Check the quality of your data
See also: Fitting distributions to data, Fitting in ModelRisk, Analyzing and using data introduction
The data you use to quantify parameters in your model may come from a variety of sources: scientific experiments; surveys; computer databases; literature searches; even computer simulations. Before committing to using a data set, you should convince yourself of the quality of the data. We offer the check list below to help you:
Is the past relevant?
If the data you are using come from historic experience, you implicitly assume that the world in which the data were observed are the same as now. Are there any tests that you can perform to see whether such an assumption is correct? If you know that things have changed, perhaps you could estimate some correction factor. For example, maybe you are running a railway network and are looking at historic delay events (when trains are held up). If there is a strong increase in the number of services you will be offering next year, or if you have some plan to work on a main line for a significant period, historic rates would need to be modified. Sometimes there is a proportional relationship that you could use, but often it is non-linear in which case you may find that historic data help you estimate the relationship.
Are the data a representative and random sample?
'Representative' and 'random' both need to be thought about. Samples can be representative, but also deliberately non-random. For example, if your country has 10 departments, you might deliberately take a survey of 100 people in each department, irrespective of its size. Samples can also be random but not representative: for example a random survey within one department may well not be representative of the whole population.
Are the data relevant to the current problem?
A problem we often come across is that people have worked so hard to collect a set of data that they are quite determined to use it. You need to be objective about what model can be constructed to inform decision-makers, and that may not use the hard-won data. In some situations, there can be a lot of pressure to use certain types of data to validate, for example, the existence of a research program.
Is parameter independent of others in the model?
If you are using data to estimate some model parameter, you will need to ask whether that parameter is independent of others in your model, and whether it would be possible to test that independence by analyzing, or collecting further, data.
What quality checks can you do?
It is such a big question, and the answers should be fairly apparent if you pose the question. Can you think of ways in which the data can be inaccurate? Rounding errors, and biases towards numbers like 1 to 10, 20, 30, etc. rather than 17 can be important.
Are there incentives to the correct or incorrect reporting of data?
In our experience, this is the most important question because it is quite pervasive and the most difficult to recognise. We offer some example from our experience - it might help you develop the required cynicism:
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National statistics of oil imports that showed a 24000 ton import in one cargo of an oil used in electronics, because the ship's captain had some 120 different oil categories to chose from when making his customs declaration;
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Companies (and researchers) that submitted to a regulator (and for publication) only data from experiments that supported their claim, and not those that did not;
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A company that claimed difficulty in finding/collating last year's (really bad) sales data for its operations until the purchaser was too committed to back out;
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A fellow risk analyst who quoted parts of papers (even parts of sentences) that support his client's position, and produce bogus but highly complicated models, then presented the results of those models as if they were fact rather than the result of (biased) conjecture;
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Not our own experience: employees in a nuclear fuels reprocessing company copy/pasted columns of measurements rather than go through the tedious practice of measuring each reprocessed batch;
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A diamond mining company that got low paid workers to go deep into the mine shaft and bring back rock samples, to help better correlate the geology with models. The workers broke off rock from near the entrance rather than bother making the long trip.
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Students doing surveys being paid for each completed form. They get friends round, have some beers, and fill out a few dozen each. Much better (for them) than being in the rain, and they earn more money.
Systematic and non-systematic errors
The collected data will at times have measurement errors that add another level of uncertainty. In most scientific data collection, the random error is well understood and can be quantified, usually by simply repeating the same measurement and reviewing the distribution of results. Such random errors are described as non-systematic. Systematic errors, on the other hand, mean that the values of a measurement deviate from the true value in a systematic fashion, consistently either over- or under-estimating the true value. This type of error is often very difficult to identify and quantify. You may be able to estimate the degree of suspected systematic measurement error by comparing with measurements using another technique that is known (or believed) to have little or no systematic error.
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- Risk management
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- Approximating one distribution with another
- Approximations to the Inverse Hypergeometric Distribution
- Normal approximation to the Gamma Distribution
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- Stirlings formula for factorials
- Normal approximation to the Beta Distribution
- Approximation of one distribution with another
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- Normal_approximation_to_the_Binomial_distribution
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- Correlation modeling in risk analysis
- Common mistakes when adapting spreadsheet models for risk analysis
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- SIDs
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- Sum of a random number of random variables
- Moments of an aggregate distribution
- Aggregate modeling in ModelRisk
- Aggregate modeling - Fast Fourier Transform (FFT) method
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- Simulation for six sigma
- ModelRisk's Six Sigma functions
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- Modeling expert opinion
- Modeling expert opinion introduction
- Sources of error in subjective estimation
- Disaggregation
- Distributions used in modeling expert opinion
- A subjective estimate of a discrete quantity
- Incorporating differences in expert opinions
- Modeling opinion of a variable that covers several orders of magnitude
- Maximum entropy
- Probability theory and statistics
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- Poisson process
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- The hypergeometric process
- Number in a sample with a particular characteristic in a hypergeometric process
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- Estimate of population and sub-population sizes in a hypergeometric process
- The binomial process
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- Estimating model parameters from data
- The basics
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- The definition of probability
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- Fitting probability models to data
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- Fitting correlation structures to data
- Fitting in ModelRisk
- Fitting probability distributions to data
- Fitting distributions to data
- Method of Moments (MoM)
- Check the quality of your data
- Kolmogorov-Smirnoff (K-S) Statistic
- Anderson-Darling (A-D) Statistic
- Goodness of fit statistics
- The Chi-Squared Goodness-of-Fit Statistic
- Determining the joint uncertainty distribution for parameters of a distribution
- Using Method of Moments with the Bootstrap
- Maximum Likelihood Estimates (MLEs)
- Fitting a distribution to truncated censored or binned data
- Critical Values and Confidence Intervals for Goodness-of-Fit Statistics
- Matching the properties of the variable and distribution
- Transforming discrete data before performing a parametric distribution fit
- Does a parametric distribution exist that is well known to fit this type of variable?
- Censored data
- Fitting a continuous non-parametric second-order distribution to data
- Goodness of Fit Plots
- Fitting a second order Normal distribution to data
- Using Goodness-of Fit Statistics to optimize Distribution Fitting
- Information criteria - SIC HQIC and AIC
- Fitting a second order parametric distribution to observed data
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- Does the random variable follow a stochastic process with a well-known model?
- Fitting a distribution for a discrete variable
- Fitting a discrete non-parametric second-order distribution to data
- Fitting a continuous non-parametric first-order distribution to data
- Fitting a first order parametric distribution to observed data
- Fitting a discrete non-parametric first-order distribution to data
- Fitting distributions to data
- Technical subjects
- Comparison of Classical and Bayesian methods
- Comparison of classic and Bayesian estimate of Normal distribution parameters
- Comparison of classic and Bayesian estimate of intensity lambda in a Poisson process
- Comparison of classic and Bayesian estimate of probability p in a binomial process
- Which technique should you use?
- Comparison of classic and Bayesian estimate of mean "time" beta in a Poisson process
- Classical statistics
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- Bootstrap
- The Bootstrap
- Linear regression parametric Bootstrap
- The Jackknife
- Multiple variables Bootstrap Example 2: Difference between two population means
- Linear regression non-parametric Bootstrap
- The parametric Bootstrap
- Bootstrap estimate of prevalence
- Estimating parameters for multiple variables
- Example: Parametric Bootstrap estimate of the mean of a Normal distribution with known standard deviation
- The non-parametric Bootstrap
- Example: Parametric Bootstrap estimate of mean number of calls per hour at a telephone exchange
- The Bootstrap likelihood function for Bayesian inference
- Multiple variables Bootstrap Example 1: Estimate of regression parameters
- Bayesian inference
- Uninformed priors
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- Prior distributions
- Bayesian analysis with threshold data
- Bayesian analysis example: gender of a random sample of people
- Informed prior
- Simulating a Bayesian inference calculation
- Hyperparameters
- Hyperparameter example: Micro-fractures on turbine blades
- Constructing a Bayesian inference posterior distribution in Excel
- Bayesian analysis example: Tigers in the jungle
- Markov chain Monte Carlo (MCMC) simulation
- Introduction to Bayesian inference concepts
- Bayesian estimate of the mean of a Normal distribution with known standard deviation
- Bayesian estimate of the mean of a Normal distribution with unknown standard deviation
- Determining prior distributions for correlated parameters
- Improper priors
- The Jacobian transformation
- Subjective prior based on data
- Taylor series approximation to a Bayesian posterior distribution
- Bayesian analysis example: The Monty Hall problem
- Determining prior distributions for uncorrelated parameters
- Subjective priors
- Normal approximation to the Beta posterior distribution
- Bayesian analysis example: identifying a weighted coin
- Bayesian estimate of the standard deviation of a Normal distribution with known mean
- Likelihood functions
- Bayesian estimate of the standard deviation of a Normal distribution with unknown mean
- Determining a prior distribution for a single parameter estimate
- Simulating from a constructed posterior distribution
- Bootstrap
- Comparison of Classical and Bayesian methods
- Analyzing and using data introduction
- Data Object
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- Bayesian model averaging
- Miscellaneous
- Excel and ModelRisk model design and validation techniques
- Using range names for model clarity
- Color coding models for clarity
- Compare with known answers
- Checking units propagate correctly
- Stressing parameter values
- Model Validation and behavior introduction
- Informal auditing
- Analyzing outputs
- View random scenarios on screen and check for credibility
- Split up complex formulas (megaformulas)
- Building models that are efficient
- Comparing predictions against reality
- Numerical integration
- Comparing results of alternative models
- Building models that are easy to check and modify
- Model errors
- Model design introduction
- About array functions in Excel
- Excel and ModelRisk model design and validation techniques
- Monte Carlo simulation
- RISK ANALYSIS SOFTWARE
- Risk analysis software from Vose Software
- ModelRisk - risk modeling in Excel
- ModelRisk functions explained
- VoseCopulaOptimalFit and related functions
- VoseTimeOptimalFit and related functions
- VoseOptimalFit and related functions
- VoseXBounds
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- VoseSkewness
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- VoseKurtosis
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- VoseTimeARCH
- VoseTimeMA2
- VoseTimeGARCH
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- VoseTimeWageInflation
- VoseTimeLongTermInterestRate
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- VoseTimeShareYields
- VoseTimeYule
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- VoseDominance
- VoseLargest
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- VoseShift
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- VosePrincipleEsscher
- VoseAggregateMultiFFT
- VosePrincipleEV
- VoseCopulaMultiNormal
- VoseRunoff
- VosePrincipleRA
- VoseSumProduct
- VosePrincipleStdev
- VosePoissonLambda
- VoseBinomialP
- VosePBounds
- VoseAIC
- VoseHQIC
- VoseSIC
- VoseOgive1
- VoseFrequency
- VoseOgive2
- VoseNBootStdev
- VoseNBoot
- VoseSimulate
- VoseNBootPaired
- VoseAggregateMC
- VoseMean
- VoseStDev
- VoseAggregateMultiMoments
- VoseDeduct
- VoseExpression
- VoseLargestSet
- VoseKthSmallest
- VoseSmallestSet
- VoseKthLargest
- VoseNBootCofV
- VoseNBootPercentile
- VoseExtremeRange
- VoseNBootKurt
- VoseCopulaMultiClayton
- VoseNBootMean
- VoseTangentPortfolio
- VoseNBootVariance
- VoseNBootSkewness
- VoseIntegrate
- VoseInterpolate
- VoseCopulaMultiGumbel
- VoseCopulaMultiT
- VoseAggregateMultiMC
- VoseCopulaMultiFrank
- VoseTimeMultiMA1
- VoseTimeMultiMA2
- VoseTimeMultiGBM
- VoseTimeMultBEKK
- VoseAggregateDePril
- VoseTimeMultiAR1
- VoseTimeWilkie
- VoseTimeDividends
- VoseTimeMultiAR2
- VoseRuinFlag
- VoseRuinTime
- VoseDepletionShortfall
- VoseDepletion
- VoseDepletionFlag
- VoseDepletionTime
- VosejProduct
- VoseCholesky
- VoseTimeSimulate
- VoseNBootSeries
- VosejkProduct
- VoseRuinSeverity
- VoseRuin
- VosejkSum
- VoseTimeDividendsA
- VoseRuinNPV
- VoseTruncData
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- VoseIdentity
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- VoseSortA
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- VoseMeanExcessP
- VoseProb10
- VoseSpearmanU
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- VoseRuinMaxSeverity
- VoseMeanExcessX
- VoseRawMoment3
- VosejSum
- VoseRawMoment4
- VoseNBootMoments
- VoseVariance
- VoseTimeShortTermInterestRateA
- VoseTimeLongTermInterestRateA
- VoseProb
- VoseDescription
- VoseCofV
- VoseAggregateProduct
- VoseEigenVectors
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- VoseRawMoment1
- VosejSumInf
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- VoseShuffle
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- VoseTimeEmpiricalFit
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- VoseOptDecisionDiscrete
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- VoseMin
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- VoseSimCVARx
- VoseSimCorrelation
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- VoseOptConstraintString
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- VoseOptCVARp
- VoseOptPercentile
- VoseSimValue
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- VoseAggregateDiscrete
- VoseTimeMultiGARCH
- VoseTimeGBMVR
- VoseTimeGBMAJ
- VoseTimeGBMAJVR
- VoseSID
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- More on Conversion
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- Expert
- ModelRisk introduction
- Building and running a simple example model
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- List of all ModelRisk functions
- Custom applications and macros
- ModelRisk functions explained
- Tamara - project risk analysis
- Introduction to Tamara project risk analysis software
- Launching Tamara
- Importing a schedule
- Assigning uncertainty to the amount of work in the project
- Assigning uncertainty to productivity levels in the project
- Adding risk events to the project schedule
- Adding cost uncertainty to the project schedule
- Saving the Tamara model
- Running a Monte Carlo simulation in Tamara
- Reviewing the simulation results in Tamara
- Using Tamara results for cost and financial risk analysis
- Creating, updating and distributing a Tamara report
- Tips for creating a schedule model suitable for Monte Carlo simulation
- Random number generator and sampling algorithms used in Tamara
- Probability distributions used in Tamara
- Correlation with project schedule risk analysis
- Pelican - enterprise risk management