A priori probabilities and empirical probabilities are two different types of probabilities used in probability theory and quantitative trading/investment.
A priori probability is a probability that is determined or calculated based on knowledge, reasoning or logic, rather than being based on observation or data. A priori probabilities are often used in theoretical probability, and represent the likelihood or chance of an event occurring based on logical or deductive reasoning.
For example, if we toss a fair six-sided die, the probability of rolling a 5 is 1/6. This is an a priori probability because we can logically determine the probability based on the knowledge that there are six possible outcomes, each equally likely to occur.
Empirical probability, on the other hand, is a probability that is based on observation or data. Empirical probabilities are often used in experimental or empirical studies, such as in finance, economics, and other sciences that require the use of statistical analysis.
For example, if we conduct an experiment by tossing a coin 100 times, and the coin lands on heads 60 times, we can say that the empirical probability of getting heads is 0.6 or 60%. This is an empirical probability because we are calculating the probability based on actual observed data.
In summary, a priori probabilities are calculated based on logical and theoretical reasoning, while empirical probabilities are calculated based on actual observed data. Both types of probabilities are useful in probability theory and in quantitative trading/investment strategies, as they can provide insight into the likelihood of events occurring and help to inform decision-making processes.