Is Jim slow?

Recall that John's prior for my average reaction time M was normal with mean 240 and standard deviation 15.

After observing my less than impressive scores on the reaction test, John's posterior density for M is \(Normal(270.5, 5.8)\) shown in the figure.

John will decide that I am "slow" (and require some additional training) if the probability that M exceeds 275 is 30% or higher - this probability is the shaded region in the figure to the right.

Perform the appropriate calculation in the console with the pnorm() function, then select the right answer.

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Beginning Bayes in R

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The probability is sufficiently high to conclude that Jim is "slow".,The probability is not sufficiently high to conclude that Jim is "slow".,John is not able to make a decision based on his posterior curve.

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This chapter introduces the idea of discrete probability models and Bayesian learning. You'll express your opinion about plausible models by defining a prior probability distribution, you'll observe new information, and then, you'll update your opinion about the models by applying Bayes' theorem.

Exercise 1: Discrete probability distributions Exercise 2: Most likely spin?Exercise 3: Chance of spinning an even number?Exercise 4: Constructing a spinner Exercise 5: Simulating spinner data Exercise 6: Bayes' rule Exercise 7: The prior Exercise 8: The likelihoods Exercise 9: The posterior Exercise 10: Interpreting the posterior Exercise 11: Sequential Bayes Exercise 12: Bayes with another spin

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Exercise 1: Bayes with discrete models Exercise 2: Constructing a discrete prior Exercise 3: Updating by Bayes' rule Exercise 4: Continuous prior Exercise 5: Working with a beta curve Exercise 6: Constructing a beta prior Exercise 7: Updating the beta prior Exercise 8: Bayesian updating Exercise 9: Testing a claim Exercise 10: Bayesian inference Exercise 11: Interval estimates Exercise 12: Compare with classical methods Exercise 13: Bayesian probability interval Exercise 14: Posterior simulation Exercise 15: Simulating from a beta curve Exercise 16: Why simulate?

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Exercise 1: Normal sampling model Exercise 2: Reaction times Exercise 3: Updating by Bayes' rule Exercise 4: Bayes with a continuous prior Exercise 5: A continuous prior Exercise 6: Comparing normal priors Exercise 7: Updating the normal prior Exercise 8: The normal posterior Exercise 9: Compare with classical interval Exercise 10: Is Jim slow?

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Exercise 11: Simulation Exercise 12: Posterior simulation Exercise 13: Predictive simulation Exercise 14: Prediction vs. inference

Suppose you're interested in comparing proportions from two populations. You take a random sample from each population and you want to learn about the difference in proportions. This chapter will illustrate the use of discrete and continuous priors to do this kind of inference. You'll use a Bayesian regression approach to learn about a mean or the difference in means when the sampling standard deviation is unknown.

Exercise 1: Comparing two proportions Exercise 2: A discrete prior Exercise 3: Discrete posterior Exercise 4: Proportions with continuous priors Exercise 5: Independent beta priors Exercise 6: Posterior of proportions Exercise 7: Comparison of proportions Exercise 8: Normal model inference Exercise 9: Uniform prior Exercise 10: Learning about a percentile Exercise 11: Bayesian regression Exercise 12: Two group model Exercise 13: Standardized effect inference Exercise 14: Wrap-up and review