Code: MAD 797

Duration: 60 hours

Contents:

• Basic concepts: failure time, types of censored data.
• Elements of survival and reliability analysis.
• Distributions of failure times.
• Empirical methods of identifying models.
• Estimation for simples samples and Kaplan-Meyer.
• Regression modelos for survival and reliability analysis.
• Inference for regression models.
• Frailty.

References:

• Cox, D. R. & Oakes, D. (1984). Analysis of Survival Data. Chapman & Hall.
• Crowder, M., Kimber, A. C., Smith, R. L. & Sweeting, T. (1994). Statistical Analysis of Reliability Data. Chapman & Hall.
• Kleinbaum, D. & Klein, M. (2005). Survival Analysis a Self Learning Text (2a Ed.). Springer.
• Therneau, T. M. & Grambsch, P. M. (2000). Modeling Survival Data: Extending the Cox Model. Springer.

Code: MAD 793

Duration: 60 hours

Contents:

• Introduction to Markov Chains: basics concepts; clasification of states; stationary distribution; reversibility.
• Random walks in graphs.
• Classical examples.
• Metropolis and Glauber chains.
• Convergence and Convergência and balance relaxation.
• Coupling and convergence in distribution.
• Mixture times.
• Ergodic theorem.
• Other topics:
  • Reversible Markov chains in networks;
  • Connection between potential theory in Markov chains and electrical networks;
  • Applications in combinatorial analysis, statistics, statistical mechanics and optimizatio;
  • Cut-off and metastability;
  • Poisson processes and variations;
  • Continuous-times Markov chains;
  • Renewal theory.

References:

• Brémaud, P.(1999). Markov Chains. Gibbs Fields, Monte Carlo Simulation, and Queues. Springer.
• Galves, A; Ferrari, P. Acoplamento em Processos Estocásticos (manuscrito não publicado) http://www.ime.usp.br/~pablo/papers/libro.pdf.
• Levin, D. A.; Peres, Y.; Wilmer, E. L. (2009). Markov Chains and Mixing Times. Amer. Math. Society.
• Norris, J. (1998). Markov Chains. Cambridge Univ. Press.

Code: MAC 711

Duration: 60 hours

Contents:

• Euclidean topology.
• Basic concepts of linear algebra.
• Limits of functions of random variables.
• Continuous functions.
• Differentiable functions and chain rule.
• Higher order derivatives and Taylor’s formula.
• Riemann-Stieltjes integral and its properties.
• Sequences and series of functions.
• Convergence and improper integrals.

References:

• Bartle, R (1976) The elements of Real Analysis. Wiley (2a. edição).
• Cipolatti, R. (2000). Cálculo Avançado. IM-UFRJ.
• Rudin, W. (1976). Principles of Mathematical Analysis. Mc Graw Hill (3a. edição).

Code: MAD 771

Duration: 60 hours

Contents:

• Linear regression model.
• Properties of the ordinary least square estimators for finite samples.
• Large sample theory.
• Generalized method of moments for simple and multiple equations.
• Panel data, multicolinearity, heteroscedasticity and serial correlation.
• Binary regression.
• Dynamic models: distributed lag, expectatons and partial adjustment
• Simultaneous equations: structures, identifying and estimation methods.

Referências:

• Greene, W. H. (2012). Econometric Analysis (7th Edition). Prentice Hall.
• Hayashi, F. (2000). Econometrics. Princeton: Princeton University Press.
• Kennedy, P. (2008). A Guide to Econometrics (6th Edition). Wiley-Blackwell.
  Koop, G. (2003). Bayesian Econometrics. Wiley-Interscience.
• Lancaster, T. (2004). Introduction to Modern Bayesian Econometrics. Wiley-Blackwell.

Code: MAD 760

Duration: 60 hours

Contents:

• Stochastic simulation:
  • Random variables generation;
  • Accept-Reject methods;
• Numerical optimization:
  • Algoritmo EM;
  • Simulated annealing.
• Approximate inferencial methods:
  • Laplace approximation;
  • Importance sampling;
  • Monte Carlo integration.
• Monte Carlo Markov chain methods:
  • Gibbs sampling;
  • Metropolis e Metropolis-Hastings algoritms;
  • Convergence diagnosis.
• Calculation of marginal distribution:
  • Reversible jump MCMC;
  • Model comparison.

References:

• Gamerman, D. e Lopes,H. F. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition. Chapman & Hall, 2006.
• Givens, G. H. e Hoeting, J. A. Computational Statistics (Wiley Series in Computational Statistics), 2012.
• Robert, C.P. and Casella, G. Monte Carlo Statistical Methods. Springer, 2004.

Code: MAD 762

Duration: 60 hours

Contents:

• Geostatistics:
  • Exploratory data analysis (variogram, semivariogram, contour plots, global and local trends);
  • Gaussian processes;
  • Stationarity and isotropy;
  • Covariance functions.
• Inference in spatial processes:
  • Classical and Bayesian inference;
  • Spatial interpolation;
  • Non-stationary modelos.
• Aerial data: exploratory data analysis:
  • Moran’s I statistics;
  • CAR and SAR models;
  • Classical and Bayesian inference in CAR and SAR models.
• Point processes:
  • Point pattern analysis;
  • Intensity estimators (kernel) and spatial dependence estimators;
  • Marked point process.

References:

• Stein, M. (1999). Interpolation of Spatial Data. Springer.
• Cressie, N. (1993). Statistics for Spatial Data. Wiley.
• Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns (2a Ed). Arnold.

Code: MAD 788

Duration: 60 hours

Contents:

• Classical and Bayesian inference in the multivariate normal distribution.
• Regression and multivariate analysis of variance: classical and Bayesian approaches.
• Principal components.
• Factoral analysis.
• Canonical correlation.
• Correspondence analysis.
• Discriminant analysis.
• Cluster analysis.

References:

• Johnson e Wichern (2007). Applied Multivariate Statistical Analysis. 6th Ed. Pearson.
• Mardia, K. C., Kent, J. T. & Bibby, J. M. (1982). Multivariate Analysis. Academic Press;
• Press, S. J. (1989). Bayesian Statistics: Principles, Models and Applications. Wiley.

Code: MAD 761

Duration: 60 hours

Contents:

• Introduction to spatial statistics (geostatistics, aerial data, point processes, disntances on the globe);
• Random fields and random functions (definition, spectral dentisy, mean function);
• Covariance functions;
• Elementary properties of covariance functions (stationaruty, smoothness, separability, isotropy, nugget effect);
• Estimation (likelihood problems, prior distributions, likelihood approximation, tapering);
• Prediction and extrapolation (theoretical comparison, model comparison for prediction);
• Non-stationary models (convolution models);
• Anisotropy (spatial deformation);
• Spatio-temporal models (separability, simetry);
• Multivariate models (coregionalization models, and convolution and cross-covariance).

References:

• Banerjee, S., Carlin, B. and Gelfand, A. E. (2004). Hierarchical modeling and analysis for spatial data. Chapman & Hall.
• Cressie, N. (1993). Statistics for Spatial Data. Wiley & Sons.
• Stein, M. (1999). Interpolation of Spatial Data. Springer.

Code: MAD 781

Duration: 90 hours

Contents:

• Likelihood function.
• Elements of Inference: Bayes’ theorem, interchangeability, sufficiency, exponential family of distributions, prior distributions.
• Point and intervalar estimation: classical and Bayesian approaches.
• Sampling distributions.
• Efficiency of estimators.
• Asymptotic confidence Intervals.
• Hypothesis testing: classical and Bayesian approaches.
• Asymptotic tests.
• Tests for the normal model.
• Neyman-Pearson theory.
• Likelihood ratio test.

References:

• Migon, H. S. e Gamerman, D. (1999). Statistical Inference. Arnold.
• Bickel, P. J. e Doksum, K. A. (1977). Mathematical Statistics. Holden-Day.
• Casella, G. & Berger, R. (2006). Statistical Inference (2a Ed.). Thomson Learning.

Code: MAD 796

Duration: 60 hours

Contents:

• Classical and Bayesian estimation;
• Dynamic models (state space models) of time series;
• Models with trend and seasonality;
• Dynamic regression;
• General linear model properties;
• Transfer function models;
• Monitoring and intervention;
• Non-normal and non-linear dynamic models;
• Computational methods: Monte Carlo Markoc chains (MCMC) and particle filters.

References:

• Durbin, J. and Koopman, S. J. (2012). Time Series Analysis by State Space Methods (2nd Edition). Oxford: Oxford University Press.
• Prado, R. and West, M. (2010). Time Series Modeling, Inference and Forecasting. Boca Raton: Chapman & Hall/CRC.
• West, M. & Harrison, P. J. (1997). Bayesian Forecasting and Dynamic Models.
  Springer-Verlag (2a. edição).

Code: MAD 789

Duration: 60 hours

Contents:

• Simple linear regression.
• General linear model.
• One-factor analysis of variance.
• Multiple regression models.
• Classical and Bayesian prediction.
• Residual analysis.
• Generalized linear models.
• Models for binary and categorical data.
• Linear models.
• Models for data with constant coefficient of variation.
• Model verification.

References:

• Fahrmeir, L. e Tutz, G. (1994). Multivariate Statistical Modelling Based on Generalized Linear Models. Springer.
• Gamerman, D. e Migon, H. (1999). Statistical Inference: an Integrated Approach. Arnold.
• Jorgensen, B. (1993). The Theory of the Linear Model. Chapman & Hall.
• McCullagh, P. e Nelder, J. A. (1989). Generalized Linear Models (2a ed.) Chapman & Hall.

Code: MAD 708

Duration: 0 horas

Codes: MAD 701 to 704

Carga horária: 15 hours

Contents:

Course with varied content involving discussion of published research works or research works to be published.

Code: MAD 772

Duration: 60 hours

Contents:

• Stationary ARMA processes.
• Maximum likelihood estimation.
• Asymptotic distribution theory.
• Aspects of Bayesian estimation in time series.
• Multivariate time series.
• Spectral analysis.
• Conditional heteroscedasticity models: univariate and multivariate cases.
• Nonlinear time series models.
• VAR models.
• Unit roots and cointegration.

References:

Code: MAD 777

Duration: 60 hours

Contents:

• Subjective probability and its elicitation,
• Utility theory and rational preferences,
• Decision functions,
• Admissibility,
• Scoring rules.
• Decision trees.
• Decisions with multiple attributes.
• Optimal design.

References:

• DeGroot, M. H. (1970). Optimal Statistical Decisions. McGraw-Hill.
• French, S and Rios Insua, D (2000) – Statistical decision theory. Kendal’s library of statistics 9. Arnold.
• Parmigiani, G. e Inoue, L., (2009) – Decision Theory – principles and approaches – Wiley.
• Smith J. (2010) Bayesian decision analysis – Cambridge University Press.

Code: MAD 790

Duration: 90 hours

Contents:

• Probability spaces.
• Random variables and random vectors.
• Expected values.
• Generating functions and characteristic functions.
• Conditional distribution and expectation.
• Laws of large numbers.
• Types of convergence.
• Limit theorems.

References:

• James, B. R. (1981). Probabilidade: Um Curso de Nivel Intermediário. Projeto Euclides, IMPA;
• Shiryayev, A. N. (1984). Probability. Springer.

Code: MAD 784

Duration: 60 hours

Contents:

• Applications in finance and actuarial.
• Asymptotic results for block maximums and excesses.
• Extreme value and generalized Pareto distributions (Inference in these distributions).
• Extremal index, quantile estimation.
• Calculation of VaR and shortfall.
• Graphical estimators (mean excess plots, peaks over thresholds).
• Likelihood and Bayesian estimation methods.

References:

• Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag.
• Embrechts, P., Kluppelberg, C & Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer-Verlag.

Codes: MAD 711 and 712

Carga horária: 60 horas

Contents:

• Course with free content. It can accommodate various situations such as specific courses by collaborating or visiting professors.

Codes: MAD 786 and 787

Duration: 60 hours

Contents:

• Course with free content. It can accommodate various situations such as specific courses by collaborating or visiting professors.

Codes: MAD 713 and 714

Carga horária: 60 hours

Contents:

• Course with free content. It can accommodate various situations such as specific courses by collaborating or visiting professorss.

Code: MAD 851

Duration: 60 hours

Contents:

• Probability spaces.
• Reviewing concepts of measure theory: expectation and distributions.
• Conditional expectation.
• Conditional distribution.
• Limit theorems for independent variables: law of large numbers, convergence of series, central limit theorem (Gaussian case).
• Convergence of measures in metric spaces.
• Introduction to the Brownian motion.
• Donsker’s theorem.
• Infinitely divisible distributions.
• Central limit theorem for independent variables (general case).
• Stationary processes and Birkhoff’s ergodic theorem.

References:

• Araújo, A.; Giné, E. (1981). The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley.
• Billingsley, P. (1995). Probability and Measure (3a. edição). Wiley.
• Billingsley, P. (1968). Convergence of Probability Measures.
• Chung, K. L. (1974). A Course in Probability Theory. Academic Press.
• Durrett, R. (1991). Probability: Theory and Examples. Duxbury.
• Loève, M. Probability Theory I (1977). Springer.
• Loève, M. Probability Theory II (1978). Springer.
• Varadhan, S.R.S. (2001). Probability Theory. Courant Lecture Notes, 7. Amer. Math.Soc.

Code: MAD 852

Duration:

Contents:

• Martingales with discrete and continuous parameter.
• Brownian motion.
• Markov processes.
• Stochastic integration and the Itô formula.
• Stochastic differential equations and diffusions.
• Other topics according to the interest of the instructor and the class.

References:

• Sato, K. (1999) Lévy processes and Infinitely divisible distributions. Cambridge University Press.
• Karatzas, I.; Shreve, S. (2008). Brownian Motion and Stochastic Calculus (2ª edição). New York, Springer-Verlag.
• Revuz, D.; Yor, M. (2004). Continuous Martingales and Brownian Motion (3ª edição). Springer-Verlag.
• Varadhan, S.R.S. (2007). Stochastic Processes. Courant Lect Notes 16, Am. Math. Soc.

Codes: MAD 801 to 804

Duration: 15 hours

Contents:

Course with varied content based on presentation of published works or works to be published in a specific research area.

Code: MAD 862

Duration: 60 horas

Contents:

• Statistical models: interchangeability, partial interchangeability, sufficiency and invariance.
• Conjugate analysis, reference priors and asymptotic theory.
• Credibility intervals and regions.
• Model comparison: hypothesis testing, Bayes factors, discrepancy measures and predictive distributions.

References:

• Bernardo, J. M. e Smith, A. F. M. (1994). Bayesian Theory. Wiley;
• Robert, C. (1995). The Bayesian Choice. Springer-Verlag.

Code: MAD 861

Duration: 60 hours

Contents:

• Exponential family and sufficiency.
• Loss functions.
• Estimators:
  • information inequality,
  • bias,
  • complete families and uniformly minimum-variance,
  • minimax estimation and admissibility.
• Likelihood: asymptotic optimality and invariance.
• Hypothesis testing:
  • Neyman-Pearson’s lemma,
  • greater uniform power,
  • confidence limits,
  • non-biased tests,
  • invariance and conditional tests.

References:

Codes: MAD 821 and 822

Duration: 60 hours

Contents:

• Course with free content. It can accommodate various situations such as specific courses by collaborating or visiting professors.

Codes: MAD 854 and 855

Duration: 60 hours

Contents:

• Course with free content. It can accommodate various situations such as specific courses by collaborating or visiting professors.

Code: MAD 842

Duration: 60 hours

Contents:

• Course with free content. It can accommodate various situations such as specific courses by collaborating or visiting professors.

Code: MAD 873

Duration: 60 hours

Contents:

• Course with free content in Sampling. It can accommodate various situations such as specific courses by collaborating or visiting professors.

Code: MAD 871

Duration: 60 hours

Contents:

• Course with free content in Bayesina Computation. It can accommodate various situations such as specific courses by collaborating or visiting professors.

Code: MAD 874

Duration: 60 hours

Contents:

• Course with free content in Spatial Statistics. It can accommodate various situations such as specific courses by collaborating or visiting professors.

Code: MAD 877

Duration: 60 hours

Contents:

• Course with free content in statistics applied to Finance. It can accommodate various situations such as specific courses by collaborating or visiting professors.

Code: MAD 872

Duration: 60 hours

Contents:

• Course with free content in Dynamic Models. It can accommodate various situations such as specific courses by collaborating or visiting professors.

Code: MAD 875

Duration: 60 hours

Contents:

• Course with free content in Robustness. It can accommodate various situations such as specific courses by collaborating or visiting professors.