Bayesian Statistics

• Probability is a mathematical language for expressing our uncertainty.
• Bayesian statistics rely on conditional probabilities–the probability of an event A given event B
• Conditional probability is the chance of an event happening, given that another event has already occurred (given=certainity)
• The chance of a child displaying aggressive behavior (Event A) given that they are exposed to violent video games (Event B). This is an example of a conditional probability
• Conditional probability: the probability of someone experiencing a phobia (Event A) given that they had a traumatic experience related to the phobia in the past (Event B).
• pipe symbol `|’ means given in conditional reasoning
• Sensitivity refers to a test's ability to correctly detect individuals who have a certain condition
• Specificity, on the other hand, refers to a test's ability to correctly identify individuals who do not have a certain condition
• An increase in false positives, increases sensitivity capturing more cases of etc
• Prevalence: This term refers to the percentage of a population that has a specific health-related condition during a particular time period
• Sensitivity: This refers to how accurately a test identifies true positives, meaning individuals who have the condition the test is checking for
• Specificity: This term is used to describe how accurately a test identifies true negatives, meaning individuals who don't have the condition the test is checking for.
• Prior Probability: This is your initial belief about the probability of an event before new evidence is introduced.
• Likelihood: This refers to how likely the observed data is, assuming a particular hypothesis is true.
• Posterior Probability: This is the updated belief about the probability of an event after considering new evidence
• Key components of Bayesian statistics include?

  prior probability, likelihood, and posterior probabilities
• Bayesian Theorm it can be used to evaluate the strength of evidence for different hypotheses
• P(A|B): Probability of event A given event B has occurred.
• P(A) and P(B): The independent probabilities of events A and B.
• P(B|A): Probability of event B given event A has occurred.
• • A Bayes factor less than 1 indicates that the data is more likely under the bottom hypothesis (in favor of alternative).
  • A Bayes factor more than 1 indicates that the data is more likely under the top hypothesis (in favor of null hypothesis) .
• • BF10 = 3 means hypothesis, this more than 1 (H1), which means we favour the top hypothesis (often the null), and it is 3 times more likely than the bottom hypothesis
• BF10= -2 means that the hypothesis is less than 1, and in favor of the bottom hypothesis often deemed as the alternative
• When the prior distribution widens what happens?

  Posterior distribution would move towards the likelihood distribution

  
• Specificity do not have something
• Sensitivity do have something