How are ##P(x,\theta|D)## and ##P(x|\theta,D)## defined? I took a lot of classes in probability and mathematical statistics, but it has been many years ago. I don't recall seeing this notation.Avatrin said:Hi
In Dudas Pattern Classification, he Writes that [itex] P(x,\theta|D) [/itex] can always be written as [itex] P(x|\theta,D)P(\theta|D) [/itex]. However, I cannot find any justification for this. So, why are these Equal?
Mark44 said:How are ##P(x,\theta|D)## and ##P(x|\theta,D)## defined? I took a lot of classes in probability and mathematical statistics, but it has been many years ago. I don't recall seeing this notation.
Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is denoted as P(A|B), where A is the event of interest and B is the event that has already occurred.
Equality in conditional probability is a measure of fairness in decision making. It ensures that the probability of an outcome is the same regardless of different characteristics or conditions that may be present.
One example of equality in conditional probability is in the hiring process. If the probability of a male candidate being hired is the same as the probability of a female candidate being hired, regardless of their gender, then there is equality in conditional probability.
Equality in conditional probability is calculated by comparing the conditional probabilities of different groups. If the conditional probabilities are equal, then there is equality in conditional probability.
Equality in conditional probability is important in scientific research because it ensures that the results are not biased or affected by certain characteristics or conditions. It allows for fair and unbiased conclusions to be drawn from the data.