A Presentation of ‘Bayesian Models for Gene Expression With DNA Microarray Data’ by Ibrahim, Chen, and Gray. Presentation By Lara DePadilla. Goal. To “develop a novel class of parametric statistical models for analyzing DNA microarray data’.
Presentation By Lara DePadilla
Why? Because of the sheer number of genes in the human genome we must identify which one are relevant to our purpose.
Why? We must develop models to explain the patterns in order to recognize them.
The next step invokes Bayes rule
2. f(Ө,y) = f(Ө) * f(y|Ө)
Now we know what we are looking for.
3. This step is evaluate and improve upon what we have done.
Data Structure of Observations
More Data Preparation
⇒ c0 is the threshold value for a gene is considered not
expressed (and therefore not what we are seeking), so
if x = c0, it is not expressed
so, x = c0 with probability p
x = c0 +ywith probability 1 – p
where y is the level of expression
pjg = P(xjig = c0) = P(δ = 1)
1 – pjg= P(xjig = c0 + yjig) = P(δ = 0)
D = (x111,…, x2,n2,G)
П j = 1 to 2 П I = 1 to nj П g = 1 to G (pjgδjig)(1- p)1 - δjig *p(yjig| μjg,σ2jg) 1 - δjig
Interpreted: This is the product of the probability distribution function (the probability that a gene qualifies for being of interest to the study) of each data point to give the overall likelihood.
which is the probability given the data (the individuals in the study) that the ratio will exceed 1.
⇒how well the model predictions compare to the
⇒ the variability of the predictions
Number of genes to be declared different based on Several Choices of Hyperparameters and Various Choices of γ0