INTRODUCTION A Theory of Not Quite Everything

Question 1

What is the general rule in psychiatry regarding theories that explain everything?

Answer 1

If you think you’ve found a theory that explains everything, diagnose yourself with mania and check yourself into the hospital.

Question 2

Can you predict the future? Provide examples.

Answer 2

Yes, examples include:
* Breathing
* Heartbeat
* Sunrise
* Train arrival times
* Population growth

Question 3

What are the two types of predictability mentioned in the text?

Answer 3

Predictability of:
* Newtonian dance of the planets
* Lorenzian chaos of the weather

Question 4

What does the term ‘deterministic’ imply in the context of predictions?

Answer 4

It implies that with perfect knowledge of the universe, one could predict everything.

Question 5

What type of game does the text compare life to, and why?

Answer 5

Life is compared to poker, as it involves making decisions with limited information.

Question 6

What is Bayes’ theorem primarily about?

Answer 6

Probability and how likely something is, given the evidence we have.

Question 7

What does P(A|B) represent in Bayes’ theorem?

Answer 7

The probability of event A happening, given that event B has happened.

Question 8

What is an example of conditional probability involving a deck of cards?

Answer 8

The probability of drawing a heart after drawing a club changes from 1/4 to 13/51.

Question 9

What does Bayes’ theorem reveal about medical testing?

Answer 9

It shows that even a highly accurate test can lead to misleading probabilities.

Question 10

What does ‘99 percent sensitive’ mean in the context of a disease test?

Answer 10

If you have the disease, there’s a 99 percent chance the test will correctly identify it.

Question 11

What is the significance of the false negative and false positive rates?

Answer 11

They indicate the likelihood of incorrect test results:
* False negative rate of 1 percent
* False positive rate of 1 percent

Question 12

How does Bayes’ theorem affect our understanding of test results?

Answer 12

It emphasizes that prior probabilities influence the interpretation of test results.

Question 13

What is the probability of having breast cancer after a positive test in a low-risk population?

Answer 13

Approximately 7 percent.

Question 14

What happens to the probability of having breast cancer in a high-risk population?

Answer 14

It increases to approximately 47 percent.

Question 15

What does Bayes’ theorem help us understand in the context of conspiracy theories?

Answer 15

It explains why individuals with differing beliefs interpret the same evidence differently.

Question 16

What is an implication of Bayes’ theorem for artificial intelligence?

Answer 16

AI uses Bayesian principles to make predictions based on training data.

Question 17

What do we mean by ‘prior probability’?

Answer 17

The likelihood of an event before considering new evidence.

Question 18

Fill in the blank: Bayes’ theorem helps us adjust our beliefs based on _______.

Answer 18

[new evidence].

Question 19

True or False: Bayes’ theorem is only applicable in medical testing.

Answer 19

False.

Question 20

What is the mathematical operation used in Bayes’ theorem?

Answer 20

Multiplication and division.

Question 21

What does a positive test result indicate about the probability of having a disease?

Answer 21

It indicates the probability of having the disease given a positive test result.

Question 22

What does ‘80 percent sensitive’ mean in the context of medical testing?

Answer 22

It means the probability of seeing the test result given that the disease is present.

Question 23

What is the term used in Bayes’ theorem for the probability of a disease before testing?

Answer 23

Prior probability.

Question 24

How can prior probability be determined in medical testing?

Answer 24

It can often be estimated from recorded diagnoses in general practice records.

Question 25

What is the significance of understanding prior probability in testing?

Answer 25

It is crucial for interpreting test results accurately.

Question 26

What is an example of a situation where determining prior probability is difficult?

Answer 26

Estimating the likelihood of Russia invading Ukraine.

Question 27

In Bayes' theorem, what is the posterior probability?

Answer 27

The probability of having the disease after obtaining a positive test result.

Question 28

True or False: A test with 99 percent accuracy guarantees a 99 percent chance that it is correct.

Answer 28

False.

Question 29

What was the prior probability of having COVID-19 in Britain around April 2020?

Answer 29

Approximately 3 percent.

Question 30

What does a 95 percent sensitivity and specificity in an antibody test imply?

Answer 30

It indicates that the test is highly accurate, but actual results depend on prior probabilities.

Question 31

What is the risk of issuing immunity passports based on a flawed understanding of test results?

Answer 31

It could lead to millions being mistakenly told they are safe when they are not.

Question 32

What happens to the proportion of false positives if the prevalence of a disease is low?

Answer 32

It increases the proportion of false positives among positive test results.

Question 33

What is the sensitivity of the prostate-specific antigen (PSA) test at a cutoff of three nanograms per milliliter?

Answer 33

Approximately 32 percent.

Question 34

Fill in the blank: The prostate-specific antigen test has a specificity of ______.

Answer 34

85 percent.

Question 35

What is the chance of actually having prostate cancer if a man in his fifties receives a positive PSA test result?

Answer 35

About 4 percent.

Question 36

What is the trade-off when adjusting the cutoff level in medical tests?

Answer 36

Increasing specificity comes at the cost of sensitivity, and vice versa.

Question 37

What percentage of women undergoing annual mammograms for ten years receive at least one false positive result?

Answer 37

60 percent.

Question 38

What is the positive predictive value for Down's syndrome in non-invasive prenatal testing?

Answer 38

82 percent.

Question 39

What is the positive predictive value for Patau's syndrome in non-invasive prenatal testing?

Answer 39

49 percent.

Question 40

What is the positive predictive value for Edwards syndrome in non-invasive prenatal testing?

Answer 40

37 percent.

Question 41

Why is understanding Bayes' theorem important in the context of cancer screening?

Answer 41

It helps evaluate the effectiveness and implications of screening tests.

Question 42

What is the main challenge when interpreting medical test results?

Answer 42

Determining the prior probability and its impact on the results.

Question 43

What is the positive predictive value for Down's syndrome in NIPT tests?

Answer 43

82 percent ## Footnote Positive predictive value refers to the percentage chance that a positive test result is a true positive.

Question 44

What is the positive predictive value for Edwards syndrome in high-risk pregnancies?

Answer 44

84 percent ## Footnote This value significantly increases when tests are limited to high-risk categories.

Question 45

What is Bayes' theorem primarily concerned with?

Answer 45

Updating probabilities based on new data ## Footnote It emphasizes the importance of prior probability in making decisions.

Question 46

What fallacy occurs when interpreting DNA evidence in a criminal case?

Answer 46

Prosecutor's fallacy ## Footnote This fallacy involves misinterpreting the probability of a DNA match without considering prior probabilities.

Question 47

In the case of DNA evidence, what is the prior probability if there are 65 million Britons and one criminal?

Answer 47

One in 65 million ## Footnote This illustrates the importance of considering the base rate of the population.

Question 48

What happens to the prior probability if the suspect pool is narrowed down to ten individuals?

Answer 48

It becomes 10 percent ## Footnote This significantly alters the interpretation of the DNA evidence.

Question 49

What was the outcome of Andrew Deen's case regarding DNA evidence?

Answer 49

His conviction was overturned ## Footnote This occurred because the questions regarding DNA evidence were misunderstood.

Question 50

What mistake did the defense make in the O. J. Simpson trial?

Answer 50

They used the prior probability without updating it with new information ## Footnote This led to a misunderstanding of the likelihood of the husband being the murderer.

Question 51

How does Gerd Gigerenzer's analysis relate to domestic abuse victims?

Answer 51

He quantified the risk of murder among domestic abuse victims ## Footnote He highlighted how many women might be murdered based on prior probabilities.

Question 52

What is inverse probability?

Answer 52

The probability of a hypothesis given observed data ## Footnote This concept was popularized by Reverend Thomas Bayes.

Question 53

What is the relationship between Bayes' theorem and decision-making under uncertainty?

Answer 53

Bayes' theorem represents ideal decision-making ## Footnote It illustrates how good decisions can be made using updated probabilities.

Question 54

What does the phrase 'I predict, therefore I am' imply?

Answer 54

Our conscious experience is based on prior probabilities ## Footnote This suggests our perception of reality is shaped by predictions.

Question 55

True or False: A 99 percent accurate test is right 99 percent of the time.

Answer 55

False ## Footnote This statement overlooks the importance of prior probabilities in interpreting test results.

Question 56

Fill in the blank: The annual probability that a man who beats his wife will murder her might be _____ in twenty-five hundred.

Answer 56

one ## Footnote This statistic highlights the statistical misconceptions in criminal cases.

Question 57

What does the ideal Bayesian reasoner take into account when making decisions?

Answer 57

Prior beliefs and new evidence ## Footnote This dual consideration leads to more accurate conclusions.