Archive for Stephen Senn

statistics in Nature [a tale of the two Steves]

Posted in Books, pictures, Statistics with tags , , , , , , , , , on January 15, 2019 by xi'an

In the 29 November issue of Nature, Stephen Senn (formerly at Glasgow) wrote an article about the pitfalls of personalized medicine, for the statistics behind the reasoning are flawed.

“What I take issue with is the de facto assumption that the differential response to a drug is consistent for each individual, predictable and based on some stable property, such as a yet-to-be-discovered genetic variant.”S. Senn

One (striking) reason being that the studies rest on a sort of low-level determinism that does not account for many sources of variability. Over-confidence in causality results. Stephen argues that improvement lies in insisting on repeated experiments on the same subjects (with an increased challenge in modelling since this requires longitudinal models with dependent observations). And to “drop the use of dichotomies”, favouring instead continuous modeling of measurements.

And in the 6 December issue, Steven Goodman calls (in the World view tribune) for probability statements to be attached as confidence indices to scientific claims. That he takes great pain to distinguish from p-values and links with Bayesian analysis. (Bayesian analysis that Stephen regularly objects to.) While I applaud the call, I am quite pessimistic about the follow-up it will generate, the primary reply being that posterior probabilities can be manipulated as well as p-values. And that Bayesian probabilities are not “real” probabilities (dixit Don Fraser or Deborah Mayo).

selected parameters from observations

Posted in Books, Statistics with tags , , , , , , , on December 7, 2018 by xi'an

I recently read a fairly interesting paper by Daniel Yekutieli on a Bayesian perspective for parameters selected after viewing the data, published in Series B in 2012. (Disclaimer: I was not involved in processing this paper!)

The first example is to differentiate the Normal-Normal mean posterior when θ is N(0,1) and x is N(θ,1) from the restricted posterior when θ is N(0,1) and x is N(θ,1) truncated to (0,∞). By restating the later as the repeated generation from the joint until x>0. This does not sound particularly controversial, except for the notion of selecting the parameter after viewing the data. That the posterior support may depend on the data is not that surprising..!

“The observation that selection affects Bayesian inference carries the important implication that in Bayesian analysis of large data sets, for each potential parameter, it is necessary to explicitly specify a selection rule that determines when inference  is provided for the parameter and provide inference that is based on the selection-adjusted posterior distribution of the parameter.” (p.31)

The more interesting distinction is between “fixed” and “random” parameters (Section 2.1), which separate cases where the data is from a truncated distribution (given the parameter) and cases where the joint distribution is truncated but misses the normalising constant (function of θ) for the truncated sampling distribution. The “mixed” case introduces an hyperparameter λ and the normalising constant integrates out θ and depends on λ. Which amounts to switching to another (marginal) prior on θ. This is quite interesting even though one can debate of the very notions of “random” and “mixed” “parameters”, which are those where the posterior most often changes, as true parameters. Take for instance Stephen Senn’s example (p.6) of the mean associated with the largest observation in a Normal mean sample, with distinct means. When accounting for the distribution of the largest variate, this random variable is no longer a Normal variate with a single unknown mean but it instead depends on all the means of the sample. Speaking of the largest observation mean is therefore misleading in that it is neither the mean of the largest observation, nor a parameter per se since the index [of the largest observation] is a random variable induced by the observed sample.

In conclusion, a very original article, if difficult to assess as it can be argued that selection models other than the “random” case result from an intentional modelling choice of the joint distribution.

 

another Sally Clark?

Posted in Statistics, University life with tags , , , , , , on February 22, 2015 by xi'an

“I don’t trust my own intuition when an apparent coincidence occurs; I have to sit down and do the calculations to check whether it’s the kind of thing I might expect to occur at some time and place.” D. Spiegelhalter

I just read in The Guardian an article on the case of the nurse Benjamin Geen, whose conviction to 30 years in jail in 2006 for the murder of two elderly patients rely on inappropriate statistical expertise. As for Sally Clark, the evidence was built around “unusual patterns” of deaths associated with a particular nurse, without taking into account the possible biases in building such patterns. The case against the 2006 expertise is based on reports by David Spiegelhalter, Norman Fenton, Stephen Senn and Sheila Bird, who constitute enough of a dream team towards reconsidering a revision of the conviction. As put forward by Prof Fenton, “at least one hospital in the country would be expected to see this many events over a four-year period, purely by chance.”