Lecture 4 Flashcards
What is the base rate neglect?
People tend to focus on the evidence provided by the test (specificity and sensitivity) and downplay the precense of prevelance
What is sensitivity?
Sensitivity is a quantification of how well a test identifies people that have the disease and are tested positive
What is specificity?
A quantification of how well the test identifies people that do NOT have the disease and are tested negative
What is a true positive?
It is the proportion of people that are sick and are identified as such by the test
What is a false positive (or false alarm)?
Proportion of people that are NOT sick but are identified as sick by the test
What is a true negative?
Proportion of people that are NOT sick and are identified as such by the test
What is a false negative?
Proportion of people that are sick but are not identified as sick by the test
What is bayesian inference?
the outcome of a learning process that is governed by relative predictive success
What is the generative model?
State of the world > (predictions) > data
What does bayesian wish to do with the generative model? Give an example in the context of sensitiviy, etc.
Invert is so data can predict the state of the world
Instead of “given the disease, what is the probability of a positive test result”»_space; “given the test is positive, what is the probability that I have the disease”
What is positive predictive value (ppv)?
Quantification of how well the positive results in a test are actually predictive of disease
What is negative predictive value (npv)?
Quantification of how well the negative results in a test are actually predictive of health
What happens with the ppv when diseases are very rare?
It decreases drastically because the disease population is incredibly small, so the false positive population has a large effect
What does transposing the conditional mean? give example
An error type where a condition P(a!b) is very different when turned around P(b!a)
P(shark attack!blood loss) does not equate P(blood loss!shark attack)
What is baye’s rule (words)?
Current knowledge of world = past knowledge about world x predictive updating factor
What are the two key ideas of baye’s rule?
- Hypothesis that predicted the new data well will see a boost in plausibility and hypothesis that predicted it badly will see a decrease in plausibility
- extraordinary claims require extraordinary evidence aka extreme claims need more data to counteract prior beliefs
Which two factors give can make a test provide strong evidence, why may this sometimes still not be enough?
Sensitivity and specificity > still may not be enough to overturn effect of prevalence
Baye’s rule (true formula and in context of disease)?
p(θ) x p(data!θ)/p(data) = p(θ!data)
p(D)/p(H) x p(t!D)/p(t!H) = p(D!t)/p(H!t)
Theory aside, it is unlikely to know the exact numbers of specificity, etc. how is this “solved”?
With a credible interval, in which (typically) there is a 95% chance that the true number is between point a and b
What is the difference between credible and confidence interval?
The confidence interval is the interval which will contain the true value on 95% of occasions if a study were repeated many times, however the credible interval means there is a 95% chance that the true number is between point a and b
Calculation: prevalence =.1, sensitivity = .3 and specificity = .99
What is the ppv?
answer is .77 (circa), look at notes for calculation
If the “marker” (signal detection theory - SDT) increases, what does this mean?
A higher probability of you having the disease
What is the treshold? What does it indicate? SDT
Basically the value you decide to go off of for the marker, it indicates the trade-off between true positives and false positives
What is the receiver-operating characteristic (ROC)?
The relationship btwn hit rates (tp) and false alarms (positives)
What is the exact relationship between true positives and false positives in the context of moving the treshold?
When true positive rate increases (sensitivity), so do the false positives, which is the trade-off
