Prerequisites

Participants will be primarily using ModelRisk (version 3.0 or newer) with Microsoft Excel to solve the exercises. It is essential that all participants are reasonably proficient in Excel (see prerequisites). Also, the R statistical language and WinBugs will be used for a few sections. However, participants can also choose to use another Monte Carlo package of their choice (@Risk, CrystalBall, etc). We will provide participants with a CD with the installer files for ModelRisk, R, and WinBugs, but participants should come to the class with all the required software installed. Participants can find trial versions of ModelRisk here http://www.vosesoftware.com/trial.php, the R installer here http://cran.r-project.org/, and WinBugs's installer here http://mathstat.helsinki.fi/openbugs/OpenBUGS.zip. As the trial license of ModelRisk lasts 30 days, participants should install it only a few days before the course.

In addition to ModelRisk, R and WinBugs, participants are required to bring laptops loaded with Microsoft Word, PowerPoint, and Excel, and with a functional CD drive.

For @Risk users, trial copies are available free of charge from Palisade's web-site but it should not be installed too early as trial versions run out after 10 days.

Participants very proficient in the R statistical language can develop the exercises using this platform. The instructor will help them solve their problems, but the solutions to group problems will be shown in Excel and ModelRisk.

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Free risk analysis reference

The ModelRisk help file is a comprehensive risk analysis training reference and is free of cost. This help file provides an in-depth explanation of all of the risk analysis concepts, techniques and methods introduced in this course and greatly complements the course material. The help file is included in the installation file of ModelRisk and remains active even after the demo version expires. It can also be accessed directly from Vose Software's website here

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Teaching philosophy

All of Vose Consulting's courses aim to help the participants understand (rather than 'learn') risk analysis, which can only be achieved through a relaxed, informal and interactive environment, through plenty of examples and hands-on exercises where students apply and adapt what they have learned.

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Course content

Day 1

Introduction to risk analysis

• Background of risk analysis and risk management
• Risk analysis as a team effort
• Dealing with the limits of current knowledge
• Difficulties in modeling biological systems

Introduction to basic statistical descriptors

• Mean, mode, standard deviation, skewness, kurtosis, percentiles

Introduction to probability theory

• The use of distributions: uncertainty, variability and inter-individual variability
• Probability concepts
• Graphical representations of risk events: Venn diagrams, fault trees and event trees
• A look at some basic probability distributions

Introduction to risk modeling

• Monte Carlo simulation, Excel add-ons (@Risk) and more advanced simulation tools (R, S-Plus)
• Calculation vs. simulation
• Typical risk analysis results, their presentation and interpretation
• Practical problems to solve

Day 2

Basic stochastic processes

• Binomial Process
• Binomial, beta, negative binomial and geometric distributions
• Poisson Process
• Poisson, gamma, and exponential distributions
• Practical problems to solve

Day 3

Basic stochastic processes (continued)

• Extra Binomial and Poisson problems
• Hypergeometric process
• Hypergeometric and inverse Hypergeometric distributions
• Practical problems to solve

Good practices in risk modeling

Common mistakes and how to prevent them

Day 4

Analyzing and using data for risk analysis in epidemiology

• Statistical and Epidemiological techniques
• Why we need uncertainty distributions, not confidence intervals in risk analysis
• Creating uncertainty distributions with standard tests
• t-tests, z-tests, Chi-squared tests
• Examples of estimation of population mean and standard deviation
• Quick introduction to alternatives to standard tests - Bayesian and non-parametric methods
• Determining distributions from data
• Assessing validity of data
• Distribution fitting

Day 5

Disease spread (epidemic) simulation modeling

• Introduction to disease spread modeling
• The dynamics of infectious diseases in populations, state transition diagrams, and basic disease parameters
• Difference and differential equations, "agent-based" simulation models
• The simple SIR and SEIR models
• Extensions to the simple models: stochastic, spatially explicit models, multiple species/epidemiological populations
• Hands-on development of a stochastic model using Excel and @Risk

Example risk analyses based on epidemiological data (if time permits)

Wrap up and course evaluation

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Dr. Francisco Zagmutt has an impressive command of the tools used in conducting a quantitative risk analysis which include frequentist and Bayesian probability theories, statistics, mathematics, and programming in Excel, R, WinBugs and ModelRisk, that go well beyond his formal education. He offered a wide array of references with a degree of technical difficulty that reflects his strong interest in the subject matter and his commitment to stay current. In addition to an impressive knowledge base, Francisco is an excellent teacher. The class contained individuals with diverse backgrounds from professional to academic degrees and he brought us all along with him. He was able to answer all questions and provide hands-on exercises that were relevant to conducting a QRA. I highly recommend the class.

Vicki Lancaster, Ph.D.
Mathematical Statistical FDA/CVM