Uncommon Ground

UConn

Alan Gelfand on the history of MCMC and the future of statistics (in a world of data science)

I am fortunate to have known Alan Gelfand for a couple of decades. I first met him in the late 1990s when I walked over to the Math/Science building to talk with him about some problems I was having in my early exploration of Bayesian inference for F-statistics. I was using BUGS (this was pre-WinBUGS), but it was the modeling I needed some advice on. I didn’t realize until a couple of years later that Alan was the Gelfand of Gelfand and Smith, “Sampling-Based Approaches to Calculating Marginal Densities” (Journal of the American Statistical Association 85:398-409; 1990 – doi: 10.1080/01621459.1990.10476213)  and Gelfand et al. “Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling” (Journal of the American Statistical Association 85:972-985; 1990 – doi: 10.1080/01621459.1990.10474968). Fortunately, Alan is too nice to have pointed out how naive I was. He simply gave me a lot of help. I haven’t seen him as often since he moved to Duke, but our paths still cross every year or two, because he and John Silander continue to collaborate on various problems in community ecology.

Alan was a keynote speaker at the Statistics in Ecology and Environmental Monitoring Conference in Queenstown, NZ last December, and David Warton posted a YouTube interview on the Methods Blog of the British Ecological Society. Alan describes the early history of MCMC, mentions his concern about the emergence of “data science”, and talks about what excites him most now – applying statistics to difficult problems in ecology and environmental science.

Trait-environment relationships in Pelargonium

Almost 15 years ago Wright et al. (Nature 428:821–827; 2004 – doi: 10.1038/nature02403) described the worldwide leaf economics spectrum “a universal spectrum of leaf economics consisting of key chemical, structural and physiological properties.” Since then, an enormous number of articles have been published that examine or refer to it – more than 4000 according to Google Scholar. In the past few years, many authors have pointed out that it may not be as universal as originally presumed. For example, in Mitchell et al. (The American Naturalist 185:525-537; 2015 – http://www.jstor.org/stable/10.1086/680051) we found a negative relationship between an important component of the leaf economics spectrum (leaf mass per area) and mean annual temperature in Pelargonium from the Cape Floristic Region of southwestern South Africa, while the global pattern is for a positive relationship.1

Now Tim Moore and several of my colleagues follow up with a more detailed analysis of trait-environment relationships in Pelargonium. They demonstrate several ways in which the global pattern breaks down in South African samples of this genus. Here’s the abstract and a link to the paper.

  • Functional traits in closely related lineages are expected to vary similarly along common environmental gradients as a result of shared evolutionary and biogeographic history, or legacy effects, and as a result of biophysical tradeoffs in construction. We test these predictions in Pelargonium, a relatively recent evolutionary radiation.
  • Bayesian phylogenetic mixed effects models assessed, at the subclade level, associations between plant height, leaf area, leaf nitrogen content and leaf mass per area (LMA), and five environmental variables capturing temperature and rainfall gradients across the Greater Cape Floristic Region of South Africa. Trait–trait integration was assessed via pairwise correlations within subclades.
  • Of 20 trait–environment associations, 17 differed among subclades. Signs of regression coefficients diverged for height, leaf area and leaf nitrogen content, but not for LMA. Subclades also differed in trait–trait relationships and these differences were modulated by rainfall seasonality. Leave‐one‐out cross‐validation revealed that whether trait variation was better predicted by environmental predictors or trait–trait integration depended on the clade and trait in question.
  • Legacy signals in trait–environment and trait–trait relationships were apparently lost during the earliest diversification of Pelargonium, but then retained during subsequent subclade evolution. Overall, we demonstrate that global‐scale patterns are poor predictors of patterns of trait variation at finer geographic and taxonomic scales.

doi.org/10.1111/nph.15196

  1. If you read The American Naturalist paper, you’ll see that we wrote in the Discussion that “We could not detect a relationship between LMA and MAT in Protea….” I wouldn’t write it that way now. Look at Table 2. You’ll see that the posterior mean for the relationship is 0.135 with a 95% credible interval of (-0.078,0.340). I would now write that “We detected a weakly supported positive relationship between LMA and MAT….” Why the difference? I’ve taken to heart Andrew Gelman’s observation that “The difference between significant’ and ‘not significant’ is not itself statistically significant” (blog post; article in The American Statistician). I am training myself to pay less attention to which coefficients in a regression and which aren’t and more to reporting the best guess we have about each relationship (the posterior means) and the amount of confidence we have about them (the credible intervals). I recently learned about hypothesis() in brms, which will provide an estimate of the posterior probability that the you’ve got the sign of the relationship right. I need to investigate that. I suspect that’s what I’ll be using in the future.

Honoring Ruth Millikan

Ruth Millikan is Emeritus Board of Trustees Distinguished Professor of Philosophy at UConn. Quoting from her web page, Ruth’s “research interests span many topics in the philosophy of biology, philosophy of mind, philosophy of language, and ontology.” She is a highly respected and influential philosopher. From her Wikipedia page:

She was awarded the Jean Nicod Prize and gave the Jean Nicod Lectures in Paris in 2002.[3] She was elected to the American Academy of Arts and Sciences in 2014 [4] and received, in 2017, both the Nicholas Rescher Prize for Systematic Philosophy from the University of Pittsburgh[5] and the Rolf Schock Prize in Logic and Philosophy.[6]

On April 30th I had the great honor of presenting a few remarks at an event held to celebrate Ruth’s contributions and to inaugurate the Ruth Garrett Millikan Endowment to support graduate students. Daniel Dennett was the featured speaker, and he highlighted Ruth’s contributions, focusing especially on one of her early books – Language, Thought, and Other Biological Categories – and her most recent one – Beyond Concepts. If you want to understand why her work is so important, you’ll need to read those books yourself. Her Wikipedia page provides only a very brief summary.

My comments focused on why graduate education, particularly PhD education, and financial support for graduate education is vital. On the off chance you’re interested in reading what I had to say, the full text of my remarks follows.

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