Question

Expected value approach (Bayes' decision rule), expected payoff (EP)

a) Bayes' decision rule primarily relies on:
i) Posterior probabilities
ii) Conditional probabilities
iii) Marginal probabilities
iv) Joint probabilities

Answer 1

Bayes' decision rule relies on posterior probabilities, which are calculated using Bayes' theorem, combining prior probabilities and conditionals. Expected value calculations involve predicting the long-term average outcome using the probability distribution function of a discrete random variable.

Step-by-step explanation:

Bayes' decision rule primarily relies on posterior probabilities, which involve updating the probability of a hypothesis, or a model parameter in this case, given the data. Bayesian statistics is fundamentally concerned with calculation of the posterior probability of a parameter θ (theta) given the data x, using Bayes' theorem, which combines the prior probability of θ and the likelihood of the data x given θ. This posterior probability is represented by P(θ|x), which is proportional to the product of the likelihood P(x|θ) and the prior P(θ).

The calculation of the expected value or mean (μ) of a discrete random variable involves using a probability distribution function to predict the long-term average of outcomes if an experiment is repeated many times. In the context of making decisions under uncertainty, the expected payoff (EP) is calculated by weighing each possible outcome by its probability and summing these products to determine what one would expect on average over many trials.