This research is based on a variant of the Multinomial Bayes Theorem. In order to explain the research design, probability theory is described first.
A probability distribution is a visual representation of all the possible values that your random variable could be plus the probabilities for each of those values. For instance, if I flip a coin and hide the result from you, you might half believe it is heads and half believe it’s tails, until I tell you what it is. Same for if I roll a die and hide the result from you, you might believe about one-sixth that it is a one or two or three or four or five or six until I show you the result. Thus, probability distribution can be a believe about something before you measure it. To illustrate this, the frequency of age is plotted against age for all men on the dating platform.
Here we can see that most people that are active on the platform are around 26 to 32 years old.
Probability is way of assigning a value to every event between zero and one, with the requirement that all possible events (and their results) are known. This can be done for the age of a men that is active on the dating platform, since all possible ages are known. To get the likelihood of an event occurring, we can divide the frequency of each age by the total amount of users, which represents the probability (or proportion) of each age category. Thus, this number can be used to calculate the probability that a new man that joins the platform falls into a certain age category. Therefore, the probability of discrete event E occurring is defined as:
P(E) = is the probability of and event occurring
F(x) = a point in the sample space regarding the probability value
So the probability of the entire age space is 1, and the probability of the null event is 0.
For example, if a man joins the platform there is a probability of 7,8% that the man is 28 years old.
Law of large numbers
The Bayes theorem is a formula that tells you how to calculate conditional probabilities to a hypothesis given a piece of evidence. The formula can be used to see how the probability of an event occurring is affected by new information, supposing the new information is true.
Conditional probability is a measure of the probability of an event given that another event has occurred. If an event called A and an event called B take place, then the conditional probability of event. For example, a simple question could be “What is the probability that a person who has an age of 30 liked a woman who was 20 years old?” Conditional probability takes this question a step further by asking “What is the probability that a person who has an age of 30 liked a women who is 20 years old given that he liked a 20 year woman old earlier”.
Event A given event B is written as:
Before I can elaborate on this, follow concepts need to be explained.
Joint probability is the probability of both A and B occurring. This is the same as the probability of A occurring times the probability that B occurs given that A occurred, described as:
Using the same reasoning, is also the probability that B occurs times the probability that A occurs given that B occurs, expressed as:
Which can be combined to:
Where and are the probabilities of event A and B independently of each other.
Bayesian Theorem is a prior (a hypothesis before evidence) that can be updated based on measurements gathered to get a revised set of beliefs.