Written by Christian Page July 2011
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I.   Preface	
II.  Introduction to the biological problem to model
III. Assuptions under the model
IV.  Input/output for the model
V.   Documentation of funcitons
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I.
This program is under NO copyright, and may be used for any purposes. 
The use of this program is at your own risk, and comes with ABSOLUTLY NO WARRANTY. 
The program uses the library GSL (Gnu scientific library), so this should be installed 
before compiling and running the program. 


II.
This program is used in relation to a genetic circuit in E. coli for a double repressor.

The biological component in the systems should react under stress (eks. heat). 
Any stress in the cell will initiate the production of the stress protein ppGpp, 
which inhibits the production of lacI, from the Lac operon, lacI inhibits the 
production of mCherry (RPF, Red Fluorecens Protein), so if ppGpp is present, 
then mCherry should be expressed, and the cell turns red.

The problem is modeled as a stochastic process "with only one path", it completes this 
path successfully with the product of all the transitionprobabilities at each step. 
The step in the process is either an inhibitation of a gene, or a transcription. 

Any deviation from the path i the process will be considerd as a failure, and modeled as (1 - \theta), 
where \theta is the probability for a bacteria to succesfully express RFP under no data integration.

The model is a combination of a Gibbs sample and a Metropolis (Hastings) algorithm, integration data 
and prior assumptions / information.

-------Define X and Y and Z-----------------------

III.
The prior assuption is that the transition probabilityes are Beta distributed with \alpha_[i], and \beta_[i], 
where i goes from 1 to the nuber of different stages in the process, this number is adjustable.

One of the main assuption is that the probability for sucess, is independent of stress, 
that is; it is equally likely for the bacteria to glow red under stress, as for the bacteria 
to not glow red in the abstens of stress. According to the biologists this is a reasonable assumption, 
and does not violate any thing.

Assuming that the transition probability is Beta distributed, and the probability for success in the 
integrated data is binomial distributed conditioned on the transition, then the full conditional for 
the posterior theta (product of all the transition) is Beta distributited with a, only with change parameters. 

Then a Gibbs sampler is run to sample the \theta, based on the \theat one can then sample Z, 
in this program a Metroplolis-Hastings algortim was chosen, .. gibbs..?

 
IV.
The program takes inn the \alpha ´s and \beta `s for the beta distribution in for the transition probabilitys, t
the number of simulaitons has to be chosen, recommended will be from 2500 and up. The number of steps in the 
chan can also be set, but has to agree with \alpha and \beta. Last the data to integrate has to be added, 
this as the number of trails, and the nuber of successes. 

All this is set in the preface of the program under globale constants.

Out of the program comes the simulated values for Z, as one long list, with the length equal to the number of simulations.