"[…] no good model ever accounted for all the facts, since some data was bound to be misleading if not plain wrong. A theory that did fit all the data would have been ‘carpentered’ to do this and would thus be open to suspicion." (Francis H C Crick, "What Mad Pursuit: A Personal View of Scientific Discovery", 1988)
"There is no sharp dividing line between scientific theories and models, and mathematics is used similarly in both. The important thing is to possess a delicate judgement of the accuracy of your model or theory. An apparently crude model can often be surprisingly effective, in which case its plain dress should not mislead. In contrast, some apparently very good models can be hiding dangerous weaknesses." (David Wells, "You Are a Mathematician: A wise and witty introduction to the joy of numbers", 1995)
"A good model makes the right strategic simplifications. In fact, a really good model is one that generates a lot of understanding from focusing on a very small number of causal arrows." (Robert M Solow, "How Did Economics Get That Way and What Way Did It Get?", Daedalus, Vol. 126, No. 1, 1997)
"The effectiveness of an overall design is very sensitive to the quality and consistency of fine-grained design and implementation decisions. With a MODEL-DRIVEN DESIGN, a portion of the code is an expression of the model; changing that code changes the model. Programmers are modelers, whether anyone likes it or not. So it is better to set up the project so that the programmers do good modeling work." (Eric Evans, "Domain-Driven Design: Tackling complexity in the heart of software", 2003)
"A smaller model with fewer covariates has two advantages: it might give better predictions than a big model and it is more parsimonious (simpler). Generally, as you add more variables to a regression, the bias of the predictions decreases and the variance increases. Too few covariates yields high bias; this called underfitting. Too many covariates yields high variance; this called overfitting. Good predictions result from achieving a good balance between bias and variance. […] fiding a good model involves trading of fit and complexity." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)
"The definition of a ‘good model’ is when everything inside it is visible, inspectable and testable. It can be communicated effortlessly to others. A ‘bad model’ is a model that does not meet these standards, where parts are hidden, undefined or concealed and it cannot be inspected or tested; these are often labelled black box models." (Hördur V Haraldsson & Harald U Sverdrup, "Finding Simplicity in Complexity in Biogeochemical Modelling" [in "Environmental Modelling: Finding Simplicity in Complexity", Ed. by John Wainwright and Mark Mulligan, 2004])
"A model is a good model if it:1. Is elegant 2. Contains few arbitrary or adjustable elements 3. Agrees with and explains all existing observations 4. Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out." (Stephen Hawking & Leonard Mlodinow, "The Grand Design", 2010)
"One good experiment is worth a thousand models […]; but one good model can make a thousand experiments unnecessary." (David Lloyd & Evgenii I Volkov, "The Ultradian Clock: Timekeeping for Intracelular Dynamics" [in "Complexity, Chaos, and Biological Evolution", Ed. by Erik Mosekilde & Lis Mosekilde, 2013)
"A complete data analysis will involve the following steps: (i) Finding a good model to fit the signal based on the data. (ii) Finding a good model to fit the noise, based on the residuals from the model. (iii) Adjusting variances, test statistics, confidence intervals, and predictions, based on the model for the noise." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)
"A good model is simple, valid, and robust. Simplicity of a model is really the key essence of what modeling is all about. The main reason why we want to build a model is that we want to have a shorter, simpler description of reality. [...] Validity of a model is how closely the model’s prediction agrees with the observed reality. This is of utmost importance from a practical viewpoint. If your model’s prediction doesn’t reasonably match the observation, the model is not representing reality and is probably useless. [...] finally, robustness of a model is how insensitive the model’s prediction is to minor variations of model assumptions and/or parameter settings. This is important because there are always errors when we create assumptions about, or measure parameter values from, the real world. If the prediction made by your model is sensitive to their minor variations, then the conclusion derived from it is probably not reliable." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)
"A mathematical model is never a completely accurate representation of a physical situation - it is an idealization. A good model simplifies reality enough to permit mathematical calculations but is accurate enough to provide valuable conclusions. It is important to realize the limitations of the model. In the end, Mother Nature has the final say." (James Stewart, "Calculus: Early Transcedentals" 8th Ed., 2016)
"Model-building requires much more than just technical knowledge of statistical ideas. It also requires care and judgment, and cannot be reduced to a flowchart, a table of formulas, or a tidy set of numerical summaries that wring every last drop of truth from a data set. There is almost never a single 'right' statistical model for some problem. But there are definitely such things as good models and bad models, and learning to tell the difference is important. Just remember: calling a model good or bad requires knowing both the tool and the task." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)
No comments:
Post a Comment