Likelihood of an algorithm-based function Forgive me if this is a dumb question, but it is way outside of my area of expertise. 
Suppose I have an algorithm that produces some sort of a fit function, but that fit is not expressed in closed form (e.g., computational models in biology or cognitive psychology). In other words, to find the optimal parameter, I have to simulate data based on the parameters, do a bunch of steps, simulate some sort of psychological or biological process, do a bunch of mathematical gymnastics, then finally I have a simulated behavior based on the $\theta$ values, which I then compare to the actual behavior. I then compute some sort of fit function that compares the simulated behavior to the actual behavior (e.g., sum of squared errors or something), then modify the $\theta$ values until the discrepancy is very small.  
What I want to do is incorporate some bayesian statistics into this computational model (so I can include prior information). I know that a poster $\propto$ likelihood $\times$ prior. I can easily get the priors (based on the literature), but how do I convert the results of the algorithm into a likelihood?
My best guess is to do the following:


*

*Run the computational model algorithm with a bunch of different values for the parameter of interest (e.g., $\theta_1$), holding other parameters constant.

*For each proposed $\theta_1$ value, compute the $sse$.

*Invert $sse$ (to come up with a crude likelihood measure that increases as fit increases).

*Scale all inverted $sse$'s such that they sum to one to compute my pdf. 

*Repeat for all $\theta_2:\theta_k$. 


Will this work to convert the results of an algorithm into a likelihood? If not, what else can I do?
Edit
Here's a bit more details. I'm trying to make an existing model of facial recognition under a criminal lineup (witness) bayesian. The basic idea is this:


*

*Simulate a vector of "features" from a uniform distribution for the criminal

*Simulate encoding of said features into one's memory by creating a new vector that is identical to the criminal vector for $\theta_1$ of features. We will call this vector the memory vector. 

*Simulate "foils" that are used in the same lineup by creating 5 additional vectors that share $\theta_2$ of the features from the criminal vector.

*Simulate picking the criminal out of a lineup by computing the dot product between the memory vector and each of the foil vectors and the criminal vector. If the dot product exceeds some value ($\theta_3$), a decision is made as to who the witness thinks committed the crime. Otherwise, the person makes no decision. 

*Record the proportion of times the simulated individuals picked the right person/wrong person/no person and compare it to the actual number of times experimental subjects picked the right/wrong/no person. This is typically done using $sse$. 

*We adjust $\theta_1-\theta_3$ until the simulated data matches closely the experimental data (typically done through genetic algorithm). 


So, how do I convert $sse|\theta_1, \theta_2, \theta_3$ into a likelihood so I can allow bayesian estimation?
 A: So you can simulate pseudo observations given the parameters. 
In this case it might be helpful to use Approximate Bayesian Computation (ABC). In its crudest form you: define a distance metric between the observed data and some pseudo data; simulate parameter values from your prior and in each simulation generate a pseudo data set; retain all parameter values where the distance between the observed and pseudo data are small. This produces an approximate sample from the posterior.
If you gave a bit more info we might be able to suggest some appropriate metric.
Response to Edit
Steps 1-6 are your means of generating a pseudo sample given the parameters. sse is your distance metric. 
So you could simulate steps 1-6 many times and only retain simulations where sse is less than some value, k say. As k goes to zero you will get a more accurate estimate of the posterior. 
If you had all the time in the world, you could only retain simulations in which the pseudo data exactly corresponded to the actual data--this is possible in your case as you have discrete outcomes (0 or 1 for each lineup) although probably infeasible if the sample size is moderate. Even if you don't, however, any distance metric you use is just an approximation of this "exact" rejection criteria.
