IGEM:IMPERIAL/2008/Prototype/Drylab/Data Analysis/Model Fit

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<html><a href=http://openwetware.org/wiki/IGEM:IMPERIAL/2008/Prototype><img width=50px src=http://openwetware.org/images/f/f2/Imperial_2008_Logo.png></img</a></html> Home The Project B.subtilis Chassis Wet Lab Dry Lab Notebook

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Fitting Models to Data

The Bayesian Approach

File:Exppos.TIF

Bayes' Theorem

Bayes' theorem states that the posterior is equal to the product of the likelihood and prior, normalised by the evidence: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.} For example, given an exponential distribution, the posterior is: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle P(\lambda|x) = \frac{P(x|\lambda)\, P(\lambda)}{P(x)}.} The amount of data we obtain is crucial in determining the amount of error associated with deriving the posterior. As the size of the data set increases, the standard deviation of the posterior decreases and its maximum increases. The figure on the right shows the posterior of an exponential distribution plotted against its parameter Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda} for various sizes of data sets.



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