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4 changes: 2 additions & 2 deletions bookdown/04.09-probability.Rmd
Original file line number Diff line number Diff line change
Expand Up @@ -124,7 +124,7 @@ What are the advantages and disadvantages to the Bayesian approach? The main adv

Now that you've seen each of these two views independently, it's useful to make sure you can compare the two. Go back to the hypothetical robot soccer game at the start of the section. What do you think a frequentist and a Bayesian would say about these three statements? Which statement would a frequentist say is the correct definition of probability? Which one would a Bayesian do? Would some of these statements be meaningless to a frequentist or a Bayesian? If you've understood the two perspectives, you should have some sense of how to answer those questions.

Okay, assuming you understand the different, you might be wondering which of them is *right*? Honestly, I don't know that there is a right answer. As far as I can tell there's nothing mathematically incorrect about the way frequentists think about sequences of events, and there's nothing mathematically incorrect about the way that Bayesians define the beliefs of a rational agent. In fact, when you dig down into the details, Bayesians and frequentists actually agree about a lot of things. Many frequentist methods lead to decisions that Bayesians agree a rational agent would make. Many Bayesian methods have very good frequentist properties.
Okay, assuming you understand the difference, you might be wondering which of them is *right*? Honestly, I don't know that there is a right answer. As far as I can tell there's nothing mathematically incorrect about the way frequentists think about sequences of events, and there's nothing mathematically incorrect about the way that Bayesians define the beliefs of a rational agent. In fact, when you dig down into the details, Bayesians and frequentists actually agree about a lot of things. Many frequentist methods lead to decisions that Bayesians agree a rational agent would make. Many Bayesian methods have very good frequentist properties.

For the most part, I'm a pragmatist so I'll use any statistical method that I trust. As it turns out, that makes me prefer Bayesian methods, for reasons I'll explain towards the end of the book, but I'm not fundamentally opposed to frequentist methods. Not everyone is quite so relaxed. For instance, consider Sir Ronald Fisher, one of the towering figures of 20th century statistics and a vehement opponent to all things Bayesian, whose paper on the mathematical foundations of statistics referred to Bayesian probability as "an impenetrable jungle [that] arrests progress towards precision of statistical concepts" @Fisher1922b. Or the psychologist Paul Meehl, who suggests that relying on frequentist methods could turn you into "a potent but sterile intellectual rake who leaves in his merry path a long train of ravished maidens but no viable scientific offspring" @Meehl1967. The history of statistics, as you might gather, is not devoid of entertainment.

Expand Down Expand Up @@ -335,7 +335,7 @@ knitr::kable(data.frame(stringsAsFactors=FALSE,
"cumulative probability of",
"generate random number from", "q qnorm() qbinom()"),
Prefix = c("d", "p", "r", "q"),
Normal.distribution = c("dnorm()", "dnorm()", "rnorm()", "qnorm()"),
Normal.distribution = c("dnorm()", "pnorm()", "rnorm()", "qnorm()"),
Binomial.distribution = c("dbinom()", "pbinom()", "rbinom()", "qbinom(")
), caption= "The naming system for R probability distribution functions. Every probability distribution implemented in R is actually associated with four separate functions, and there is a pretty standardised way for naming these functions.")

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