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Are probability and uncertainty different?
Can you explain what 'probability' really means? Can you have uncertainty about a probability? Can you have uncertainty about your uncertainty? The language of risk can get very confusing. In this paper we explain the different concepts that are given names like probability and uncertainty, and when it might be useful to distinguish between them.
The statistics of penis length
A paper published recently in a peer-reviewed scientific journal has captured the attention of the press this week, largely because of the subject matter. The paper aims to help doctors address the concerns of patients with "small penis syndrome". Unfortunately, like so many scientific papers, they got the very basic statistical analysis wrong, the press have quoted their statistical results, and nobody seems to have spotted the mistakes. It's a good opportunity to show you how scientists can mess up the stats, and have a bit of fun at the same time.
How to play the lottery
We're not the first to offer advice on how to win the lottery. YouTube videos display a wide range of methods: some are very entertaining too, inviting you to activate your dormant superhuman powers, etc. They have one thing in common - they are complete nonsense. In this white paper, we explain a tactic that will get you the most from your lottery ticket.
Correlation at the White House
In August 2014, Omar Gonzalez, a US war veteran who had been wounded in Iraq and psychologically affected by his experience, managed to enter the White House with a knife evading all security. In this white paper, we look at how all the security measures could have failed at the same time.
Solution for a solid risk management
We have our accounts prepared by a qualified accountant, we use a lawyer to write a contract, and we go to a doctor for medical advice. So if your business or government agency needed to make a very important, risk-based decision would you make sure that the risk assessment was done by an experienced, trained risk analyst? Or an even bigger question - if you are have a corporate risk management process in place, is it designed and maintained by a really good risk analyst? The answer, unfortunately, is very probably 'no'. So businesses make do with what they have, which frankly is often not very much at all. We can do much better. In this whitepaper we look at the problem and give a few solutions.
Do your projects meet their budgets?
Projects cost overruns can dramatically affect a company's performance and jeopardise strategic goals. Yet, in our experience, company executives are rarely provided with actionable information that give them an overview of the performance of projects in meeting their budgets across the business. This article outlines two very simple analyses that can fill that gap.
The Perplexing Math of Uncertainty
Add, subtract, multiply, divide - we have learned how to use them with numbers at school by the age of ten at the latest, and we take it for granted that we have mastered them. It is hard to imagine a risk analysis model in any field that does not include some of these four operations. Yet these basic operations very often do not work in the same way when those numbers are uncertain. Very worryingly, nearly every person we encounter who is involved in risk modeling is to some degree unaware or unclear about the correct ways of manipulating uncertain variables in a model, perhaps because we don't give a second thought to calculations using + - * /. In this white paper we'll have a closer look at calculation with probability distributions.
Fitting distributions to data
A common problem in risk analysis is fitting a probability distribution to a set of observations for a variable. One does this to be able to make forecasts about the future. The most common situation is to fit a distribution to a single variable (like the lifetime of a mechanical or electrical component), but problems also sometimes require the fitting of a multivariate distribution: for example, if one wishes to predict the weight and height of a random person, or the simultaneous change in price of two stocks. There are a number of software tools on the market that will fit distributions to a data set, and most risk analysis tools incorporate a component that will do this. Unfortunately, the methods they use to measure the goodness of fit are wrong and very limited in the types of data that they can use. This paper explains why, and describes a method that is both correct and sufficiently flexible to handle any type of data set.
Ten Steps To Incorporating Risk Analysis
There is universal agreement that having effective risk management practices is an essential component of good business planning. Respected risk management guidelines (ISO, COCO, NASA, etc) all state that Quantitative Risk Analysis should be an integral part of a high quality risk management process. The problem for many senior management teams is how to achieve this in practice, or even what quantitative risk analysis actually entails. David Vose, our founder, has written a white paper to help answer these questions. It describes in some detail a set of 10 steps that, based on 25 years of experience as a risk analyst, provides a very practical, structured road map to help you establish quantitative risk analysis within your organization.
No need for Latin Hypercube Sampling
Most risk analysis simulation software products offer Latin Hypercube Sampling (LHS). It is a method for ensuring that each probability distribution in your model is evenly sampled. The technique dates back to 1980. It was, at the time, an appealing technique because it allowed one to obtain a stable output with a much smaller number of samples than simple Monte Carlo simulation, making simulation more practical with the computing tools available at the time. However, LHS does not deserve a place in modern simulation software. In this paper we explain why.
Project schedule risk analysis
We constantly hear in the news about high profile projects being delayed. With so much at stake, you might wonder why the delivery time of mission-critical projects is so frequently under-estimated. Often it is because no schedule risk analysis model had been built, or the model was built too late to be useful. Sometimes the risk analysis model was based on poor estimates, sometimes it just got ignored because the results were inconvenient. Almost without exception, a schedule risk analysis model will demonstrate that a delivery date based on "most likely" estimates of duration is extremely unlikely to be achieved. The rest of this short paper explains why and gives some pointers to better schedule risk modeling.
Compendium of probability distributions
The precision of a risk analysis relies very heavily on the appropriate use of probability distributions to accurately represent the uncertainty and variability of the problem. In our experience, inappropriate use of probability distributions has proved to be a very common failure of risk analysis models. This compendium of over 100 distributions provides a complete summary of the distributions used in risk analysis, an explanation of where and why they are used, and any theory behind them.