# Statisticals Methods and Simulation

**Year**

1

**Academic year**

2022-2023

**Code**

02037678

**Subject Area**

Física Médica

**Language of Instruction**

Portuguese

**Other Languages of Instruction**

English

**Mode of Delivery**

Face-to-face

**Duration**

SEMESTRIAL

**ECTS Credits**

6.0

**Type**

Compulsory

**Level**

2nd Cycle Studies - Mestrado

## Recommended Prerequisites

Not applicable.

## Teaching Methods

Lecturing, demonstrating, discussion and practical problem resolution.

## Learning Outcomes

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.

## Work Placement(s)

No## Syllabus

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

## Head Lecturer(s)

Alexandre Miguel Ferreira Lindote

## Assessment Methods

Assessment

*Resolution Problems: 25.0%*

*Laboratory work or Field work: 25.0%*

*Exam: 50.0%*

## Bibliography

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

MCNP manual.