Wisdom of the Groundhogs

In this video, I briefly explain a thought experiment I conducted that attempts to rectify the famed Puxatauny Phil’s abysmal attempt to predict extended winter weather. The experiment uses data gathered from about thirty-eight weather-predicting groundhogs, Naive Bayes Theory, and Laplace Smoothing to create a “Wisdom of the Groundhogs” with the hope of producing a probability of prediction accuracy that will be at least greater than Phil’s 39% accuracy. Through a principled analysis method, I arrived at a 7% increase in predictive power. This number (around 46%) is much closer to breaking even than Phil’s previous attempts alone. Furthermore, when compared to the NOAA’s estimate for human weather forecasting accuracy over extended periods, 46% may not be terrible.

Most of us are aware of the yearly celebration involving Puxatauny Phil — an immortal groundhog who is renowned for his ability to predict the weather. But what many people aren’t aware of is exactly how inaccurate Phil often is. According to the National Oceanic and Atmospheric Administration, Phil boasts an abysmal 39% accuracy rating — that’s worse than flipping a fair coin. In fact, you’d have better odds of predicting the weather if you chose to believe the opposite of what Phil told you. But perhaps it’s not entirely Phil’s fault. My name is Erik and I’m an undergraduate student in statistics here at George Mason. During my senior year here I’ve been studying how we can better use the natural world around us to predict change, by applying statistical principles. To help Phil, we’re going to apply an optimal classifier analysis called Bayes Theory, specifically Naive Bayes Theory. Across the Northern US and Canada, there are at least thirty-eight groundhogs who are supposed to have the ability to forecast the arrival of an early spring. By combining the insight of these furry weather-mammals I hope to arrive at a number at least better than Phil’s 39%. Bayes Theory, attributed to Thomas Bayes, an 18th-century statistician, is a principled method of statistical analysis that allows us to update probabilities given additional information. For example, in this case, we’re attempting to update the probability of whether spring will arrive early (A) given that Phil has not seen his shadow (B). This method becomes even more powerful when you apply it to multiple entities and fortunately, as I’ve said previously, Phil is no longer the only gifted groundhog. However, having multiple entities introduces a new problem to the analysis: Independence. Fortunately, it’s a problem we can address with the Naive approach to Bayes Theory. But what is the Naive approach? We can utilize the Naive Bayesian Classifier, which assumes the independence of data because it is highly unlikely that the groundhogs are conspiring amongst themselves about their predictions beforehand. Another problem arises because some of our groundhogs are relatively new to the predictive scene. To answer this, we can utilize another concept known as Laplace Smoothing. Laplace Smoothing, attributed to Pierre-Simon Laplace, is a technique that controls for the presence of zero-probability outcomes. Laplace postulated this idea in a provoking, thought-experiment that sought to predict the probability the sun would rise tomorrow, given that we have never seen a day where it had not previously risen. This is to say, we can apply his smoothing technique in any case in which we would be dividing by zero, due to either a lack of data or data which is uniquely one-sided. In this case, some groundhogs may only have predicted one way or the other due to relative newness and we can therefore invoke Laplace’s smoothing technique. To compare the groundhogs I must use a slightly more advanced version of Bayes Theory, as shown in the first formula. This version says much the same thing as the basic version but it allows for comparisons between entities — and thus easier aggregation. For ease of understanding, in the second formula, I’ve decided to utilize shorthand. “NS” stands for “No Shadow”. As you can see, in the third formula, with some fairly basic algebra we arrive at about a 7% increase in predictive power when utilizing the aggregate predictions as opposed to Phil’s alone. Of course, the final question is why does any of this matter? How does a result which is close to a coin-flip, seem any better than Phil’s abysmal 39%? NOAA states that a seven-day forecast is correct about 80% of the time but a forecast ten or more days in advance usually only achieves a 50% accuracy rating. Given that we are asking the groundhogs to predict the weather approximately forty-two days in advance, 46% isn’t terrible! Ironically, the Farmer’s Almanac declares that groundhogs (including Phil) are correct about 50% of the time — which appears may have some truth behind it. Similar to other thought experiments, such as the wisdom of the crowd upon which my idea was based, the aggregation of predictive ability or wisdom of the groundhogs, does appear to affect the aptitude of weather prediction in groundhogs. Though I’m not suggesting that everyone should ignore weather forecasts and instead seek out the nearest open field for a furry friend. I remain certain that nature provides key data for more efficiently predicting how the world around us changes and how we as stewards interact with it. I hope that this experiment has inspired some further curiosity and that the next time you see Phil and his shadow, you’ll consider what you’ve watched here. Thank you for your time.