What’s the Chance a Random Problem Has a Solution?
Consider a graph, which is a set of vertices connected with edges. Your task is to assign two colors to the vertices of the graph, but under the constraint that if vertices share an edge, then they must be different colors. Can you solve this problem and satisfy the constraint? Now suppose that the edges of the graph are chosen randomly; for example, by flipping a coin for every two vertices to determine if there is an edge connecting them. What’s the chance that you can still find a coloring which satisfies the constraint?
Bridging the Gap: A Journey Through Generalizability and Transportability
In an increasingly data-driven world, the ability to draw accurate conclusions from research and apply them to a broader context is essential. Enter generalizability and transportability, two critical concepts researchers consider when assessing the applicability of their findings to different populations and settings. In their article “A Review of Generalizability and Transportability,” published in the Annual Review of Statistics and Its Application in 2023, Irina Degtiar and Sherri Rose delve into these critical concepts, providing valuable insights into their nuances and potential applications.
Choosing the Right Forecast
Nobel laureate Niels Bohr is famously quoted as saying, “Prediction is very difficult, especially if it’s about the future.” The science (or perhaps the art) of forecasting is no easy task and lends itself to a large amount of uncertainty. For this reason, practitioners interested in prediction have increasingly migrated to probabilistic forecasting, where an entire distribution is given as the forecast instead of a single number, thus fully quantifying the inherent uncertainty. In such a setting, traditional metrics of assessing and comparing predictive performance, such as mean squared error (MSE), are no longer appropriate. Instead, proper scoring rules are utilized to evaluate and rank forecast methods. A scoring rule is a function that takes a predictive distribution along with an observed value and outputs a real number called the score. Such a rule is said to be proper if the expected score is maximized when the predictive distribution is the same as the distribution from which the observation was drawn.