Johnson Graduate School of Management Prof Examines FiveThirtyEight Election Predictions using @RISK
The midterm Senate race is fast approaching—and so are the speculations on its outcome. The stats-centered news site, FiveThirtyEight, builds interactive forecasts that are updated almost daily. As of this writing, the model predicts that Democrats have a 42.4% chance of retaining the Senate next year.
"They’ve also included a correlation, of a type in their model," says Dr. Lawrence Robinson, Professor of Operations Management at Cornell University’s Johnson Graduate School of Management. "But they do not explicitly use a correlation coefficient—instead, they change the distribution of the candidate’s lead." Robinson explains that FiveThirtyEight introduces correlation through an additional random variable representing what they’ve labelled "national error," which they generate and add to the mean margin of victory of every candidate. "Unfortunately, nowhere in their post do they specify the probability distribution for his new ‘national error’ random variable," Robinson says. "Thus it is not possible to know how correlated the individual races are with one another."
Robinson wanted to devise a way to arrive at these forecasts using his own statistical methods, and to use a correlation that is explicitly defined. Instead of just using FiveThirtyEights’s "Leader’s chance of winning," which was only given to the nearest percent, Robinson started with the mean and (estimated) standard deviation of the margin of victory, and calculated the probability of winning by assuming that the margin of victory on Election Night was normally distributed. "Although Silver says he assumes that the victory margin is leptokurtic [has fat tails] for finding the probability of winning, he never specifies its probability distribution," says Robinson. "I found that the standard assumption that the margin was normally distributed better matched his reported analysis."
Robinson built a Monte Carlo simulation model in Excel using @RISK, treating the outcome of each race as a Bernoulli (0/1, win/lose) random variable. He then introduced a correlation matrix that captured the correlation between every pair of races, and ran 27 different simulations (each one simulating 400,000 elections) for correlations ranging between 0% and 100%. His results closely match that of FiveThirtyEight’s, showing the probability that Democrats will retain control of the Senate as a function of the correlation among races. Robinson points out the benefit:
The advantage of this approach is that
we specify the correlation precisely, and
that we conduct robustness analysis to
see how the results change with the
Dr. Lawrence Robinson - Cornell University
Johnson Graduate School of Management
Professor of Operations Management
» More detail about Robinson’s model
» Download Robinson’s spreadsheets
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Jobshop and Production Floor Scheduling
Excerpted from Evolver Solutions for Business,
by Roy Nersesian, published by Palisade Corp.
A jobshop is characterized by individual jobs taking different amounts of time for each operation. Suppose that a jobshop consists of four operations: sanding, varnishing, etching, and finishing. Each job is unique with regard to the amount of time required for each operation. This example has 6 jobs. Once a job is sanded, the sanding operation can proceed immediately to the next without delay. Once the first job is sanded, it can immediately be varnished, etched and finished without intervening delays. However, there are two conditions that have to be met for the remaining scheduling. For the second job to be
varnished, it must first have been sanded and the first job must have completed being varnished. What is the length of time to do all the jobs in sequential order? What is the sequence of jobs to optimize performance; that is, minimize the length of time to complete all six jobs? Find out by using Evolver and this downloadable example.
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Delimiters and Discrete Distributions
Q: I have a RiskPoisson(3) distribution, and I click Define Distributions, or Browse Results after a simulation. I set the delimiters to 0 and 6, and @RISK shows a probability of 91.7% between them. But Excel's POISSON.DIST(6,3,TRUE) shows a cumulative probability of 96.6%. Which one is right?
This seems strange at first, but there's an explanation. This is nothing special about the Poisson distribution; it applies to RiskBinomial, RiskDiscrete, and all the other discrete distributions.
@RISK and Excel are both right, but they're measuring different things. Excel is reporting the cumulative probability from x=minus infinity to x=6. @RISK reports the cumulative probability from x=0 to x=6. But the Poisson distribution doesn't extend to negative x, so why aren't those two the same?
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The DecisionTools Suite is part of complex analyses published in white papers.
Quantitative Risk Assessment on the Public Health Impact of Pathogenic Vibrio parahaemolyticus in Raw Oyster
Center for Food Safety and Applied Nutrition
Food and Drug Administration, U.S. Department of Health and Human Services
The Center for Food Safety and Applied Nutrition Food and Drug Administration
of the U.S. Department of Health and Human Services analyzed scientific data that was used to model and predict the public health impact of pathogenic Vibrio parahaemolyticus in raw oysters. The assessment focused on comparing the relative risk among different geographic regions, seasons, and harvest practices. The scientific data and the mathematical models developed during the risk assessment, in conjunction with @RISK and Monte Carlo simulation, facilitate a systematic evaluation of strategies to reduce the public health impact of pathogenic Vibrio parahaemolyticus associated with the consumption of raw oysters. Questions that were addressed include:
- What is known about the dose-response relationship between consumption of Vibrio parahaemolyticus and illnesses?
- What is the frequency and extent of pathogenic strains of Vibrio parahaemolyticus in shellfish waters and in oysters?
- What environmental parameters (e.g., water temperature, salinity) can be used to predict the presence of Vibrio parahaemolyticus in oysters?
- How do levels of Vibrio parahaemolyticus in oysters at harvest compare to levels at consumption?
- What is the role of post-harvest handling on the level of Vibrio parahaemolyticus in oysters?
- What reductions in risk can be anticipated with different potential intervention strategies?
Read the full paper here
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