quant.bio ^{PREVIEW} | A mathematical way to think about biology | main site | handouts | @ | + ■ ■ ■ ■ ■ - | + ■ ■ ■ ■ ■ - |
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© Copyright 2011-2015 David Liao. Open access and copyright information |
Information overload is neither necessary nor sufficient for developing strategic insight.
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Excellent site for both basic and advanced lessons on applying mathematics to biology. |
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The appendix includes a discussion of algebra, precalculus, and calculus. |
Even though academic tradition is a major contributor to the adoption of criteria for declaring statistical "significance," for example, the arbitrary p < 0.05 criterion, it is possible to choose criteria in a more rational manner. For example, a pharmaceutical company could compare potential research and legal costs with potential profits to conclude that it can only afford to move on to Phase III trials for experimental therapies that rule out a null hypothesis at a p < 0.01 level during Phase II trials.
95% confidence intervals do not necessarily thread the means of their associated parent distributions 95% of the time. Confidence intervals can be meaningless when derived from faulty assumptions.
Rejecting models having p < 0.1 does not ensure that 90% of surviving models are valid. Human imagination easily contrives a large number mutually incompatible models, each of which is consistent with a given set of experimental data at the p > 0.1 level. This consistency cannot logically guarantee that 90% of the models are valid since, by construction, most of them are false.
[6] PDF Nuzzo, Nature 506: 150-152 (2014).The ability of a system of DEs to produce solutions that resemble data does not rule out alternative descriptions of dynamics.
[8] PDF Ferrell, Jr., Tsai, and Yang, Cell, 144: 874-885 (2011).The success of a non-spatial model in mimicking aggregate population dynamics does not rule out a spatially-resolved model.
If closed universes (eventually) explore all accessible states equally, then small subsystems can be studied using partition functions
DISCLAIMER: The following video chapter is a simplified introduction that can be used in algebra-based high school physics classes. This is not a replacement for the references below.