Expected Value vs. Mean

• Expected value: a value calculated based on probabilities to predict the future; a prediction of possible future outcomes (inductive—future predictions based on experience/observation/evidence)

• Mean: a value calculated from existing data from a frequentist perspective; a definite value based on data that has already been observed (deductive—judgment based on data that is already known)

Why do twist smc and LLMs use expected values? Aren’t the mean and expected value the same thing? LLMs use expected values because they take a Bayesian perspective, continually updating the prior based on uncertain quantities using prior information.

Is this the difference in perspective between Gaussian and Bayesian approaches?!

Gaussian: analyzing phenomena and drawing conclusions from observed values such as frequencies (normal distribution) Bayesian: predicting the future based on empirical probabilities (probability)