Inference, Prediction, and Forecast

Welcome back to our series of introductions to causal inference. In this article, we will explore the differences and connections between inference, prediction, and forecast. These are three important concepts in causal inference, but they are often confused or misunderstood. Let's try to clarify them with some examples and humor.

What is inference?

Inference is the process of drawing conclusions from data. For example, if you want to know whether smoking causes lung cancer, you need to do inference. You need to collect data on smoking habits and lung cancer rates, and then use statistical methods to estimate the causal effect of smoking on lung cancer. Inference is about answering questions like "what if?" or "why?".

One way to think about inference is that it is using X to find dY/dX, that is, to find the slope of X and Y. The slope tells you how much Y changes when X changes by one unit. For example, if X is smoking and Y is lung cancer, the slope tells you how much the lung cancer rate changes when the smoking rate changes by one percentage point. The slope is also called the causal effect or the treatment effect.

Another way to think about inference is that it is finding dY/dX. That is, you have observed some values of X and Y, and you want to estimate the slope based on those observations. For example, if you have data on smoking rates and lung cancer rates for different countries, you can use regression analysis to estimate the slope based on those data points.

What is prediction?

Prediction is the process of making guesses about future or unknown outcomes based on data. For example, if you want to know whether it will rain tomorrow, you need to do prediction. You need to collect data on weather patterns and historical rainfall, and then use machine learning methods to predict the probability of rain tomorrow. Prediction is about answering questions like "what will?" or "how much?".

One way to think about prediction is that it is using X to predict Y. That is, you have some information about X, and you want to use that information to guess the value of Y. For example, if X is weather patterns and Y is rainfall, you can use a neural network to predict the amount of rainfall based on the weather patterns.

Another way to think about prediction is that it is finding Y given X. That is, you have observed some values of X, and you want to guess the values of Y based on those observations. For example, if you have data on weather patterns for today, you can use a decision tree to predict the rainfall for tomorrow based on those data points.

What is forecast?

Forecast is a special type of prediction that involves time series data. Time series data are data that are collected over time and have temporal dependencies. For example, stock prices, GDP growth, and temperature are time series data. Forecasting is the process of making guesses about future or unknown outcomes based on time series data. For example, if you want to know what the stock price will be next week, you need to do forecasting. You need to collect data on stock prices over time, and then use time series analysis methods to forecast the stock price next week. Forecasting is about answering questions like "what will?" or "how much?" for time series data.

One way to think about forecasting is that it is using X(t) to predict Y(t+1). That is, you have some information about X at time t, and you want to use that information to guess the value of Y at time t+1. For example, if X(t) is stock price at time t and Y(t+1) is stock price at time t+1, you can use an autoregressive model to predict the stock price next week based on the stock price this week.

Another way to think about forecasting is that it is finding Y(t+1) given X(t). That is, you have observed some values of X up to time t, and you want to guess the values of Y at time t+1 based on those observations. For example, if you have data on stock prices for the past year, you can use a moving average model to forecast the stock price next week based on those data points.

Summary

In this article, we have learned the differences and connections between inference, prediction, and forecast. We have seen that inference is about finding dY/dX given X and Y; prediction is about finding Y given X; and forecast is about finding Y(t+1) given X(t). We have also seen some examples and methods for each concept.

We hope you enjoyed this article and learned something new.