Computer Age Statistical Inference: Algorithms, Evidence, by Bradley Efron

By Bradley Efron

The twenty-first century has obvious a wide ranging enlargement of statistical method, either in scope and in impact. 'Big data', 'data science', and 'machine studying' became widely used phrases within the information, as statistical tools are delivered to undergo upon the big facts units of recent technological know-how and trade. How did we get the following? And the place are we going? This e-book takes us on an exciting trip throughout the revolution in information research following the advent of digital computation within the Nineteen Fifties. starting with classical inferential theories - Bayesian, frequentist, Fisherian - person chapters absorb a chain of influential themes: survival research, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after version choice, and dozens extra. The pretty glossy method integrates technique and algorithms with statistical inference. The ebook ends with hypothesis at the destiny path of data and knowledge technology.

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X/), that is, “the posterior odds ratio is the prior odds ratio times the likelihood ratio,” a memorable restatement of Bayes’ rule. 1 Two Examples A simple but genuine example of Bayes’ rule in action is provided by the story of the Physicist’s Twins: thanks to sonograms, a physicist found out she was going to have twin boys. ” she asked. The doctor answered that one-third of twin births were Identicals, and two-thirds Fraternals. In this situation , the unknown parameter (or “state of nature”) is either Identical or Fraternal with prior probability 1/3 or 2/3; X, the possible sonogram results for twin births, is either Same Sex or Different Sexes, and x D Same Sex was observed.

Bayesian inference requires a prior distribution g. /. When past experience provides g. /, as in the twins example, there is every good reason to employ Bayes’ theorem. If not, techniques such as those of Jeffreys still permit the use of Bayes’ rule, but the results lack the full logical force of the theorem; the Bayesian’s right to ignore selection bias, for instance, must then be treated with caution. x/, designed to answer the specific question at hand. This adds an arbitrary element to the inferential process, and can lead to meterreader kinds of contradictions.

1 suggests. x/ given model F . The first of these was Fisher’s theory of maximum likelihood estimation and the Fisher information bound: in parametric probability models of the type discussed in Chapter 4, the MLE is the optimum estimate in terms of minimum (asymptotic) standard error. In the same spirit, the Neyman–Pearson lemma provides an optimum hypothesis-testing algorithm. This is perhaps the most elegant of frequentist constructions. x/. x/ says which choice, 0 or 1, we will make having observed data x.

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