How do you choose between confidence interval and prediction interval for forecasting?

Following probabilities and statistics in forecasting is one of the most difficult steps to actually become an actuarial scientist for your own decisions. In statistics confidence interval gives you a range of values within, which is a mean and prediction interval is used for predicting an individual number. In either of the cases you have to choose the best version of your educated guess in terms of whatever aligns with your sustainability more. Forecasting is one of the best mathematical tool humanity has ever come up with, but its also very precision centric to how you deal with your numbers and which ones make more sense.

El intervalo de confianza es un rango de valores en el que se espera que se encuentre un parámetro de interés, como la media o la proporción, con cierto nivel de confianza. Por ejemplo, un intervalo de confianza del 95% para la media de una población indica que si se tomaran 100 muestras, se espera que el verdadero valor de la media esté dentro de este intervalo en el 95% de las ocasiones. El intervalo de confianza proporciona una medida de la incertidumbre alrededor de una estimación y es útil para evaluar la precisión de los resultados y tomar decisiones informadas.

Choosing between a confidence interval and a prediction interval depends on your specific situation. A confidence interval highlights the uncertainty around the estimate of a population parameter like the mean sales of a product in a month. It's computed using a sample of past sales data and tells you that if you keep on repeating the sampling, the true mean sales will be within that interval 95% of the time. It's greatly affected by your sample size, data variability, and the chosen confidence level. So, in simple words, confidence intervals are more about estimates but not about future predictions.??

It provides a range of values within which the true population parameter is expected to lie with a certain level of confidence. It is used for testing hypotheses and comparing models. A confidence interval is narrower than a prediction interval because it accounts for sampling error but not prediction error. It is useful for understanding the uncertainty in estimating the population mean

The confidence interval is a range of values in which a parameter of interest, such as the mean or proportion, is expected to lie with a certain level of confidence. For example, a 95% confidence interval for the mean of a population indicates that if 100 samples were taken, the true value of the mean is expected to be within this interval in 95% of the occasions. The confidence interval provides a measure of uncertainty around an estimation and is useful for evaluating the accuracy of results and making informed decisions.

Prediction intervals are extremely valuable in quantifying uncertainty while forecasting. The generation of the intervals is different depending on the techniques used. Some of the 'traditional methods' are Monte Carlo Dropout, Quantile Regression, and Mean-Variance Estimation. However, there are new methods, such as 'conformal prediction', gaining popularity because of their robust performance.

a confidence interval is used to estimate the precision of the mean, while a prediction interval is used to estimate the range of individual values, considering both sampling and prediction errors

Key considerations: Focus: Are you interested in the general range of future values (population parameter) or a specific prediction for a single value? Sample size: Larger samples make prediction intervals more reliable. Outliers: If outliers are expected, prediction intervals offer a more robust estimate. Uncertainty tolerance: Wider prediction intervals reflect higher uncertainty, but you're more likely to capture the true value. General guide: Confidence interval: For understanding potential variation in future values, especially with large samples or focus on population parameters. Prediction interval: For individual values, especially when accounting for outliers or dealing with smaller samples and higher uncertainty is acceptable.

Prediction intervals provide a means for quantifying the uncertainty of a single future observation and are best suited for quantifying the uncertainty associated with a predicted response in linear regression. They are useful for making decisions and communicating risks, as they reflect the uncertainty of individual predictions, not just the estimation of the mea

When using forecasts, almost always you care about prediction intervals. Rarely do confidence intervals matter. If you want to determine buffers, like safety stock, decoupling points, safety lead times, etc, then prediction intervals are what matters. These need to buffer for the possible demand and supply variation. Confidence intervals are more important when questioning the validity of the underlying assumptions of the forecast. The data scientist cares about confidence intervals; the planner cares about prediction intervals.

Para elegir entre el intervalo de confianza y el intervalo de predicción en la previsión de la demanda, es importante entender las diferencias entre ambos, considerar el tipo de previsión, el nivel de confianza y la interpretación de los resultados. Es esencial identificar el tipo de previsión. Si la previsión se basa en una regresión lineal o un modelo de tiempo discretos, es más común utilizar el intervalo de confianza basado en la distribución t de Student. Si la previsión se basa en una regresión no lineal o un modelo de tiempo continuo, es más común utilizar el intervalo de confianza basado en la distribución normal.

When interpreting prediction intervals, it's important to consider the level of confidence associated with the interval. For example, a 95% prediction interval implies that if the estimation process were repeated many times, 95% of the calculated prediction intervals would contain the true value. This provides a measure of the reliability of the prediction. Additionally, understanding the width of the prediction interval is crucial. A wider prediction interval indicates greater uncertainty in the prediction, while a narrower interval suggests higher confidence in the forecast.