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Dynamic mixture-of-experts models for longitudinal and discrete-time survival data
Stockholm University, Faculty of Social Sciences, Department of Statistics. Sveriges Riksbank, Sweden.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We propose a general class of flexible models for longitudinal data with special emphasis on discrete-time survival data. The model is a finite mixture model where the subjects are allowed to move between components through time. The time-varying probabilities of component memberships are modeled as a function of subject-specific time-varying covariates. This allows for interesting within-subject dynamics and manageable computations even with a large number of subjects. Each parameter in the component densities and in the mixing function is connected to its own set of covariates through a link function. The models are estimated using a Bayesian approach via a highly efficient Markov Chain Monte Carlo (MCMC) algorithm with tailored proposals and variable selection in all sets of covariates. The focus of the paper is on models for discrete-time survival data with an application to bankruptcy prediction for Swedish firms, using both exponential and Weibull mixture components. The dynamic mixture-of-experts models are shown to have an interesting interpretation and to dramatically improve the out-of-sample predictive density forecasts compared to models with time-invariant mixture probabilities.

Keyword [en]
Bayesian inference, Markov chain Monte Carlo, Bayesian variable selection, Survival analysis, Mixture-of-experts
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:su:diva-118133OAI: oai:DiVA.org:su-118133DiVA: diva2:820444
Funder
VINNOVA, 2010-02635
Available from: 2015-06-12 Created: 2015-06-12 Last updated: 2015-07-30
In thesis
1. Bayesian Inference in Large Data Problems
Open this publication in new window or tab >>Bayesian Inference in Large Data Problems
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In the last decade or so, there has been a dramatic increase in storage facilities and the possibility of processing huge amounts of data. This has made large high-quality data sets widely accessible for practitioners. This technology innovation seriously challenges traditional modeling and inference methodology.

This thesis is devoted to developing inference and modeling tools to handle large data sets. Four included papers treat various important aspects of this topic, with a special emphasis on Bayesian inference by scalable Markov Chain Monte Carlo (MCMC) methods.

In the first paper, we propose a novel mixture-of-experts model for longitudinal data. The model and inference methodology allows for manageable computations with a large number of subjects. The model dramatically improves the out-of-sample predictive density forecasts compared to existing models.

The second paper aims at developing a scalable MCMC algorithm. Ideas from the survey sampling literature are used to estimate the likelihood on a random subset of data. The likelihood estimate is used within the pseudomarginal MCMC framework and we develop a theoretical framework for such algorithms based on subsets of the data.

The third paper further develops the ideas introduced in the second paper. We introduce the difference estimator in this framework and modify the methods for estimating the likelihood on a random subset of data. This results in scalable inference for a wider class of models.

Finally, the fourth paper brings the survey sampling tools for estimating the likelihood developed in the thesis into the delayed acceptance MCMC framework. We compare to an existing approach in the literature and document promising results for our algorithm.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2015. 50 p.
Keyword
Bayesian inference, Large data sets, Markov chain Monte Carlo, Survey sampling, Pseudo-marginal MCMC, Delayed acceptance MCMC
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-118836 (URN)978-91-7649-199-7 (ISBN)
Public defence
2015-09-07, Ahlmannsalen, Geovetenskapens hus, Svante Arrhenius väg 12, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
VINNOVA, 2010-02635
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Submitted. Paper 2: Submitted. Paper 3: Manuscript. Paper 4: Manuscript.

Available from: 2015-08-14 Created: 2015-07-08 Last updated: 2015-08-13Bibliographically approved

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