Statistics is commonly understood as a set of tools used to collect, analyze and interpret data, and make correct decisions. In particular, statistical methods can be very useful in scientific research, finance and banking, industry, marketing, etc. The constant advancements in computing power caused that the simulation methods have recently gained much popularity in modern statistics. Moreover, in many cases, such as for example the high complexity of the phenomenon under study or too small amount of data, simulation methods are the only alternative to the classical statistical inference.

The course covers a wide range of modern statistics, including the classical statistical inference, non-parametric methods as well as the state-of-the-art simulation-based methods. During the course there will be presented issues related to the random numbers generation. The special attention will be given to the most popular stochastic models. Every concept addressed in the course will be illustrated by examples and practical exercises carried out in R statistical system. By participating in course you will learn the basics of methodology for modeling random phenomena and you will gain skills in classical and modern statistical methods.

What will you learn?

  • You will learn basics of statistical inference.
  • You will know how to simulate random variables and how to use them in modeling real world problems.
  • You will familiarize with the most popular stochastic models.
  • You will learn how to build regression models.
  • During the course you will gain practical skills in classical and modern computational statistical methods. We use free R Statistical System R.
  • You will be provided with R-scripts and comprehensive materials that will greatly facilitate further work with your own data.

For whom is this training?

For all who use statistical methods and simulations in their work.

Shortened agenda

  • Introduction to statistics — statistical inference
  • Regression and correlation analysis
  • Nonparametric statistical methods
  • Simulation techniques and stochastic modeling

Full agenda

  1. Introduction to statistics — statistical inference
    • the basis of statistical models — random variables and their distributions
    • point and interval estimation — the objectives and applications
    • overview of estimation methods (least squares method, maximum likelihood method, method of moments)
    • to introduction to statistical hypothesis testing
    • the relationship between hypothesis testing and confidence intervals construction
    • selected parametric and non-parametric tests (tests of significance, goodness of fit tests, tests of independence)
    • statistical hypothesis testing in practice:
      • choosing the correct statistical test
      • interpretation of results
      • assumptions and requirements of statistical tests
      • power analysis of tests
      • sample size determination
    • examples of statistical hypotheses testing for real data from banking and industry
    • selected aspects of the design of experiments
  2. Regression and correlation analysis
    • the relationships between quantitative variables — the basic tools (correlation coefficient, scatterplot)
    • introduction to regression methods — the objectives and applications
    • linear regression — the model structure and assumptions
    • practical aspects related to building regression models
      • fitting the model
      • assessing of model goodness-of-fit (regression diagnostics): statistical significance of parameters and residual analysis
      • interpretation of the constructed model
    • choosing the best model
    • prediction based on fitted model (point and interval prediction)
    • selecting subset of relevant variables
    • additional issues in regression analysis
      • data transformation
      • outliers and influential points
      • collinearity analysis
    • logistic regression model
  3. Nonparametric statistical methods
    • parametric and nonparametric methods in statistical inference
    • why and when use nonparametric methods?
    • selected applications of non-parametric methods
      • estimation of the probability density
      • estimation of the regression function
      • estimation of the intensity function
      • estimation of the trend function
    • selected non-parametric methods
      • kernel smoothing
      • projection-based methods
      • local regression models (loess)
      • smoothing splines
      • resampling methods (jackknife, bootstrap, subsampling)
      • real-world examples of applications of non-parametric statistical methods
  4. Simulation techniques and stochastic modeling
    • comparison of stochastic and deterministic modeling strategy
    • the basis of stochastic models — random variables and their distributions
    • mechanisms of computer generated random numbers
    • methods for simulating random variables from given distribution (continuous or discrete)
      • dedicated algorithms (e.g. for normal or beta distribution)
      • universal methods (e.g. von Neumann’s method, inverse CDF (cumulative distribution function) method)
    • selected stochastic models
      • Markov chains
      • diffusion processes (Brownian motion)
      • point processes (Poisson processes)
      • queuing systems
    • real-world examples of applications of stochastic models

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