INTRODUCTION A Theory of Not Quite Everything Flashcards
What is the general rule in psychiatry regarding theories that explain everything?
If you think you’ve found a theory that explains everything, diagnose yourself with mania and check yourself into the hospital.
Can you predict the future? Provide examples.
Yes, examples include:
* Breathing
* Heartbeat
* Sunrise
* Train arrival times
* Population growth
What are the two types of predictability mentioned in the text?
Predictability of:
* Newtonian dance of the planets
* Lorenzian chaos of the weather
What does the term ‘deterministic’ imply in the context of predictions?
It implies that with perfect knowledge of the universe, one could predict everything.
What type of game does the text compare life to, and why?
Life is compared to poker, as it involves making decisions with limited information.
What is Bayes’ theorem primarily about?
Probability and how likely something is, given the evidence we have.
What does P(A|B) represent in Bayes’ theorem?
The probability of event A happening, given that event B has happened.
What is an example of conditional probability involving a deck of cards?
The probability of drawing a heart after drawing a club changes from 1/4 to 13/51.
What does Bayes’ theorem reveal about medical testing?
It shows that even a highly accurate test can lead to misleading probabilities.
What does ‘99 percent sensitive’ mean in the context of a disease test?
If you have the disease, there’s a 99 percent chance the test will correctly identify it.
What is the significance of the false negative and false positive rates?
They indicate the likelihood of incorrect test results:
* False negative rate of 1 percent
* False positive rate of 1 percent
How does Bayes’ theorem affect our understanding of test results?
It emphasizes that prior probabilities influence the interpretation of test results.
What is the probability of having breast cancer after a positive test in a low-risk population?
Approximately 7 percent.
What happens to the probability of having breast cancer in a high-risk population?
It increases to approximately 47 percent.
What does Bayes’ theorem help us understand in the context of conspiracy theories?
It explains why individuals with differing beliefs interpret the same evidence differently.
What is an implication of Bayes’ theorem for artificial intelligence?
AI uses Bayesian principles to make predictions based on training data.
What do we mean by ‘prior probability’?
The likelihood of an event before considering new evidence.
Fill in the blank: Bayes’ theorem helps us adjust our beliefs based on _______.
[new evidence].
True or False: Bayes’ theorem is only applicable in medical testing.
False.
What is the mathematical operation used in Bayes’ theorem?
Multiplication and division.
What does a positive test result indicate about the probability of having a disease?
It indicates the probability of having the disease given a positive test result.
What does ‘80 percent sensitive’ mean in the context of medical testing?
It means the probability of seeing the test result given that the disease is present.
What is the term used in Bayes’ theorem for the probability of a disease before testing?
Prior probability.
How can prior probability be determined in medical testing?
It can often be estimated from recorded diagnoses in general practice records.
What is the significance of understanding prior probability in testing?
It is crucial for interpreting test results accurately.
What is an example of a situation where determining prior probability is difficult?
Estimating the likelihood of Russia invading Ukraine.
In Bayes’ theorem, what is the posterior probability?
The probability of having the disease after obtaining a positive test result.
True or False: A test with 99 percent accuracy guarantees a 99 percent chance that it is correct.
False.
What was the prior probability of having COVID-19 in Britain around April 2020?
Approximately 3 percent.
What does a 95 percent sensitivity and specificity in an antibody test imply?
It indicates that the test is highly accurate, but actual results depend on prior probabilities.
What is the risk of issuing immunity passports based on a flawed understanding of test results?
It could lead to millions being mistakenly told they are safe when they are not.
What happens to the proportion of false positives if the prevalence of a disease is low?
It increases the proportion of false positives among positive test results.
What is the sensitivity of the prostate-specific antigen (PSA) test at a cutoff of three nanograms per milliliter?
Approximately 32 percent.
Fill in the blank: The prostate-specific antigen test has a specificity of ______.
85 percent.
What is the chance of actually having prostate cancer if a man in his fifties receives a positive PSA test result?
About 4 percent.
What is the trade-off when adjusting the cutoff level in medical tests?
Increasing specificity comes at the cost of sensitivity, and vice versa.
What percentage of women undergoing annual mammograms for ten years receive at least one false positive result?
60 percent.
What is the positive predictive value for Down’s syndrome in non-invasive prenatal testing?
82 percent.
What is the positive predictive value for Patau’s syndrome in non-invasive prenatal testing?
49 percent.
What is the positive predictive value for Edwards syndrome in non-invasive prenatal testing?
37 percent.
Why is understanding Bayes’ theorem important in the context of cancer screening?
It helps evaluate the effectiveness and implications of screening tests.
What is the main challenge when interpreting medical test results?
Determining the prior probability and its impact on the results.
What is the positive predictive value for Down’s syndrome in NIPT tests?
82 percent
Positive predictive value refers to the percentage chance that a positive test result is a true positive.
What is the positive predictive value for Edwards syndrome in high-risk pregnancies?
84 percent
This value significantly increases when tests are limited to high-risk categories.
What is Bayes’ theorem primarily concerned with?
Updating probabilities based on new data
It emphasizes the importance of prior probability in making decisions.
What fallacy occurs when interpreting DNA evidence in a criminal case?
Prosecutor’s fallacy
This fallacy involves misinterpreting the probability of a DNA match without considering prior probabilities.
In the case of DNA evidence, what is the prior probability if there are 65 million Britons and one criminal?
One in 65 million
This illustrates the importance of considering the base rate of the population.
What happens to the prior probability if the suspect pool is narrowed down to ten individuals?
It becomes 10 percent
This significantly alters the interpretation of the DNA evidence.
What was the outcome of Andrew Deen’s case regarding DNA evidence?
His conviction was overturned
This occurred because the questions regarding DNA evidence were misunderstood.
What mistake did the defense make in the O. J. Simpson trial?
They used the prior probability without updating it with new information
This led to a misunderstanding of the likelihood of the husband being the murderer.
How does Gerd Gigerenzer’s analysis relate to domestic abuse victims?
He quantified the risk of murder among domestic abuse victims
He highlighted how many women might be murdered based on prior probabilities.
What is inverse probability?
The probability of a hypothesis given observed data
This concept was popularized by Reverend Thomas Bayes.
What is the relationship between Bayes’ theorem and decision-making under uncertainty?
Bayes’ theorem represents ideal decision-making
It illustrates how good decisions can be made using updated probabilities.
What does the phrase ‘I predict, therefore I am’ imply?
Our conscious experience is based on prior probabilities
This suggests our perception of reality is shaped by predictions.
True or False: A 99 percent accurate test is right 99 percent of the time.
False
This statement overlooks the importance of prior probabilities in interpreting test results.
Fill in the blank: The annual probability that a man who beats his wife will murder her might be _____ in twenty-five hundred.
one
This statistic highlights the statistical misconceptions in criminal cases.
What does the ideal Bayesian reasoner take into account when making decisions?
Prior beliefs and new evidence
This dual consideration leads to more accurate conclusions.
