Like (C) it is simple, but reflects different decisions about which information to discard or retain. (D) The New Haven property map of the region around Osborn Memorial Laboratory, showing property lines and plot numbers. (C) An even more simplified map, focused on showing the Yale Shuttle routes. It has less information, but is more useful for some tasks such as navigation. (B) A street map of the same region, also from Google Maps. This image has a very large amount of information. (A) A satellite image of New Haven, including much of Yale campus, from Google Maps.

The simplification is often what makes the map useful.įigure 3.1: Four maps of the Yale campus, varying in complexity and focus. So all maps are simplifications (Figure 3.1). Of the things you would like to do with a map. A “perfect” map would basicallyīe a copy of the whole world, which wouldn’t be that much more useful than the world itself already is for many Rough approximations of a system, another scientist may be interested in second and third order effectsįor which more complexity is needed for adequate explanation.Ĭartography is an interesting analogy for the way we will use statistical models. In the eye of the beholder – one scientist will be perfectly happy with a model that makes reasonable They areĪs simple as possible, while adequately describing the phenomenon of interest. Instead, the most useful models strike a trade-off between simplicity and adequacy. Real data are far too complex for any model to do this. The goal of a model isn’t to be “right” in the sense of being a perfect explanation ofĭata. Statisticians often note that “All models are wrong but someĪre useful”, a common aphorism expanded from a quote by Box ( 1976). Want models that give us the right answer for the right reasons. We don’t just want models that give us the right answer, we often Many of our questions have to do with the mechanisms that underlay the processes In science, though, we often care very much about the model because The model does a reasonable job of making useful

Purchasing rates and all the other things that impact stock, so long as the Need to stock at each store, they likely don’t care if their models properly consider 2001).įor example, if data scientists at a large retail chain are trying to predict how much toothpaste they Processes, as long as it generates useful output ( Breiman et al. Matter if model structure reflects actual underlying They are abstractions in the sense that they leave out things that aren’t thought to be important, and they are idealized in the sense that they are deliberately simplified ( Godfrey-Smith 2013, 21). A.1 Probability theory and General statistics.A Statistical and mathematical fundamentals.11.4 Phylogenetic structure is the expected covariance structure.11.3 Phylogenetic Independent Contrasts.11.2 Inferring covariance in the absence of phylogenetic structure.10 Ancestral character state reconstruction.9.3.1 Mathematical implications of age constraints.6.1.3 Adding complexity to DNA evolution models.5.7 Combining information across multiple genome regions.5.5 Working with publicly available data.5.4.2 Identification of homologous genome regions.5.4 Data processing upstream of phylogenetic analyses.3.8 Scaling from a single site to multiple sites.

3.7 Scaling from a single branch to a whole tree.3.5 Plugging some numbers into the expanded model.2.9 The information contained in phylogenies.1.3 A unified perspective on phylogenetic studies.

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