# The question about Turing likelihood
**URL:** https://discourse.julialang.org/t/the-question-about-turing-likelihood/129293
**Category:** New to Julia
**Tags:** question, turing
**Created:** [May 24, 2025, 2:31pm UTC](https://discourse.julialang.org/t/the-question-about-turing-likelihood/129293 "2025-05-24T14:31:27Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Cyan](https://discourse.julialang.org/u/Cyan)
#### Post date: [May 24, 2025, 2:31pm UTC](https://discourse.julialang.org/t/the-question-about-turing-likelihood/129293/1 "2025-05-24T14:31:27Z")
Hi, all. I am new to Julia, I am trying to fit an image model, I aim to minimize the model image and observed image:
```julia
minimize(sum(model_intensity - data_obs))
```
both model\_intensity and data\_obs are 2d-array.
I am not sure the following likelihood meets my requirement:
```julia
for i in eachindex(data_obs)
data_obs[i] ~ Normal(model_intensity[i], sigma)
end
```
---
### Author:  [@sethaxen](https://discourse.julialang.org/u/sethaxen)
#### Post date: [May 24, 2025, 4:26pm UTC](https://discourse.julialang.org/t/the-question-about-turing-likelihood/129293/2 "2025-05-24T16:26:00Z")
The problem with minimizing the sum is that it’s numerically the same as
```julia
minimize(sum(model_intensity) - sum(data_obs))
```
So you’re effectively collapsing each image down into a single scalar and then comparing those scalars, which is not very informative. You probably want to minimize the mean squared error (corresponds to a Normal likelihood) or mean absolute error (corresponds to a Laplace likelihood).
---
### Author:  [@Cyan](https://discourse.julialang.org/u/Cyan)
#### Post date: [May 24, 2025, 4:28pm UTC](https://discourse.julialang.org/t/the-question-about-turing-likelihood/129293/3 "2025-05-24T16:28:33Z")
Thank you for your replay. Yes, I want to minimize the mean square error. Is the above formula correct?
---
### Author:  [@ForceBru](https://discourse.julialang.org/u/ForceBru)
#### Post date: [May 24, 2025, 7:24pm UTC](https://discourse.julialang.org/t/the-question-about-turing-likelihood/129293/4 "2025-05-24T19:24:41Z")
Looks correct to me. MSE is the negative log-likelihood of a normal distribution with fixed variance. Your code says that each `data_obs[i]` is normally distributed with the expected value given by your model, which is correct.