finite length) sequences from (relatively small) finite alphabet: DNA sequences, protein alignments, written texts, binary codes. One of the central questions is how to measure the similarity (or homology in genetics) of two sequences. There are several methods for that, mostly it is done via so-called similarity score, the most popular score is the length of the longest common subsequence - the longer is the longest common subsequence, the more related are the sequences deemed to be. To incorporate the variety, the sequences are modeled as random processes (often iid) and not-related sequences are taken as an independent. Now the score is a random variable as well and to distinguish the independent sequences from dependent ones, one has to know the (asymptotic) behavior of the score. Unfortunately, analyzing the score is a notoriously hard mathematical problem and since the limit laws are absent, one starts with simpler yet important questions like what is the speed growth of expected score, variation, and other moments. The standard tools of probability theory allow rather easily find some upper bounds to the moments, but lower bounds need a different approach. Together with international partners from GeorgiaTech (mainly H. Matzinger), a general method for lower bounds is worked out. This method requires neither the sequences being independent nor consisting of independent entries (as it is in the case of many standard tools for upper bounds), hence also applicable for pairwise Markov models (as described in the previous section) linking the two research areas of the group. Besides lower bounds, several other questions like path structure of longest common subsequences, the influence of score parameters, suboptimal alignments, etc are studied.

Maximum spacing method and model validation. In statistical modeling, it is essential to find a model that is in some sense most suitable for describing reality. Unlike information criteria such as Akaike or Bayes, the maximum spacing method (MSP) enables together with parameter estimation to decide about the suitability of the assigned model class for given data. The purpose is to study the properties of MSP estimators and the possibilities of the method as a model validation tool for model classes of different complexity.

Moran-type evolution models. The evolution model describes the dynamics of the genetic structure of the population as time evolves. These dynamics are usually driven by two components: selection and mutation. There are a large variety of evolution models, some of them model the evolution time in generations (e.g. Wright-Fisher model), some of them in terms of individuals – a new individual with a certain genotype is born and, to keep the population size fixed, another individual with possibly but not necessarily different genotype is discarded. Typically the births and deaths are modeled as being random and so the models become stochastic. To every genotype is attached a number – fitness – that describes how the given type influences the probability of birth or death of the individual. More fit individuals have smaller probabilities to die. Or, when fitness influences the birth, then the more fit is a type, the bigger is the probability that a newborn individual is of that type. The classical individual-level model is the so-called Moran model. Since the genetic structure of the population after birth/death event depends on the structure before the event and additional randomness, the genetic structure of the population is a (discrete-time) Markov process. The properties of the process, its stationary distribution, reversibility, limit laws as the population size increases – these are the research questions of the group. Evolution models are a rather new field for the group. The main collaborators are C. Watkins (RHUL) and F. Zucca, D. Bertacchi (Milano). The group investigates already existing models (e.g. so-called Guiol-Machado-Schinazi model) as well as proposes new models.

Research Group staff

Topics

  • Stochastic modeling: mainly models related to Hidden Markov models (HMMs, pairwise and triplet Markov models (PMM and TMM)), segmentation (Viterbi related algorithms) parameter inference, limit theorems in segmentation, infinite alignments, Bayesian modeling, applications.
  • Random sequence comparison: longest common subsequence related scores and optimal alignments, asymptotic properties, PMMs in sequence comparison.
  • Maximum spacing methods: asymptotic properties of MSP estimators in the case of multivariate observations; extension of MSP method to dependent observations; MSP method as a model validation tool.
  • Evolution models: Moran-like reversible models, large population limits, Dirichlet processes, Polya urn models, GMS models.

Research Group projects

Current projects

  • PI: IUT34-5 Mathematical statistics: theory and applications
  • PRG865 Statistical modelling with hidden Markov models and model validation

Main past projects

  • ETF9288 Hidden Markov models and random sequence comparison (The project is a continuation of the ETF grants 5694 and 7553.) (01.2012-07.2016)
  • SF0180015s12 Stochastics: theory and applications (01.2012-12.2014)

Relevant publications

Hidden Markov models (HMMs) and related fields:

Random sequence comparison:


Maximum spacing method and model validation:

Moran type evolution models: