CHAPTER ONE From The Book of Common Prayer to the Full Monte Carlo Flashcards
(234 cards)
1
Q
Where is the graveyard known as Bunhill Fields located?
A
Near Old Street Tube station, in Shoreditch in East London
2
Q
Name three famous individuals buried in Bunhill Fields.
A
- William Blake
- Daniel Defoe
- John Bunyan
3
Q
Who is the most well-known person buried in Bunhill Fields, according to the text?
A
Reverend Thomas Bayes
4
Q
What was Thomas Bayes’ profession?
A
Eighteenth-century Presbyterian minister and hobbyist mathematician
5
Q
What is Thomas Bayes best known for?
A
His theorem, published in ‘An Essay towards Solving a Problem in the Doctrine of Chances’
6
Q
What significant historical event took place in England in 1533?
A
Henry VIII took England out of the Catholic Church
7
Q
What document did Archbishop Cranmer introduce in 1549?
A
The Book of Common Prayer
8
Q
What was the Act of Uniformity passed by Parliament in 1662?
A
It required the Book of Common Prayer to be used in all services in England
9
Q
What term refers to clergymen who refused to obey the Act of Uniformity?
A
Dissenters or Nonconformists
10
Q
What did the Act of Toleration in 1688 allow for Dissenters?
A
Freedom of worship
11
Q
What restrictions did Dissenters still face after the Act of Toleration?
A
- Required licenses for places of worship
- Banned from holding public office
- Banned from attending English universities
12
Q
Where did Nonconformist scholars and would-be ministers typically study?
A
- Scottish universities, notably Edinburgh
- Dutch universities, particularly Leiden
13
Q
What was Richard Bayes known for?
A
Getting rich in the Sheffield steel industry, making cutlery
14
Q
What was the fate of Samuel Bayes regarding the Act of Uniformity?
A
He was removed from his parish for refusing to obey it
15
Q
How many children did Joshua Bayes and his wife Anne have?
A
Seven children
16
Q
What was unusual about the survival rate of Joshua and Anne’s children?
A
All seven survived to adulthood, which was rare at the time
17
Q
What educational background did Thomas Bayes likely have?
A
Educated by John Ward and possibly Abraham de Moivre
18
Q
What university did Thomas Bayes attend for his studies?
A
University of Edinburgh
19
Q
What was the purpose of Thomas Bayes’ studies in Edinburgh?
A
To prepare for his life as a minister
20
Q
What is known about Thomas Bayes’ beliefs?
A
He was a Nonconformist, possibly an Arian or a Socinian
21
Q
What was the title of Bayes’ first publication?
A
Divine benevolence: Or, an attempt to prove that the principal end of the divine providence and government is the happiness of his creatures
22
Q
What philosophical issue does Bayes’ work Divine Benevolence address?
A
Theodicy: explaining why God allows evil in the world
23
Q
What was Bayes’ view on God’s nature according to Divine Benevolence?
A
He believed God is benevolent and wants us to be happy
24
Q
What controversial stance did Bayes likely hold regarding the Trinity?
A
He probably denied the Trinity, aligning with Arian or Socinian beliefs
25
Who was Thomas Bayes?
An 18th-century statistician and theologian known for Bayes' theorem
## Footnote
Bayes was a Presbyterian minister with unorthodox Christian views, likely influenced by his associations with Nonconformist ministers.
26
What was the profession of Thomas Bayes' father?
Moderate Calvinist minister
## Footnote
Bayes' father, Joshua, tolerated a variety of views.
27
What is Arianism?
A belief that denies the full divinity of Jesus Christ
## Footnote
Arianism was deemed heretical by mainstream Christianity.
28
Who was James Foster?
A Dissenting minister and friend of Thomas Bayes
## Footnote
Foster wrote a pamphlet arguing that the Trinity was not essential to Christianity.
29
What significant financial contribution did Bayes make upon his death?
He left £200 to John Hoyle and Richard Price
## Footnote
Both were Nonconformist ministers who were Arian in faith.
30
What notable mathematical position did William Whiston hold?
Lucasian professor of mathematics at Cambridge
## Footnote
He succeeded Isaac Newton in this prestigious role.
31
What was the primary interest of Philip Stanhope, the 2nd Earl Stanhope?
Amateur mathematics and science
## Footnote
He was part of a network of scientists and mathematicians, including Bayes.
32
What was 'An Introduction to the Doctrine of Fluxions'?
A paper by Thomas Bayes defending Newton's calculus
## Footnote
It addressed critiques from philosopher George Berkeley.
33
What misconception did Gerolamo Cardano have regarding probabilities?
He believed rolling a die multiple times multiplied the probability of outcomes
## Footnote
This led to incorrect assumptions about the odds of rolling a six.
34
Who were Pascal and Fermat?
Mathematicians who contributed to the foundations of probability theory
## Footnote
Their correspondence addressed problems of chance and fair division of winnings.
35
What is a derivative in mathematics?
The rate of change of a function with respect to a variable
## Footnote
It represents the slope of the tangent line at a specific point on a graph.
36
Fill in the blank: The probability of rolling a six on a single die is ______.
1/6
37
What is an infinite series?
A mathematical series that continues indefinitely
## Footnote
Examples include sums like 1 + 1/2 + 1/4 + 1/8... which converge to a finite value.
38
What was the outcome of the correspondence between Gombaud and Pascal?
They discussed how to fairly divide a pot in interrupted games of chance
## Footnote
This led to foundational ideas in probability.
39
True or False: Thomas Bayes was a modern academic focused on research agendas.
False
## Footnote
Bayes was more of an amateur mathematician, engaging in mathematics for personal pleasure.
40
What is the probability of rolling at least one six in four rolls of a die?
Approximately 0.52
## Footnote
This is calculated by determining the probability of not rolling a six and subtracting from 1.
41
What is the significance of the theorem found in Stanhope's papers?
It was a theorem related to derivatives and infinite series, discovered later by Lagrange
## Footnote
This shows the historical importance of Bayes' work in calculus.
42
Fill in the blank: The chance of not rolling a double six in twenty-four rolls is ______.
0.51
43
What was a key observation made by Gombaud regarding betting?
That betting on rolling at least one six is profitable, while betting on double sixes is not
## Footnote
His empirical observations led to deeper questions about probability.
44
How many points does the first player have in the interrupted game?
Fifty points.
45
How many points does the second player have in the interrupted game?
Twenty points.
46
According to Pacioli, how should the winnings be split?
Five-sevenths of the pot to the first player.
47
What was Cardano's criticism of Pacioli's solution?
He found it absurd because it seemed unfair.
48
What does Cardano suggest should determine the division of stakes?
The number of rounds each player has yet to win.
49
What is the progression of a number?
The sum of that number and all the integers below it down to one.
50
What was Cardano's example involving two players?
One player had three points to win, the other had one.
51
How did Cardano propose to divide the pot?
In a six-to-one ratio in favor of the second player.
52
What key insight did Pascal and Fermat realize about winning?
It’s the number of possible outcomes that remain that matters.
53
In Pascal's example, what was the total pot amount?
Sixty-four pistoles.
54
What was the fair distribution of the pot when the score was 2-1?
Three-quarters of the pot to the first player.
55
How many possible outcomes are there if two players are at a score of 2-1?
Four possible outcomes.
56
If Player One is up 2-0, what is the fair division according to Pascal?
Fifty-six pistoles out of sixty-four.
57
What does Pascal's triangle help calculate?
The number of possible outcomes in probability.
58
What is the formula for calculating the probability of an event?
Number of ways the event can occur divided by total number of outcomes.
59
What does the Law of Large Numbers state?
The more trials conducted, the closer the results will be to the true probability.
60
Who introduced the next stage of probability theory after Pascal and Fermat?
Jacob Bernoulli.
61
What happens to the probability results as the number of trials increases?
They get closer to the true probability.
62
What is the significance of Bernoulli's claim?
It applies to real-world scenarios beyond simple games of chance.
63
What were Pascal and Fermat's letters the beginning of?
The modern idea of probability theory.
64
Fill in the blank: The doctrine of chances is an early name for ______.
Probability theory.
65
True or False: Bernoulli's findings only apply to games of chance.
False.
66
What is the difference between sampling probabilities and inferential probabilities?
Sampling probabilities predict about a sample given knowledge of the whole, while inferential probabilities predict about the whole based on a sample.
67
Who was Bernoulli and what was his main interest?
Bernoulli was a Swiss mathematician interested in games of chance and the probability of outcomes in uncertain situations.
68
What is 'moral certainty' as defined by Bernoulli?
Moral certainty is a given degree of confidence in a spread of results, rather than absolute certainty.
69
What does Bernoulli's theorem address?
Bernoulli's theorem addresses how confident we can be in the contents of an urn after drawing a sample.
70
What is the relationship between sample size and confidence in Bernoulli's findings?
A larger sample size increases the likelihood that the sample result is close to the true ratio in the population.
71
Fill in the blank: Bernoulli's theorem states that for any probability we wish, the absolute difference between the sample proportion m/n and the true proportion p is less than or equal to some number ______.
∊
72
How did Bernoulli suggest one could achieve a desired level of confidence?
By specifying the number of observations needed to achieve a certain level of confidence in the results.
73
True or False: Bernoulli believed that we could achieve absolute certainty through sampling.
False
74
What significant concept did Bernoulli contribute to the understanding of empirical evidence?
He created a philosophically robust way of using empirical evidence to establish probabilities.
75
Who extended Bernoulli's ideas about probability?
Abraham de Moivre extended Bernoulli's ideas about probability.
76
What is a binomial distribution?
A binomial distribution describes the outcomes of a scenario with two equally likely outcomes, such as flipping a coin.
77
What is the mathematical significance of factorials in probability calculations?
Factorials are used to calculate the number of ways outcomes can occur in probability, but they can become very large and complex.
78
Fill in the blank: The factorial of five is ______.
120
79
What did de Moivre notice about the shape of probability distribution curves?
He noticed that the curves have a bulge in the middle and flattened edges, especially with larger sample sizes.
80
What is the implication of Bernoulli’s findings for fields beyond gambling?
His findings have implications for fields like medicine, criminal justice, and any area requiring inferential statistics.
81
What was a key limitation in Bernoulli's approach according to Aubrey Clayton?
Bernoulli did not clearly distinguish between sampling probabilities and inferential probabilities.
82
What is the false positive rate Bernoulli aimed for in his studies?
0.001, or a false positive rate of 1 in 1,000.
83
What did de Moivre notice about the shape of the curve in probability?
The curve has a bulge in the middle and flattened edges.
84
What is the mathematical expression derived by de Moivre for probability outcomes?
Normal distribution.
85
What is the standard deviation a measure of?
How spread out your data is around the mean.
86
How do you calculate variance?
By taking each value, subtracting the mean, squaring the result, and averaging those squares.
87
If the mean height of three children is 160 cm, what does a standard deviation of 2.4 cm imply?
The heights vary within 2.4 cm from the mean.
88
What percentage of values fall within 1 standard deviation (SD) of the mean in a normal distribution?
68 percent.
89
What does a standard deviation (SD) of 42.4 indicate in the example of eight-year-olds and a basketball player?
The two eight-year-olds are 0.7 SD below the mean, and the basketball player is 1.4 SD above the mean.
90
How does the accuracy of data relate to sample size according to de Moivre?
The accuracy grows in proportion to the square root of the sample size.
91
What percentage of the time is it expected to see sixty or more heads in one hundred coin flips?
About 2.8 percent of the time.
92
What is the main question Bernoulli and de Moivre were trying to answer?
How likely am I to see this data, given a certain hypothesis?
93
What significant contribution did Thomas Simpson make to statistics?
He advocated using the mean of observations to estimate true positions in measurement error.
94
What was Bayes's key insight regarding probability?
Probability is subjective and reflects our lack of knowledge about the world.
95
What is the difference between inferential probability and sampling probability?
Inferential probability asks 'How likely is a hypothesis true, given this data?' while sampling probability asks 'How likely am I to see this data, given a hypothesis?'
96
What did Bayes argue about the use of imperfect measuring instruments?
More observations with an imperfect instrument will not necessarily reduce error.
97
In Bayes's view, what must be considered to make inferential probability work?
How likely you thought the hypothesis was in the first place.
98
What metaphor did Bayes use to explain his concept of probability?
A table upon which balls are rolled.
99
What is the relationship between the mean and the errors in measurements according to Bayes?
The mean will not help if the measuring instrument is biased.
100
What is the main question to ask in inferential probability?
What are the chances that my hypothesis is true, given the data?
101
What should be taken into account when making inferential probability work?
Your subjective beliefs about the hypothesis.
102
What metaphor did Bayes use to explain his point?
A table upon which balls are rolled.
103
What type of table did later writers refer to in relation to Bayes' metaphor?
A billiard table.
104
What happens to the white ball after it is rolled on the table?
It is removed and a line is drawn across the table where it was.
105
What information is provided after rolling red balls onto the table?
How many balls lie to the left of the line and how many to the right.
106
If five balls are thrown and two land left and three right, where does Bayes suggest the line is?
Three-sevenths of the way up the table from the left.
107
What might be an intuitive but incorrect assumption about the line's position?
That it should be two-fifths of the way up the table.
108
What does Bayes emphasize must be considered in estimating the line's position?
The prior probability.
109
What does the lack of information about the line's position represent?
A form of prior information.
110
What is the subjective point of view regarding the line's possible positions?
It is equally likely to be anywhere on the table.
111
Fill in the blank: The distribution of probability graph would show how likely the line is to be in a given place on the _______.
table.
112
What is the probability of the next ball landing to the left of the line if you have no idea where the line is?
0.5 (50 percent)
## Footnote
This reflects the uncertainty in the position of the line.
113
What does Bayes' theorem suggest about incorporating new information?
You must add any new information you get to the information you already have.
114
How does Bayes' method modify the calculation of probability?
It adds one to the number of red balls on the left and two to the total number of red balls.
115
What is the concept of posterior probability distribution?
It is the updated assessment of the likely position of the line after incorporating new information.
116
What happens to the posterior distribution when new information is gathered?
It becomes the new prior for further assessments.
117
True or False: Bayes' theorem guarantees absolute certainty in probability estimates.
False
## Footnote
No matter how much evidence is gathered, absolute certainty is never achieved.
118
What is the significance of Richard Price in relation to Bayes' work?
He brought Bayes' paper to wider attention and contributed to its practical applications.
119
What was the primary focus of Bayes' original paper?
It was all theory with no hint of application.
120
What analogy does Price use to explain the application of Bayes' theorem?
The odds of the sun rising again after having seen it rise multiple times.
121
How does Price suggest one should view the probability of rare events?
They can happen, and even with many observations, one cannot reach physical certainty.
122
According to Hume, what is necessary to establish a miracle?
Testimony that is more miraculous in falsehood than the miracle itself.
123
What is a key argument Price makes against Hume's view?
Even with repeated observations, one can never be physically certain about future events.
124
Fill in the blank: Bayes' theorem allows one to update their _______ based on new evidence.
[prior beliefs]
125
What did Price argue about rolling a die with an unknown number of sides?
If it shows a certain face a million times, the best estimate for the next roll's outcome is calculable.
126
What does the 'uniform probability distribution' imply?
It indicates that all outcomes are initially considered equally likely until evidence is gathered.
127
What type of reasoning does Bayes' theorem exemplify?
Subjective probability reasoning.
128
What was one of the implications of the divide among Nonconformist ministries regarding mathematics?
Some believed it would lead to godlessness, while others thought it helped understand God's universe.
129
What was the impact of Price's pamphlet, 'Observations on the Nature of Civil Liberty'?
It significantly influenced American independence sentiments.
130
What does Price's appendix to Bayes' work discuss?
The odds of the sun rising and the implications for probability theory.
131
True or False: Bayes' theorem can be applied to inferential statistics.
True
132
What does Bayes' theorem imply about the certainty of future events?
No amount of evidence can produce absolute certainty.
133
What is the relationship between prior and posterior distributions in Bayesian analysis?
The posterior distribution becomes the new prior when new evidence is included.
134
What is the probability of the next roll coming up not-X according to Price?
1/1,000,002
## Footnote
This probability indicates the likelihood of not observing a particular outcome in a series of events.
135
What is the range of probability for not seeing an X that Price calculated?
Between 1 in 600,000 and 1 in 3 million
## Footnote
This range reflects the uncertainty surrounding rare events.
136
What philosophical point did Price make regarding rare events?
Rare events happen sometimes, and no amount of seeing them not happen will ever completely rule them out.
137
How did Hume respond to Price's criticisms of his work?
Hume removed disobliging comments and added an apologetic introduction in the second edition of his work.
138
What did Hume call Price after their exchange?
A true Philosopher
## Footnote
Hume praised Price for his civility and reasoned arguments.
139
What did Price suggest about Bayes' theorem in his foreword to Bayes' paper?
It could show that the world progressed according to fixed laws and could confirm the argument for the existence of the Deity.
140
Who independently arrived at conclusions similar to Bayes after his death?
Pierre-Simon Laplace
## Footnote
Laplace provided a more detailed account of Bayesian principles.
141
What major application did probability theory have in the social sciences according to Jacob Bernoulli?
Working out how likely someone was to live for another ten years by looking at similar individuals.
142
What did Laplace find regarding birth rates in Paris?
A bias toward boy babies with a ratio of roughly 51:49
## Footnote
He calculated a 1 in 10^42 chance of seeing such an extreme result if births were equally likely.
143
Who was Adolphe Quetelet and what was his main contribution?
A Belgian mathematician who pushed probability and statistics into the social sciences, introducing the concept of the 'average man.'
144
What did Quetelet aim to analyze through statistics?
Society along various axes such as physical attributes, moral and psychological characteristics.
145
What did Quetelet discover about measurements like height and weight?
They were normally distributed, suggesting they were influenced by many small factors.
146
What did Quetelet think about the average man?
He viewed the average man as an ideal or standard of beauty at which nature aims.
147
What controversy arose from Quetelet's work?
It conflicted with the idea of free will, suggesting behaviors were influenced by attributes.
148
What did Francis Galton contribute to the field of statistics?
He advanced the use of frequentist statistics, focusing on hypothesis testing rather than data to hypothesis.
149
What is the key difference between Bayesian and frequentist statistics?
Bayesian statistics move from data to hypothesis, while frequentist statistics move from hypothesis to data.
150
What is a major challenge with Bayesian priors?
They are subjective and depend on individual knowledge and ignorance.
151
What philosophical issue arises from Bayesian priors?
They suggest that truth may depend on personal beliefs and prior knowledge.
152
What example illustrates the complexity of choosing priors in Bayesian statistics?
The urn with black and white balls, where different assumptions lead to different prior probabilities.
153
What does the Bayesian model suggest about the truth of a statement?
Whether something is true depends on how strongly one believed it before.
154
What is the distinction between subjective probability and objective probability?
Subjective probability is a statement about beliefs, while objective probability is about real-world phenomena.
155
True or False: Subjective probability means random or baseless.
False.
156
What is the phenomenon that Galton is known for regarding offspring heights?
Regression to the mean.
157
Fill in the blank: Galton coined the phrase ______ to refer to heredity and environment.
nature and nurture.
158
What did Galton want to create a science of?
Human breeding (eugenics).
159
Who was the first appointee to the chair of eugenics at University College London?
Karl Pearson.
160
What statistical test did Karl Pearson develop?
Chi-square test.
161
What is the term coined by Pearson that measures the dispersion of a dataset?
Standard deviation.
162
What did Ronald Fisher contribute to statistics?
Analysis of variance (ANOVA), statistical significance, and maximum likelihood estimation (MLE).
163
True or False: Fisher was known for his progressive views on race and eugenics.
False.
164
What did Fisher and Pearson disagree about?
The interpretation of the maximum likelihood method and its relation to Bayesian probability.
165
What did Galton use to demonstrate the normal distribution problem?
A quincunx.
166
What happens when multiple smaller normal distributions are combined, according to Galton?
They can add up to form one larger normal distribution.
167
Fill in the blank: Galton's insight regarding smaller distributions allowed statisticians to think about ______ populations forming part of a larger one.
different.
168
What was Galton's view on the intelligence of different races?
He held racist views, considering some races inferior.
169
What was the general finding regarding the heritability of IQ?
About half of the variance in IQ is caused by genetics.
170
Fill in the blank: Galton's work inspired later statisticians like Karl Pearson and ______.
Ronald Fisher.
171
What did Galton observe about the offspring of very tall and very short parents?
They tend not to be as extreme in height as their parents.
172
True or False: The concept of statistical significance was developed by Ronald Fisher.
True.
173
What major conflict arose between Fisher and Pearson?
Their disagreement over the interpretation of likelihood ratios in statistical analysis.
174
What was the focus of Galton's book 'Hereditary Genius'?
The clustering of brilliant thinkers in families.
175
Who were notable supporters of eugenics in the early 20th century?
John Maynard Keynes, Sidney and Beatrice Webb, George Bernard Shaw, Bertrand Russell
## Footnote
These individuals were influential in socialist and liberal movements and supported selective breeding.
176
What did Fisher argue in Eugenics Review about nations and their institutions?
Nations with institutions that produce better individuals will supplant those that breed decadence
## Footnote
This reflects the eugenic belief in improving society through selective breeding.
177
What was the criticism of embryo screening and mitochondrial donation primarily associated with?
The religious right labeled them as eugenics
## Footnote
This indicates the contentious nature of eugenics in contemporary discussions.
178
What was Clayton's argument regarding the history of statistics and eugenics?
He argued that the history of frequentist statistics is intertwined with eugenics
## Footnote
Clayton suggests that the statistical methods developed were influenced by eugenic ideologies.
179
What did Fisher and Pearson seek in their statistical methods regarding eugenics?
They sought a veneer of objectivity to support their eugenic views
## Footnote
They aimed to present their beliefs as scientific truths.
180
What is Bayesianism characterized by in terms of probability?
Bayesianism treats probability as subjective, reflecting our ignorance of the world
## Footnote
This contrasts with frequentist views that treat probability as an objective measure.
181
What did John Stuart Mill criticize about the Bayesian approach?
He criticized the idea that two outcomes should be treated as equally likely without evidence
## Footnote
Mill believed that probability should reflect real-world frequencies.
182
What is a p-value in frequentist statistics?
The likelihood of observing results at least as extreme as those seen under the null hypothesis
## Footnote
It helps determine whether an observed effect is statistically significant.
183
What is the null hypothesis in the context of the IQ and shoe size example?
The hypothesis that there is no real effect of shoe size on IQ
## Footnote
It serves as a baseline for testing the validity of the observed data.
184
What was Fisher's view on Bayesianism?
He called Bayes' theorem a 'staggering falsity' and believed it should be wholly rejected
## Footnote
Fisher's strong criticism reflects the tension between frequentist and Bayesian approaches.
185
What did Venn contribute to the discussion on probability?
He emphasized that probability should reflect actual frequencies from hypothetical infinite trials
## Footnote
This approach underlines the frequentist perspective on probability.
186
Fill in the blank: Frequentist statistics involves sampling probability, the probability that _______.
Bernoulli would have recognized
## Footnote
This highlights the historical roots of frequentist statistics.
187
True or False: The eugenics movement had no influence on early scientific methods.
False
## Footnote
The eugenics movement intertwined significantly with the development of early statistical methods.
188
What did Boole note about different kinds of ignorance in Bayesian statistics?
Different kinds of ignorance lead to different priors
## Footnote
This emphasizes the subjectivity in choosing priors in Bayesian analysis.
189
What was Fisher's criticism of the rule of succession in Bayesian reasoning?
He found it to be flawed and damaging to his own work
## Footnote
This illustrates the complexity and internal conflicts within Bayesian statistics.
190
What is a p-value?
A p-value measures how likely it would be to see data like those observed under the null hypothesis.
191
If a p-value is 0.1, how often would you expect to see results as extreme as the observed ones?
One time in every ten.
192
What is the significance of a p-value of 0.05?
It indicates that results are sufficiently extreme that you’d see it only one time in every twenty.
193
What does it mean to reject the null hypothesis?
It means treating the effect as though it is real when the p-value is lower than the alpha level.
194
What is statistical significance?
Statistical significance is reached when the p-value is lower than the predetermined alpha level.
195
What is a one-sample t-test?
A statistical test that compares the mean of a sample to a known population mean.
196
In the context of hypothesis testing, what does a two-tailed test refer to?
A test that considers the probability of extreme results at both ends of the distribution.
197
What is the probability of getting at least thirty-two heads in fifty coin flips, if it is statistically significant?
0.03, or 3 percent.
198
What is the purpose of an alpha level in hypothesis testing?
It is the threshold for determining statistical significance.
199
What is the fundamental bit of hypothesis testing?
You have a null hypothesis and an alternative hypothesis, and you reject the null if the data is sufficiently extreme.
200
What does it mean if p < 0.05 results occur more often than expected?
It suggests evidence of some correlation if the null hypothesis is true.
201
What is Bayesianism?
A statistical model that incorporates prior knowledge and updates beliefs based on new evidence.
202
Who was Harold Jefferies?
A key figure in early scientific Bayesianism who applied Bayes' theorem to uncertain data.
203
What did Jefferies demonstrate about the Earth's core?
He showed that the core of the Earth is liquid.
204
What does David Howie say about Jefferies' inferences?
They were tentative and advanced with degrees of confidence that were updated with new information.
205
What is the relationship between probability and uncertainty according to Jefferies?
Probability describes all uncertainty, not just that associated with data.
206
What was Frank Ramsey's contribution to probability theory?
He suggested that probabilities are beliefs and can be quantified through betting.
207
How does Ramsey's model help in decision-making?
It allows calculation of expected subjective utility based on beliefs and desires.
208
What problem arises if your probabilities do not add up?
You can be misled by anyone offering you bets.
209
What was the significance of Bayesian methods during World War II?
They were used by scientists to make good inferences from limited data.
210
What role did Alan Turing play during World War II?
He helped crack German codes using early computers and Bayesian principles.
211
What was the challenge faced by Turing in decoding messages?
The extraordinary number of different possible combinations made it impractical to check all.
212
What did Turing have to assume about combinations of letters?
Some combinations were more likely than others based on context.
213
What is the significance of the three-letter sequence E-I-N in Turing's reasoning?
It is considered more likely than other sequences like J-X-Q.
## Footnote
This reasoning reflects Turing's use of priors in Bayesian statistics.
214
What term did Turing create to refer to a unit of information?
ban
## Footnote
This term is comparable to the modern bit or byte.
215
Which statistical methods were being used by insurance underwriters and military quality-control assessors?
Bayesian methods
## Footnote
These methods were used to set premiums and minimize testing respectively.
216
Who was the head of the Department of Statistics at University College London in the 1970s?
Dennis Lindley
## Footnote
He played a significant role in advancing Bayesian statistics.
217
What was the perception of Bayesianism outside of University College London during the 1970s?
It was viewed as a sideshow
## Footnote
Bayesianism faced skepticism and resistance in broader statistical communities.
218
What did Lindley, Bernardo, and de Finetti decide during the first international Bayesian conference in 1976?
To hold similar conferences in the future
## Footnote
This led to a series of international Bayesian meetings.
219
When was the first Bayesian world meeting held?
1979
## Footnote
It was organized in Valencia as Spain was emerging from fascist dictatorship.
220
What unique tradition developed during the Valencia conferences?
The Bayesian cabaret
## Footnote
This included humorous performances related to Bayesian statistics.
221
What was a common sentiment expressed by attendees of the Valencia conferences regarding the experience?
They were a lot of fun
## Footnote
Attendees balanced work with leisure activities like siestas and parties.
222
What did George Box parody at the first conference?
There’s No Theorem Like Bayes’ Theorem
## Footnote
This was a parody of Irving Berlin's song 'There’s No Business Like Show Business.'
223
What is the humorous claim about Bayesian statistics made during the Valencia conferences?
Bayesians have more fun
## Footnote
This was reflected in the light-hearted nature of the conferences.
224
What has contributed to the resurgence of Bayesian methods in recent decades?
The passing down of Jeffreys' book and practical applications in various fields
## Footnote
Software engineering and data science have also embraced Bayesian methods.
225
What did Dennis Lindley state about Bayesian statistics in a 1975 conference?
It is the only method that can produce sound inferences and decisions
## Footnote
This reflects the strong advocacy for Bayesian methods among its proponents.
226
How did frequentists view Bayesians during the development of Bayesian statistics?
As underdogs and up-and-comers
## Footnote
This dynamic created tension between the two camps in statistics.
227
What did George Box admit about the nature of statistical inference in his 1985 paper?
Scientific method employs both Bayesian and frequentist inference
## Footnote
This reflects a more ecumenical approach to statistics.
228
What is the term used in professional wrestling that describes maintaining an illusion of reality?
kayfabe
## Footnote
This concept was likened to the public debates between Bayesians and frequentists.
229
What does Bayesian inference allow statisticians to do in decision theory?
Make statements about the plausibility of a hypothesis
## Footnote
Bayesian methods are essential for evaluating the likelihood of different hypotheses.
230
What is the value of grabbing the snitch in Quidditch compared to scoring a goal?
Grabbing the snitch is worth fifteen times scoring a goal
## Footnote
This significantly diminishes the importance of scoring goals for the team.
231
How do you pronounce 'Lester-shire'?
It is pronounced 'Lester-sher'
## Footnote
This reflects the peculiarities of English place names.
232
What is the implication of the word 'posterior' in the context of the text?
It suggests that the term will be frequently used throughout the book
## Footnote
The author anticipates humor regarding the word.
233
Who are two notable Bayesians mentioned in the text?
* Harold Jeffreys
* E. T. Jaynes
## Footnote
They discuss 'objective Bayesianism' and the use of logical principles for priors.
234
What did Kevin McConway say about E. T. Jaynes' attempt at 'objective Bayesianism'?
He stated that Jaynes did not succeed, but he had a good try
## Footnote
This reflects differing opinions on the effectiveness of Jaynes' approach.
