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Chomsky, Chapter 1

1280px-pieter_bruegel_the_elder_-_the_tower_of_babel_vienna_-_google_art_project_-_editedThe humanities book club is currently reading Noam Chomsky’s Aspects of the Theory of Syntax first published in 1965. The following is a summary written by Mathias Cronjäger of the first chapter:

The first chapter of Chomsky’s book sets the stage for the subsequent discussion in the three later chapters of the book. Whereas he will later go into more technical detail Chomsy here paints with a rather broad brush. This frustrated some members of the group who expressed a desire to see concrete examples and exact statements. In the chapter, Chomsky outlines what he means by grammar (a model of how an idealised speaker-listener processes language), and introduces  a range of critical distinctions (such as linguistic performance versus linguistic competence). In terms of grammatical structures, he is keen to distinguish the surface structure of sentences (structural rules about how they are pronounced and expressed) from their deep structure (structural rules for how their semantic content is organized and how to interpret them). He gives a simple example of two English sentences (“I persuaded John to leave” and “I expected John to leave”) and proceeds to demonstrate that they have very different different deep structure in spite of their similar surface structure.

A further distinction made is between descriptive and explanatory theories of grammar. A descriptive account of language is just a set of rules for producing valid sentences in a language (a grammar), or a set of such, which reproduces the structure of a language in a manner that conforms to the linguistic intuitions of native speakers. An explanatory theory of language goes further by also assigning each grammar of a language a notion of “simplicity”, which accounts for what grammar gives the simplest account of a corpus of linguistic data. Such an explanatory theory is not just a theory of language structure, but also one of language acquisition. This is because such a theory can then explain why someone learning a language internalises one set of rules (the simpler ones) over another potential set of rules. The correct notion of “simplicity” in this context is therefore one that corresponds to how humans internally process language. After having introduced this notion of simplicity, Chomsky proceeds to spend a great deal of effort outlining why there is noting simple about determining which measure of simplicity actually accounts for how language acquisition works in humans.

This chapter also includes discussion of linguistic universals; a topic where Chomsky has strong opinions and with which he is often associated. He contrasts the empiricist position (that the only mental procedures universal to all language acquisition is our general capacity for inductive reasoning) with the rationalist position (that we are all born with some basic mental procedures specifically for acquiring and processing language). To put it mildly, Chomsky is not convinced by the arguments of the empiricists. The rationalist position holding true would imply the existence of universal properties that all languages posses: discovering and formalising these into a universal grammar is a project that motivates much of Chomsky’s theory-building. In particular, it is the reason why he is not content to just give an account of English or German language use: he wants to find structures that all languages share (being able to do so would also lend empirical support to the rationalist position).

Summary: Ioannidis (2005) Why Most Published Research Findings Are False

[written by Mathias C. Cronjäger]

Summary of our discussion

Compared to most other papers we have read over the course of running this reading group, Ioannidis (2005) is rather recent. In light of its large impact (it has been the most downloaded paper from PLOS Medicine) we are however comfortable referring to it as a modern classic.

It is a short and very well written paper, which does not presume technical expertise on the part of the reader: anyone familiar with basic statistics and manipulation of fractions will be able to follow the technical arguments made. It contains important insights regarding how sceptical one should be that a result reported as statistically significant indeed represents a “true” effect.

Since the basic arguments made by Ioannidis are only a slight variation on basic statistical arguments, the fact that this paper made such a large impact in other fields (such as medicine and psychology) reflects rather poorly on how well the statistical community has managed to communicate with people outside our own field.

Summary of the paper itself

The arguments in the paper revolve around computing the positive predictive value/PPV (the rate of “true” effects being detected by studies reporting positive results relative to the total number of positive results reported), given different values of  the following parameters:

  • R – the rate of “true” effects being tested relative to non-effects being tested. From a Bayesian perspective, this corresponds to the prior probability of an effect being present.
  • α – the rate of type I error. This corresponds to the probability that an individual experiment will have a statistically significant outcome in spite of no true effect being present.
  • β – the rate of type II error: This corresponds to the probability that an experiment will fail to detect that a  true effect which is present and instead yield a statistically insignificant outcome.

These three parameters are standard in the theory of the PPV. Ioannidis introduces a forth parameter to account for bias not accounted for in the above:

  • u – the probability that a false effect tested gets reported as a positive result, even though it would under ideal conditions have been statistically insignificant.

This fudge factor can incorporate anything from badly designed experiments or researchers being less sceptical of positive results to post-hoc change of study design, p-hacking or even outright fraud. Ioannidis does not go into addressing how likely any of these factors are to contribute to u, but contends himself with re-deriving an expression for the PPV if some amount of bias is taken into account.

The author then considers the effect that multiple groups investigating the same effect independently of one another will have: if just one group has a statistically significant result this is likely to get published even if the negative results of other groups is not. This means that for “hot” topics (which are subject to a great number of parallel experiments) we should be even more weary of single studies reporting statistically significant effects.

Based on his mathematical arguments, Ioannidis then proceeds to give a list of six corollaries, all of which are again reasonably well known to statisticians and most practising scientists (such as “smaller studies tend to have a lower PPV all other factors being equal” or “Greater flexibility in study design and how to measure outcomes leads to a lower PPV”).

In his discussion Ioannidis supports the polemical title of the paper by arguing that even for conservatively chosen values of R, α, β, and u, we would expect a PPV below 50%. Finally he gives an overview of how the state of affairs might be improved. Here his prescriptions are similar to what other statisticians and researches have argued for such as Increasing transparency, (pre-registration of trials; making raw data and code used in analysis available) and encouraging the publication of negative results.

The author concludes by suggesting that it is his personal belief that a number of “classics” in various fields would not hold up if replications thereof were attempted. Given the results of later replication results (such as the Open Science Collaboration 2015 replication attempts of 100 famous results in psychology in the references), this seems prescient.

References

The paper itself:

Ioannidis, J.P.A., 2005. Why Most Published Research Findings Are False. PLoS Medicine, 2(8), p.e124. Available at: http://dx.plos.org/10.1371/journal.pmed.0020124.

Later papers expanding on the topic

Colquhoun, D., 2014. An investigation of the false discovery rate and the misinterpretation of P values. Royal Society Open Science, pp.1–15. Available at: http://rsos.royalsocietypublishing.org/content/1/3/140216.

Jager, L.R. & Leek, J.T., 2014. An estimate of the science-wise false discovery rate and application to the top medical literature. Biostatistics (Oxford, England), 15(1), pp.1–12. Available at: http://biostatistics.oxfordjournals.org/content/15/1/1.

Leek, J.T. & Jager, L.R., 2016. Is most published research really false?, Available at: http://biorxiv.org/lookup/doi/10.1101/050575.

A famous replication study in Psychology

Open Science Collaboration, 2015. Estimating the reproducibility of psychological science. Science, 349(6251), p.aac4716-aac4716. Available at: http://www.ncbi.nlm.nih.gov/pubmed/26315443.

 

Next Wednesday: Why Most Published Research Findings Are False

Next meeting of the Classic papers discussion group will take place next Wednesday (1 Feb. 2017) at 9:30 in the Department of Statistics room LG.05. We will be discussing a modern classic: Why Most Published Research Findings Are False by John P. A. Ioannidis. All participants are welcome (just talk to the receptionist when you arrive if you don’t have building access, she should let you in)

Link to the paper: http://dx.doi.org/10.1371/journal.pmed.0020124

Since its publication, the paper has lead to widespread debate within science about the extent of the problem of irreproducibility: how widespread it is, and what to do about it. Given the central importance of this paper within those debates, as well as the various reproducibility-studies it has spawned, we deem this paper well worth reading, and hope that many people will show up to discuss it with us.

About the classic papers club

The aim of this club is to read the papers that everyone keeps citing but which few people have read. We plan to read a paper every third week for the next 20 years.

We tend to meet Wednesday mornings, and tend to announce the papers we will read ahead of time. Everyone is welcome: if a paper sounds interesting to you, please come by.

This reading group used to be organised on facebook. The old page can be found here.

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About the Science Book Club

This book club has been going on for ages and we have gone through many works. We read a a brisk pace and aim to meet each morning before work and discuss for 90 minutes covering 10-20 pages and then we read next segment in the evening during Oxford Term (http://www.ox.ac.uk/about/facts-and-figures/dates-of-term).
It is clearly very demanding, but we do cover a lot. At the end of the term making a lecture trying to summarise the book (like http://tinyurl.com/RECOMBINATORICS). We sometimes also submit a review of the book. Past books we have read include:

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About the Humanities Book Club

This book club is an endeavour to broaden our horizons and critically engage with good writing from across the humanities. We intend to go through a book per term, and tend to meet roughly once every 3rd week to discuss new sections of whatever book we are currently going through. Past books that we have read include:

  • The General Theory of Employment, Interest and Money, by John Maynard Keynes
  • The Qurʼān – A New Annoteted Translation, by Arthur J. Droge
  • On Politics, by Alan Ryan
  • Capital in the Twenty-First Century, by Thomas Piketty

The size of the reading group is capped at 6 persons. Current members include Jotun Hein, Mathias Cronjäger, James Anderson (former DPhil student), and Eddie Rolls (former summer school student).

Summing up 10 classic papers on Computation

For about 3 years we have every 3rd week read a classic paper in physics, statistics, probability theory, information theory, game theory and computation. So far we have gone through about 40-50 papers and the papers have generally been superb.

Søren Riis (Queen Mary, London) and Jotun Hein gave a talk to summarize 10 of the papers that fall within computation/complexity theory. The papers are Babbage, Turing, McCullough/Pitt, von Neumann, Cook, Karp, Smale, Shor, Impagliazzo, Papadimitriou.

The slides of his presentation are available here