Preparatory Courses
Code: MAD 001
Duration: 40 horas
Contents:
 Events and sampling spaces.
 Conditional probability.
 Random variables and distributions.
 Expectation.
 Main probability distributions.
 Law of the large numbers and central limit theorem.
References:
 DeGroot, M. H. (1989). Probability and Statistics. AddisonWesley (2ª. edição);
 Ross, S. (2009). A First Course in Probability. Prentice Hall (8° Edição).
M.Sc.
Code: MAD 783
Duration: 60 hours
Contents:
 Superpopulation Models.
 Introduction to the Theory of Predicting for Finite Populations:
 Optimal linear predictors;
 Empirical linear predictors.
 Informative Sampling.
 Nonresponse treatment.
 Bayesian inference for finite populations.
 Linear Bayes estimator.
 Introduction to the problem of estimating in small areas.
References:
 Chambers R. L. and Skinner, C. J.(2003). Analysis of Survey Data. Wiley Series in Survey Methodology.
 Ghosh, M. e Meeden, G. (1997). Bayesian Methods for Finite Population Sampling. Chapman & Hall.
 Moura, F.A.S(2008). Estimação em Pequenos Domínios. 180 SINAPE. ABE.
 Valiant, R. Dorfman, A. H. and Royall R. M.(2000). Finite Population Sampling and Inference: A Prediction Approach. Wiley Series in Probability and Statistics.
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 KaplanMeyer.
 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;
 Cutoff and metastability;
 Poisson processes and variations;
 Continuoustimes 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.
 RiemannStieltjes 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. IMUFRJ.
 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). WileyBlackwell.
Koop, G. (2003). Bayesian Econometrics. WileyInterscience.  Lancaster, T. (2004). Introduction to Modern Bayesian Econometrics. WileyBlackwell.
Code: MAD 760
Duration: 60 hours
Contents:
 Stochastic simulation:
 Random variables generation;
 AcceptReject 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 MetropolisHastings 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;
 Nonstationary 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);
 Nonstationary models (convolution models);
 Anisotropy (spatial deformation);
 Spatiotemporal models (separability, simetry);
 Multivariate models (coregionalization models, and convolution and crosscovariance).
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.
 NeymanPearson 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. HoldenDay.
 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;
 Nonnormal and nonlinear 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.
SpringerVerlag (2a. edição).
Code: MAD 789
Duration: 60 hours
Contents:
 Simple linear regression.
 General linear model.
 Onefactor 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:
Edition). New York: Springer.
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. McGrawHill.
 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. SpringerVerlag.
 Embrechts, P., Kluppelberg, C & Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. SpringerVerlag.
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.
Codes: MAD 791
Duration: 60 horas
Contents:
 Course with free content. It can accommodate various situations such as specific courses by collaborating or visiting professors.
Dr.Sc.
Code: MAD 808
Duration: 0 hours
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, SpringerVerlag.
 Revuz, D.; Yor, M. (2004). Continuous Martingales and Brownian Motion (3ª edição). SpringerVerlag.
 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. SpringerVerlag.
Code: MAD 861
Duration: 60 hours
Contents:
 Exponential family and sufficiency.
 Loss functions.
 Estimators:
 information inequality,
 bias,
 complete families and uniformly minimumvariance,
 minimax estimation and admissibility.
 Likelihood: asymptotic optimality and invariance.
 Hypothesis testing:
 NeymanPearson’s lemma,
 greater uniform power,
 confidence limits,
 nonbiased 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.
Code: MAD 876
Duration: 60 hours
Contents:
 Course with free content in Extreme Value Theory. It can accommodate various situations such as specific courses by collaborating or visiting professors.