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In the last decades Statistics and Probability have evolved in a very fast way, either by the theoretical development or by the new technological advances and computational development. Some application areas posed several challenges for statistical and probabilistic methods, such as Image Processing, Biotechnology, Official Statistics, Pattern Recognition, Reliability, Forensic Statistics or Criminology, Particle Physics, Quantum Physics, Information Theory, Actuary and Economics. In the same period, complex probabilistic modeling and analysis as well as the Bayesian methods acquired a special status and penetrated practically all areas of knowledge including some where the applications of Statistics and Probability seemed remote.

In our program at UFRJ we develop research on contemporary themes in various branches of Statistics and Probability, including: Analysis of Spatio-temporal Data, Survival and Reliability Analysis, Spatial Statistics, Percolation, Limit Theorems for Particle Systems and Extreme Value Theory with applications in: actuarial, environmental sciences, epidemiology, hydrology, finance, mathematical physics. In Statistics, many of our researchers use the Bayesian methodology as a philosophy and also as a tool to solve problems in the most different areas. In Probability, we have a group that stands out in Stochastic Processes with applications in different fields.

Our main areas of research are listed below.

Sampling from Finite Population

In this research area, methodological aspects of estimation of parametric models are developed in the presence of complex sampling. One of the relevant applications related to this research topic is the estimation from small domains.

The difficulty in obtaining estimates for small domains is the small sample size and therefore the need to borrow information between domains through appropriate superpopulation models.

The main research areas in our program are:

  • models for counting data in small domains
  • models for informational sampling designs
  • analysis of data with excess of zeros in small domains
  • spatial-temporal models for population prediction
  • treatment of non-informative response
  • Bayesian estimators

Survival and Reliability Analysis

A branch of statistics that concerns death in biological organisms, failures in industrial components or systems or the duration of economic events. It involves modeling data related to the time of occurrence of an event of interest. Typical issues in the area are:
What proportion of a population survives a given time?
Among the survivors, what would be the death or failure rate?
Could we have multiple causes of failure?
Which particular or covariate characteristics, in statistical language, lead to higher or lower rates of survival?

The procedures for survival and reliability analysis can be applied many areas of knowledge.

The main research areas in our program are:

  • use of non-parametric techniques to estimate the failure rate
  • analysis of frailty models
  • models with non-proportional failure rates

Econometrics and Actuaries

Econometrics is characterized by a set of methods developed for statistical analysis of economic models. These can be cross-section models or time series models. In the last decades, special emphasis has been given to modeling problems in finance in order to describe price behavior or returns to assist decision making in the development of portfolios, pricing of options, among other goals.

Actuaries is a field of mathematics that studies risk phenomena under uncertainty. Some topics relate to the theory of ruin and insurance pricing. Development of statistical methods for these models is a major demand.

The main research areas in our program are:

  • heteroscedastic regression models based on mixtures of normal distributions
  • models for stochastic production functions with multiple output
  • risk and ruin theory: models for determining reserves
  • gradation techniques for the development of survival tables

Spatial Statistics and Spatio-Temporal Models

This is the area of ​​Statistics that models phenomena described by multiple variables in different locations over time. These models mainly have the purpose of interpolation (spatial) and prediction (temporal). For example, in environmental sciences, one wants to estimate the levels of pollutants in an unmeasured location (spatial interpolation), determine the location of a network of monitoring stations, or even predict the evolution of the pollution process.

It is generally assumed that the spatial process under study is homogeneous. In many applications, this hypothesis is often questionable. Another common assumption in spatio-temporal processes is that its covariance structure is separable. This hypothesis is equally restrictive and proposed in order to allow a feasible analysis.

The main research areas in our program are:

  • non-stationary models for spatial data
  • estimation of the intensity rate in specific processes
  • non-separable spatio-temporal covariance structures
  • optimal dimensioning of monitoring networks
  • spatial confounding

Modeling of Bayesian Networks

This research area seeks to develop modeling of graphs called Bayesian networks with characteristics of temporal correlation and non-stationarity in several types of application. Bayesian inference in the structure of the network and in local distributions aid decision making in complex networks of large dimensions.

The main research areas in our program are:

  • state space models for discrete Bayesian networks
  • Bayesian network approach for health systems through eliciting the opinion of experts
  • predictive models for risk assessment in complex systems such as food security and digital preservation

Hierarchical and Dynamic Models

This is the area of S​tatistics that analyzes data through models structured at different levels, in order to adequately characterize the multiplicity of components involved. Examples include models of latent components and dynamic models. The last class involves models for univariate or multivariate data indexed in time. Dynamic or state-space models have been developed fastly in recent decades and are nowadays indispensable techniques for modern applied or theoretical statisticians.

The main research areas in our program are:

  • non-linear and non-normal dynamic models: inference and computational aspects
  • hierarchical and multivariate dynamic models, including applications
  • dynamic econometric models based on micro-foundations
  • models of latent variables or factors
  • item response theory models

Music and Mathematics

In general, this area seeks to understand musical aspects through mathematical, probabilistic and/or statistical models. The reciprocal – understanding of mathematical models through musical elements – is also viable.

For example, from the recording of a song, how can we separate the instruments or infer their chord progression? How to remove noise from musical signals obtained from physically degraded media? Are Markov chain modeling accurate to describe musical aspects (harmony, melody, texture, among others) in a particular piece or work by a composer?

Historically, music and mathematics have only come to be seen as disjoint disciplines in the last two centuries. Such rapprochement is important for aspects of cultural and cognitive preservation and understanding, and also to allow both areas to exchange ideas and intuitions with each other again.
The main research areas in our program are:

  • statistical processing of musical signals
  • retrieval of musical information via machine learning techniques
  • Bayesian methods in audio restoration
  • Mathematical and probabilistic models in music analysis and composition

Probability and Stochastic Processes

Probability Theory and Stochastic Processes are the field of mathematics focused on the study of phenomena characterized by uncertainty. In addition to its recognized use in the foundation of modern Statistics, it reveals itself, after a strong expansion in the last decades, as being of extreme importance in areas of knowledge such as Information Theory, Physics and Modern Theory of Finance.

The main research areas in our program are:

  • stochastic calculus: control theory and stochastic filtering
  • hydrodynamic behavior of particle systems
  • continuous time stochastic models with Markovian jumps in the parameters
  • stochastic models in finance
  • Markovian processes with infinite interacting components
  • scale limits for stochastic processes
  • stochastic models in neuroscience
  • random walks in dynamic and random environments
  • percolation
  • stochastic systems with interacting components

Extreme Value Theory

The Extreme Value Theory studies properties of values located at the tail of probability distributions. There are strong probabilistic results that guarantee the shape of this tail to be independent of the central part of the distribution. Thus, the estimation of extreme values can be done with relative safety. This problem arises in several contexts, such as finances – maximum valuation or devaluation of an asset – and hydrology – maximum tides.

The main research areas in our program are:

  • threshold estimation
  • mixing models for extremes
  • models for multivariate extremes