1. Introduction to Programming

a) Software installation

b) Basic language elements

c) Objects and their manipulation

d) Databases and their manipulation

2. Control Flow and Loops

a) Control flow (if)

b) Loops (for, while, repeat)

3. Implementing Functions and Script Files Coded

4. Using Files and Graphics

a) Importing and exporting files

b) Developing graphics

5. Scientific Computing Topics

a) Application examples in Management, Engineering and Science

1 Supplements of probabilities

– Random variables. Random variable functions

– Discrete and continuous distributions. Exponential family

– Generating functions

– Stochastic convergence and limit theorems

2. Classical Statistical Inference

– Completeness and sufficiency

– Point estimation. Methods of estimation. Properties

– Sample distributions

– Interval estimation

– Construction of hypothesis tests. UMP tests

– Hypothesis tests on parameters

– Goodness of fit tests

– Non-parametric tests

3. Introduction to Bayesian Statistics

– Bayesian Methodology. Classical versus Bayesian Statistics

– A priori (non-informative and conjugate) and a posteriori distribution

– Bayesian inference: point and interval estimation, hypothesis tests

4 Bivariate analysis

– Contingency tables

– Chi-square test

– Measures of association and correlation

1. Preparing data:

– Structure

– Import, export, merge and split

– Cleaning

– Missing values and outliers

– Variables and observations handling and transformation

– Indexes and selection

2. Descriptive Statistics:

– Basics

– Tables of frequencies

– Graphical representation

– Data reduction

3. Data visualisation

– Table of frequencies representation

– Graphical analysis of univariate, bivariate and multivariate and missing values

– Interactive graphs

– Visual simulation in statistics

1. Introduction to marketing research

1.1 Definition and classification of a marketing research

1.2 Examples and stages of a marketing research

1.3 Elaboration of a marketing research

2. Research model

2.1 Primary and secondary data

2.2 Exploratory research

2.3 Conclusive research

3. Sampling techniques

3.1 Probabilistic sampling

3.2 Non-probabilistic sampling

3.3 Sample size and sampling errors

4. Survey by questionnaire

4.1 Survey planning and design

4.2 Types of questions and scaling

4.3 Planning and structure of the questionnaire

4.4 Online questionnaires design tools

5. Conducting a survey

5.1 Questionnaire preparation

5.2 Data collection

5.3 Data organization and processing

5.4 Report preparation and presentation

1. Introduction to Multivariate Analysis

a) Covariance and Correlation Matrices

b) The multivariate Normal density function

c) The multivariate central limit theorem

d) Scatterplot matrix

2. Principal Components Analysis

a) Model

b) Principal components method

c) Maximum likelihood method

d) Rotation factor

e) Goodness of fit

f) Dimensionality reduction in liner regression

g) Score reliability

3. Cluster Analysis

a) Dissimilarity measures

b) Dendrogram

c) Hierarchical methods

d) Non-hierarchical methods

4. Discriminant Analysis and Classification

a) Discriminant variables selection

b) Classification statistic

c) Classification of new data

1. Simulation

– Generation of pseudo-random numbers

– Generation of discrete and continuous random variables

2. Monte Carlo methods in statistical inference

– Estimation of parameters

– Estimation of bias and mean square error of estimators

– Estimation of confidence levels

– Estimation of the level of significance and the power function of hypothesis testing

– Comparison of the performance of different statistical procedures

3. Resampling methods

– Bootstrap and Jackknife

– Bias and mean squared error

– Confidence Intervals

– Hypothesis tests

4. Maximum likelihood estimation and the EM algorithm

– Maximum likelihood method

– The use of latent variables

– EM (expectation-maximization) algorithm

– Examples of applications

5. Markov chain Monte Carlo (MCMC)

– Metropolis-Hastings algorithm

– Gibbs sampling

6. Applications in different contexts

1. Introduction to Stochastic Processes

a. Definitions and generalities

b. Stationary processes

c. Processes of stationary and independent increments

d. Markov Processes

2.  Discrete-time Markov chains

a. Definition and examples

b. Transition probability matrix and Chapman-Kolmogorov equations

c. Classification of states and limiting behavior

3.  Continuous-time Markov chains

a. Definition and examples

b. Transition probabilities and Chapman-Kolmogorov equations

c. Classification of states and limiting behavior

4.  Birth and death processes

a. Definition

b. Transient solution and limit distribution

c. Poisson processes

d. Queueing systems associated with birth and death processes

1. Linear regression

a) Interpretation and estimation

b) Model assumptions analysis

c) Inference on regression parameters

d) Quality and model comparison measures

e) Point and interval prediction

f) The use of dummy variables

2. Generalized Linear Regression

a) Link function logit, probit, log-log and complementar log-log

b) Interpretation and estimation of the models

c) Analysis of model’s assumptions

d) Inference on regression parameters

e) Quality and model comparison measures

f) Cutoff point and the ROC curve

3. Models based on panel data

a) Fixed effects models

b) Random effect models

4. Structural equation modeling

a) Latent variables and indicators

b) Measurement models: reflective versus formative measurement models

c) Specification of the structural model