Research

Research Activities

Statistics has developed in the last decades in an extremely fast form due to the new technological advances and the computatonal ease. Application areas, such as Image Processing, Biotechnology, Official Statistics, Pattern Recognition, Reliability, and Criminology, placed many new challenges for statistical methodology. In the same time, Bayesian philosophy and methodology acquired a spatial status and entered in basically all areas of Statistics, including those where applications of Statistics appeared remote.
Research in contemporaneous topics including Analysis of Spatio-temporal Data, Extreme Value Theory, Spatial Statistics, Stochastic Processes and Survival and Reliability Analysis, is developed at our Graduate Program at UFRJ, with applications to Actuaries, Environmental Sciences, Epidemiology, Finance, Hidrology,… Many of our faculty use the Bayesian methodology as philosophical basis but also as a tool to solve state-of-the-art problems in the most different areas of Statistics.

Our main lines of research (with the respective researchers, listed in alphabetical order) are:

Finite Population Sampling

Alexandra, Fernando, Helio, Marina

Methodological aspects of estimation of parametric models in the presence of complex sampling are developed in this lie of research. One of the relevant applications related to this research theme is estimation in small areas. The difficulty in obtaining estimates for small areas is the small sample size and, therefore, the need to borrow information between areas through appropriate superpopulation models.

The main lines of research in our programme are:

  • models for count data in small areas
  • models for informative sampling plans
  • data analysis with zero inflated data in small areas
  • spatio-temporal models for population forecasting

Survival and Reliability Analysis

Dani and Mariane

This is the branch of Statistics that deals with death in biological organisms, failures in industrial components or systems, or duration times of economic events. It involves modeling data related to the time to occurrence of some event of interest. Typical questions of this area are:
What proportion of a population survives a given time? what would be the failure rate among survivors?
Could there be multiple failure causes?
Which special characteristics or covariates, in statistical jargon, lead to higher or lower survival rates?
The procedures of survival and reliability analysis may be applied to a wide variety of areas of human knowledge.

The main lines of research in our programme are:

  • use of non-parametric techniques for failure rate estimation
  • analysis of frailty models
  • models with non-proportional failure rates

Econometrics and Actuaries

Alexandra, Fernando, Helio and Ralph

Econometrics is characterized by a group of methods developed for the statistical analysis of economic models. These can be cross-section or time series models. Special emphasis has been placed to modeling problems in finance in the last decades in order to describe evolution of prices or returns to aid decision making in portfolios or option pricing.

Actuaries is the branch of Mathematics that studies risk phenomena under uncertainty. Some themes are related to ruin theory and insurance princing. There is a large demand for the development of statistical methods for these models.

The main lines of research in our programme are:

  • heteroscedastic regression models based on mixture of normals
  • stochastic production frontier models with multiple output
  • risk and ruin theory: models for reserve determination
  • graduation techniques for elaboration of evolution of life tables

Spatial Statistics and Spatial-Temporal Models

Alexandra, Dani, Mariane, Marina and Thais

This is the area of Statistics that models phenomena described by multiple variables in different locations through time. These models are designed mainly to perform (spatial) interpolation and (temporal) forecasting. In environmental sciences, for example, interest lies in estimation of levels of a pollutant in an ungauged site (spatial interpolation), determination of the location of a network of monitoring stations or even prediction of the evolution of the polution process.

It is generally assumed that the spatial process under study is homogeneous. In the applications, this assumption is frequently questionable. Another common assumption in spatio-temporal processes is the separability of the process covariance. This hypothesis is equally restrictive and mostly dictated by analysis tractability.

The main lines of research in our programme are:

  • non-stationary models for spatial data
  • estimation of the intensity rate in point processes
  • non-separable spatio-temporal covariance structure
  • optimal design of monitoring networks

Hierarchical and Dynamics Models

Dani, Flavia, Helio, Mariane and Ralph

This is the area of Statistics that analyses data through models structured at different levels in order to adequately characterize the multiplicity of components involved. Examples include latent components models and dynamic models. The last class involves models for uni or mutivariate data indexed over time. Dynamic or state space models had experiencied accelerated growth in the last decades and are nowadays unavoidable techniques for the moder statistician, be him applied or theoretical.

The main lines of research in our programme are:

  • dynamic non-linear and non-normal models: inference and computationai aspects
  • hierarchical multivariate dynamic models, including applications
  • econometric dynamic models based on microfoundations
  • models with latent variables or factors
  • item response theory models

Probability and Stochastic Processes

Glauco, Leandro, Maria Eulalia

The theory of probability and stochastic processes is the branch of Mathematics dedicated to the study of phenomena characterized by uncertainty. Beyond its well-known use in the foundations of modern Statistics, it revealed itself, after a strong expansion in the last decades, as extremely important in areas such as Information Theory, Physics and modern theory of Finance.

The main lines of research in our programme are:

  • stochastic calculus: control theory and stochastic filtering
  • hydrodinamic behaviour of systems of particles
  • stochastic models in continuous time with markovian jumps on the parameters
  • stochastic models in finance
  • Markovian processes with infinite components interacting

Extreme Value Theory

Dani

Extreme value theory studies properties of values in the tail of probability distributions. Strong probability results ensure the form of this tail irrespective of the central part of the distribution. Thus, extreme value estimation can be performed with considerable safey. This problem appear in many contexts such as finance (maximum of (under)valuation of an asset) and hydrology (maximum of tides).

The main lines of research in our programme are:

  • threshold estimation
  • mixture models for extremes
  • models for multivariate extremes