tag:blogger.com,1999:blog-5822805028291837738.post7728721502175412415..comments2022-11-30T11:50:19.185-05:00Comments on Various Consequences: Chaos: A Very Short Introduction (Book Review)Joshua Stultshttp://www.blogger.com/profile/03506970399027046387noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5822805028291837738.post-14177256889501515002009-12-23T10:45:42.547-05:002009-12-23T10:45:42.547-05:00See also Accountability and Error in Ensemble Fore...See also <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.28.2662&rep=rep1&type=pdf" rel="nofollow">Accountability and Error in Ensemble Forecasting</a> by L.A. SmithJoshua Stultshttps://www.blogger.com/profile/03506970399027046387noreply@blogger.comtag:blogger.com,1999:blog-5822805028291837738.post-74134014186659165722009-12-23T10:17:02.308-05:002009-12-23T10:17:02.308-05:00Smith also wrote Chapter 2 (preview on Google Book...Smith also wrote <a href="http://books.google.com/books?id=pH_OmkD4ZaQC&lpg=PA31&ots=uM_I10Xbcw&dq=%22Smith%22%20%22Disentangling%20uncertainty%20and%20error%3A%20On%20the%20...%22%20&lr=&pg=PA31#v=onepage&q=&f=false" rel="nofollow">Chapter 2</a> (preview on Google Books) of <a href="http://www.amazon.com/gp/product/0817641637?ie=UTF8&tag=variouconseq-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0817641637" rel="nofollow">Nonlinear Dynamics and Statistics</a>, the focus of which is the predictability of nonlinear systems.<br /><br />Here's a snipet:<br />"Our agent achieves an accountable forecast by evolving a perfect ensemble under a a perfect model; once imperfect models are in use, no perfect ensemble exists. Accepting this forces us to change the interpretation and goals of forecasts. In fact, it calls into question what is meant by the state of a physical system."<br /><br /><i>Ensemble</i> here refers to the set of different initial conditions given to the model to reflect observational uncertainty. Smith's claim is that you can only get an 'accountable probabilistic forecast' from such a set given to a <i>perfect</i> model as initial conditions. <br /><br />The Bayesian rightly observes that no model has a prior probability of exactly 1 (in the perfect case) , or exactly 0 (for every other model), but every real model has some finite prior. The reason that every model has some finite prior is that our state of knowledge is limited and imperfect, it would be dishonest for us too assign a prior of 1 or 0 to a model, we can never really be that sure. This fact is exploited in <a href="http://j-stults.blogspot.com/2009/12/bayesian-climate-model-averaging.html" rel="nofollow">Bayesian Climate Model Averaging</a>.Joshua Stultshttps://www.blogger.com/profile/03506970399027046387noreply@blogger.com