Dear Julia community,

I am new to julia and try to implement a complex bayesian inference procedure on a ODE system, using turing.

I base my code on the great turing tutorial: Bayesian Estimation of Differential Equations

While the simple case works, I would like to extend this tutorial to two more realistic problems for my research.

- Let’s say I have a Lotka-Volterra model with X and Y the variables. In this case, X and Y can be different by several magnitudes and then I want to log-transform my data and my predicted ode solution when estimating the likelihood.

From the tutorial example, I tried the following code:

```
Turing.setadbackend(:forwarddiff)
@model function fitlv(data, prob1)
σ ~ InverseGamma(2, 3) # ~ is the tilde character
α ~ truncated(Normal(1.5,0.5),0.5,2.5)
β ~ truncated(Normal(1.2,0.5),0,2)
γ ~ truncated(Normal(3.0,0.5),1,4)
δ ~ truncated(Normal(1.0,0.5),0,2)
p = [α,β,γ,δ]
prob = remake(prob1, p=p)
predicted = solve(prob,Tsit5(),saveat=0.1)
temp = predicted .+ 1 .- minimum(predicted)
for i = 1:length(predicted)
log_predicted = log10.(temp[i])
data[:,i] ~ MvNormal(log_predicted, σ)
end
end
model = fitlv(log10.(odedata .+ 1 .- minimum(odedata)), prob1)
chain = mapreduce(c -> sample(model, NUTS(.65),1000), chainscat, 1:3)
```

But I got some problems because given the set of parameters, `predicted`

can be badly estimated by the ode solver and be <0, then log(predicted) can give a complex number and then the sampling stop … do you have any insights on what would be the best option to implement this?

- Now let’s say that X and Y data are not homogeneous and doesn’t have the same time vector and size. How do you implement this in turing? Espcially when estimating the likelihood because if X has 10x more data points than Y then the fit will be weighted on the X channel.

Many thanks for all your help!