Statisticals Methods and Simulation
2nd Cycle Studies - Mestrado
Lecturing, demonstrating, discussion and practical problem resolution.
To analyze data using appropriate statistical procedures;
To use suitable software tools to perform statistical calculations;
To plan correctly statistical studies in biomedical sciences;
To judiciously evaluate the results of studies published in the literature;
The student should be aware of the limitations of pseudorandom numbers and the corresponding generators. He/she should understand the fundamentals of the Monte Carlo method and the scope of this simulation technique. He/she should be able to simulate a given data sample and to obtain, from the simulation, the expected result and its uncertainty. He/she should be able to make a Monte Carlo model of a physical process (and a sequence of physical processes) in order to predict and reproduce some results, particularly in the context of the transport and interaction of radiation in physical and biological systems. Must be able to develop a basic application in Geant4.
Introd to exploratory data analysis
Descript statist and data visualization. Databases
Probab: concept and algebra. Random variables and probab functions. Discrete probab distributions: binomial and Poisson. Cont probab distributions normal, normal standard and t-Student. Central limit theorem
Inferential statistics.Sample, population and sampling techniques.The estimation theor.
Statistical hypothesis and hypothesis testing. Level of significance and power of a test. P value. Parametric and non-parametric tests
Meth of regression and correlation
Statistical meth of supervised and unsupervised classif
Monte Carlo meth
Discrete, continuous and cumulative probab. Uniform and non-uniform distributions
Change in probab density. Importance sampling
Monte Carlo methods in Medical Physics. Radiation transport algorithm
Description and use of different software packages in Medical and Radiation Physics
Basic of Monte Carlo simulat within the Geant4 framework
P sessions of Geant4 simulation
João Carlos Lopes Carvalho
Resolution Problems: 25.0%
Laboratory work or Field work: 25.0%
Análise Estatística, com utilização do SPSS; João Maroco, Edições Silabo;
Fundamentals of Biostatistics, Bernard Rosner, Thomson Brooks/Cole, 2006
Bioestatística, Epidemiologia e Investigação, A. Gouveia de Oliveira, Lidel
Métodos Quantitativos em Medicina, Massad, Menezes, Silveira & Ortega ed. Manole, 2004
Pattern Classification; Richard Duda, Peter Hart, David Stork; John Wiley & Sons, Inc
An Introduction of Support Vector Machines; Nello Christianini, John Shawe-Taylor; Cambridge University Press
Knuth, The Art of Computer Programming, 3rd vol, Addison-Wesley, 1999.
Press et al., Numerical Recipies in c, Camb. Univ. Press, 1992.
Wong, Computational Methods in Physics and Engineering, 2nd ed, Prentice-Hall, 1997.
Alex F Bielajew; Fundamentals of Monte Carlo Transport for neutral and Charged particles, University of Michigan, 1998-2001
Geant4 manual in http://geant4.web.cern.ch/
PENELOPE manual in https://www.oecd-nea.org/dbprog/courses/nsc-doc2015-3.pdf