IGEM:IMPERIAL/2008/Prototype/Drylab/Data Analysis: Difference between revisions

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In this '''[[IGEM:IMPERIAL/2008/Prototype/Drylab/Data_Analysis/Model_Fit|first level of inference]]''', we apply Bayes' Theorem. We first assume a particular model, and go on to derive the parameters of our model which maximises the data obtained.
In this '''[[IGEM:IMPERIAL/2008/Prototype/Drylab/Data_Analysis/Model_Fit|first level of inference]]''', we apply Bayes' Theorem. We first assume a particular model, and go on to derive the parameters of our model which maximises the data obtained.
===Mechanical Model===
The following trajectories were fitted based on the above equations, and corresponding parameters determined:
{| border="1" cellpadding="5" cellspacing="0" align="center"
|-
|[[Image:V15Cell1.JPG|thumb|center|300px|100908 Video 15 Cell 1 Trajectory]]
|[[Image:V15Cell2.jpg|thumb|center|300px|100908 Video 15 Cell 1 Trajectory]]
|-
|A=[-102.2628  -67.2227], B=[362.5003  -92.3339], alpha=0.2500
|A=[-109.7191  -7.7453], B=[219.2134 -154.1100], alpha=0.4342
|-
|[[Image:V15Cell3.jpg|thumb|center|300px|100908 Video 15 Cell 1 Trajectory]]
|[[Image:V15Cell4.jpg|thumb|center|300px|100908 Video 15 Cell 1 Trajectory]]
|-
|A=[57.0606  -29.0868], B=[12.0191  25.8818], alpha=2.4867
|A=[28.8774  116.5196], B=[-790.7562  -1162.5363], alpha=0.1231
|-
|}


==Assigning Preferences to Alternative Models==
==Assigning Preferences to Alternative Models==

Revision as of 10:01, 23 September 2008

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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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Model Fitting

Alternative Models

Models of run velocity include a Gaussian Distribution, or the Maxwell Distribution which govern the velocities and energies of molecules. An exponential distribution may describe the memoryless characteristic of run duration. We will build up a database of models, for future model fitting.

Mechanical Model

We have created a simple mechanical model of motile bacteria, depicted in the figure below.

Fitting Models to Data

In this first level of inference, we apply Bayes' Theorem. We first assume a particular model, and go on to derive the parameters of our model which maximises the data obtained.

Mechanical Model

The following trajectories were fitted based on the above equations, and corresponding parameters determined:

100908 Video 15 Cell 1 Trajectory
100908 Video 15 Cell 1 Trajectory
A=[-102.2628 -67.2227], B=[362.5003 -92.3339], alpha=0.2500 A=[-109.7191 -7.7453], B=[219.2134 -154.1100], alpha=0.4342
100908 Video 15 Cell 1 Trajectory
100908 Video 15 Cell 1 Trajectory
A=[57.0606 -29.0868], B=[12.0191 25.8818], alpha=2.4867 A=[28.8774 116.5196], B=[-790.7562 -1162.5363], alpha=0.1231

Assigning Preferences to Alternative Models

In this second level of inference, we use the evidence contributed by the data to compare fitted models. Using Occam's Razor, we are then able to deduce the best model which fits our data.


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