All three explanations describe exactly the same theory — the same function from n to h, over the entire domain of possible values of n. Thus we could prefer A or B over C only for reasons other than the theory itself.
We might find that A or B gave us a better understanding of the problem. A and B are certainly more useful than C for figuring out what happens if Congress exercises its power to add an additional associate justice.
Theory A might be most helpful in developing a theory of handshakes at the end of a hockey game when each player shakes hands with players on the opposing team or in proving that the number of people who shook an odd number of hands at the MIT Symposium is even.
How successful are statistical language models?
Chomsky said words to the effect that statistical language models have had some limited success in some application areas. Let's look at computer systems that deal with language, and at the notion of "success" defined by "making accurate predictions about the world.
Their operation cannot be described by a simple function. Some commercial systems use a hybrid of trained and rule-based approaches. Of the language pairs covered by machine translation systems, a statistical system is by far the best for every pair except Japanese-English, where the top statistical system is roughly equal to the top hybrid system.
All systems use at least some statistical techniques. Now let's look at some components that are of interest only to the computational linguist, not to the end user: The majority of current systems are statistical, although we should mention the system of Haghighi and Kleinwhich can be described as a hybrid system that is mostly rule-based rather than trained, and performs on par with top statistical systems.
|What did Chomsky mean, and is he right?||Random sample and Random assignment For a given dataset that was produced by a randomization design, the randomization distribution of a statistic under the null-hypothesis is defined by evaluating the test statistic for all of the plans that could have been generated by the randomization design. In frequentist inference, randomization allows inferences to be based on the randomization distribution rather than a subjective model, and this is important especially in survey sampling and design of experiments.|
|Ramsey described his work as an elaboration of some pragmatic ideas of C. Popularized the "Ramsey test" for eliciting subjective probabilities.|
|Conditional Probability and Independence. Density and Mass Functions.|
|List of important publications in statistics - Wikipedia||
Part of speech tagging: Most current systems are statistical. The Brill tagger stands out as a successful hybrid system: There are many parsing systems, using multiple approaches. Almost all of the most successful are statistical, and the majority are probabilistic with a substantial minority of deterministic parsers.
Clearly, it is inaccurate to say that statistical models and probabilistic models have achieved limited success; rather they have achieved a dominant although not exclusive position. Another measure of success is the degree to which an idea captures a community of researchers. As Steve Abney wrote in"In the space of the last ten years, statistical methods have gone from being virtually unknown in computational linguistics to being a fundamental given.
But I made the switch: And I saw everyone around me making the same switch. And I didn't see anyone going in the other direction.
We all saw the limitations of the old tools, and the benefits of the new. And while it may seem crass and anti-intellectual to consider a financial measure of success, it is worth noting that the intellectual offspring of Shannon's theory create several trillion dollars of revenue each year, while the offspring of Chomsky's theories generate well under a billion.
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derided researchers in machine learning who use purely statistical methods to produce behavior that mimics something in the world, but who don't try to understand the meaning of that behavior.
This is a list of important publications in statistics, Bayesian Inference in Statistical Analysis. Author: (following lecture notes of George W. Brown). Bases inference on the randomization distribution objectively defined by the experimental protocol, rather than a so-called "statistical model" expressing the subjective beliefs of a.
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