Advice on choosing a likelihood distribution for data in logaritmic units I have a Bayesian model to fit a set of parameters given some observables (flux from astronomical objects). Since many users will prefer to define the priors using logarithmic units and I could remove some exponentials I decided to write the mathematical model in log scale.
My issue arrived while defining the likelihood: I decided on a normal distribution since it represents the physics well in which the $\mu=\log(y_{\text{model}})$.
My issue lies in defining the $\sigma$ for this distribution for which I wanted to use the observational uncertainty. To start $\log \sigma_{\text{obs}}$ is negative in my case so it cannot be applied to define the normal distribution sigma. If I take the absolute value the likelihood is actually so wide the model is poorly fitted since basically all proposal values are accepted. 
I wonder if anyone could point out the error in my logic or advice me which distribution I should be using to define a likelihood for data where $\log y_{\text{obs}} <0$ and $\log \sigma_\text{obs} <0$.
UPDATE:
If I were in linear scale I would generate a normal distribution with $N(\mu,\sigma^{2})$, however I have $\log \mu < 0$ and $\log \sigma<0$. Which is the equivalent distribution for this case?
 A: If you are going to use logarithms on your data, and then model the transformed data with a normal distribution, you are implicitly using a log-normal distribution for your untransformed data.  If you do this, you need to take logarithms of all the individual data points first, and then model these using a normal distribution.  The parameters $\mu$ and $\sigma$ then describe the mean and standard deviation of the logarithms, which is not the same as the logarithms of the mean and standard deviation of the original (untransformed) data.  It makes no sense to first take the standard deviation and then take the logarithm of that value.
From your description, it sounds like you have some original (untransformed) data $y_1,...,y_n$ and you are modelling this as $\ln Y_i \sim \text{IID N}(\mu, \sigma^2)$, which is the same as the model:
$$Y_i \sim \text{IID Log-N}(\mu, \sigma^2).$$
Using the moment properties of the normal distribution, the parameters can be interpreted as:
$$\mu = \mathbb{E}(\ln Y_i) \quad \quad \quad \sigma^2 = \mathbb{V}(\ln Y_i).$$
Alternative, using the moment properties of the log-normal distribution, and a bit of algebra, the parameters can be interpreted in terms of the original data values as:
$$\mu = - \frac{1}{2} \ln \mathbb{E}(Y_i^2) \quad \quad \quad \sigma^2 = \ln \mathbb{E}(Y_i^2) - \ln \mathbb{E}(Y_i)^2.$$
