Hi you all!

I've got a problem when trying to analyze some biological data in my PhD. Let's say that I'm interested in performing an analysis using observed values of a random variable (

Where

What I would like to do here is:

I guess that, if it is possible to obtain a likelihood function from here, calculating an expression for maximize likelihood for a parameter is more or less straight forward.

I would like to add some extra information about the analysis and variable I'm working with:

* There is no complete independence between observations. For example, observation

* Regression can be done, since

I've got a problem when trying to analyze some biological data in my PhD. Let's say that I'm interested in performing an analysis using observed values of a random variable (

*O*), whose distribution is unknown, and their expected values (*E*) using a model like:*Ei*=*k1 * exp ( - k2 · xi )*Where

*k1*and*k2*are known constants,*Ei*is the expected value of the variable in an observation*i*, and*xi*is the value of a variable in the observation*i*, that I also can calculate.What I would like to do here is:

**1)**to calculate how likely is the data (*O*) given this model (*E*), that is:*p(O|E)*. So I wonder if non-parametric likelihood (NPMLE) is what I have to try here. In that case, what would be a good start point? I know nothing about NPMLE.I guess that, if it is possible to obtain a likelihood function from here, calculating an expression for maximize likelihood for a parameter is more or less straight forward.

**2)**Once done**1)**and, since variable x depends also in another variable y, given two different scenarios,*E1*(*x1*,*y1*) and*E2*(*x2*,*y2*), it would be possible to calculate a p-value in order to evaluate differences in*E1*and*E2*?I would like to add some extra information about the analysis and variable I'm working with:

* There is no complete independence between observations. For example, observation

*i=1*can be independent of*i=2*, but*i=1*and*i=3*can be highly dependent. So some test like Pearson's chi squared test should be avoid to solve this task.* Regression can be done, since

*log(Ei)*=*log(k1) - k2*x1*, but I'm looking for an additional analysis that does not need*log*transformation.
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