Probability can either be interpreted as a long-run frequency (Frequentist) or a measure of belief and uncertainty (Bayesian)
Bayes’ Rule is a good framework for many things. Update conjectures based on supporting evidence that is likely observed.
The hyperparameters of a model refer to the parameters of the distribution of the priors (from a Bayesian Perspective). The hyperparameters encode our beliefs about the distribution.

Central Limit Theorem

Assumption: We have random variables that are independent and identically distributed each with mean and .
The Central Limit Theorem states that as , then the distribution of the sum approaches the Normal Distribution.
Another way to say this is that the sampling distribution tends towards the normal distribution for a large number of samples even if the original variables are not normally distributed.
The implication is that analysis using normal distributions are usually sufficient since many distributions tend to this in the limit.

Monte Carlo Simulation

Monte Carlo is one approach to approximating a function of a random variable. This is done by approximating the probability distribution of the function by taking many samples and then taking the empirical probability distribution.
More formally, it approximates Where .
By the Central Limit Theorem, the above approximation becomes better with more samples. This can be quantified using the standard error computed as