First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
STATISTICAL SCIENCES
Course unit
THEORY AND METHODS OF INFERENCE
SCP4063246, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2016/17

Information on the course unit
Degree course Second cycle degree in
STATISTICAL SCIENCES
SS1736, Degree course structure A.Y. 2014/15, A.Y. 2017/18
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Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination THEORY AND METHODS OF INFERENCE
Website of the academic structure http://scienzestatistiche.scienze.unipd.it/2017/laurea_magistrale
Department of reference Department of Statistical Sciences
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge ALESSANDRA SALVAN SECS-S/01
Other lecturers NICOLA SARTORI SECS-S/01

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines SECS-S/01 Statistics 9.0

Mode of delivery (when and how)
Period Second semester
Year 2nd Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Lecture 9.0 64 161.0 No turn

Calendar
Start of activities 26/02/2018
End of activities 01/06/2018

Syllabus
Prerequisites: First year Masters courses, especially Probability Theory and Statistics (Advanced).
Target skills and knowledge: The course aims at offering students a deep understanding of the likelihood based frequentist theory of statistical inference, inviting them as well to personal work on recent research in the field. An introduction to Bayesian inference will also be provided.
Examination methods: 1/3 homework, 1/3 final written exam, 1/3 written and oral presentation rewiewing one or two recent research papers.
Assessment criteria: Student’s assessment will consider how the topics presented are mastered in problems and applications, how finely the main methodologies are appreciated in their strenghths and weaknesses, how deep the personal interaction with recent research papers appears. PhD students can sit the exam only once, in the exam session following the course.
Course unit contents: - Statistical models and uncertainty in inference. Statistical models. Paradigms of inference: the Bayesian and frequentist paradigms. Prior specification. Model specification (data variability). Levels of model specification. Problems of distribution (variability of statistics). Simulation. Asymptotic approximations and delta method.
- Generating functions, moment approximations, transformations. Moments, cumulants and their generating functions. Generating functions of sums of independent random variables. Edgeworth and Cornish-Fisher expansions. Notations Op(·) and op(·). Approximations of moments and transformations. Laplace approximation.
- Likelihood: observed and expected quantities, exact properties. Dominated statistical models. Sufficiency. Likelihood: observed quantities. Examples: a two-parameter model, grouped data,
censored data, sequential sampling, Markov chains, Poisson processes. Likelihood and sufficiency. Invariance properties. Expected likelihood quantities and exact sampling properties.
Reparameterizations.
- Likelihood inference: first-order asymptotics. Likelihood inference procedures. Consistency of the maximum likelihood estimator. Asymptotic distribution of the maximum likelihood estimator. Asymptotic distribution of the log-likelihood ratio: simple null hypothesis, likelihood confidence regions, asymptotically equivalent forms, non-null asymptotic distributions, composite null hypothesis (nuisance parameters), profile likelihood, asymptotically equivalent forms and one-sided versions, testing constraints on the components of the parameter. Non-regular models.
- Bayesian Inference. Non-informative priors. Inference based on the posterior distribution. Point estimation and credibility regions. Hypothesis testing and the Bayes factor. Linear models.
- Likelihood and Bayesian inference: numerical and graphical aspects in R. Scalar and vector parameter examples. EM algorithm.
- Estimating equations and pseudolikelihoods. Misspecification. Estimating equations. Quasi likelihood. Composite likelihood. Empirical likelihood.
- Data and model reduction by marginalization and conditioning. Distribution constant statistics. Completeness. Ancillary statistics. Data and model reduction with nuisance parameters:
lack of information with nuisance parameters, pseudo-likelihoods. Marginal likelihood. Conditional likelihood. Profile and integrated likelihoods.
- The frequency-decision paradigm. Statistical decision problems. Optimality in estimation: Cram´er-Rao lower bound, asymptoticefficiency, Godambe efficiency, Rao-Blackwell-Lehmann-Scheffe theorem. Optimal tests: Neyman-Pearson lemma, composite hypotheses: families with monotone likelihood ratio, locally most powerful tests, two-sided alternatives, other constraint criteria. Optimal confidence regions.
- Exponential families, Exponential dispersion families, Generalized linear models. Exponential families of order 1. Mean value mapping and variance function. Multiparameter exponential
families. Marginal and conditional distributions. Sufficiency and completeness. Likelihood and exponential families: likelihood quantities, conditional likelihood, profile likelihood and mixed parameterization. Procedures with finite sample optimality properties. First-order asymptotic theory. Exponential dispersion families. Generalized linear models.
- Group families. Groups of transformations. Orbits and maximal invariants. Simple group families and conditional inference. Composite group families and marginal inference.
Planned learning activities and teaching methods: Lectures, homework, students' written and oral presentations.
Additional notes about suggested reading: Course material will be available on the course web page.
Textbooks (and optional supplementary readings)
  • Davison, Anthony Christopher, Statistical Models. New York: Cambridge University Press, 2003. Cerca nel catalogo
  • Pace, Luigi; Salvan, Alessandra, Principles of Statistical Inference, from a Neo-Fisherian Perspective. Singapore: World Scientific, 1997.
  • Severini, Thomas A., Likelihood Methods in Statistics. Oxford: Oxford University Press, 2000. Cerca nel catalogo
  • Severini, Thomas A., Elements of Distribution Theory. Cambridge: Cambridge University press, 2005. Cerca nel catalogo
  • Young, G. A.; Smith, R. L., Essentials of Statistical Inference. Cambridge: Cambridge University Press, 2005. Cerca nel catalogo