Hi,

I am wondering if it is possible to do parameter inference using Turing for a DiffEqJump model?

I understand that this type of problem might be better handled using an optimizer, but I am curious if it can be done in Bayesian mode? The jumps would make it hard for AD, I suppose, and cause it to be inefficient in exploring the parameter space. But perhaps there is a better parameterization or choice of options that might make it work? Or better still, I just did something silly and easily fixed?

Here is a toy model to make it clearer and for you to pick apart:

```
using DiffEqJump, Turing, Catalyst
# create dummy data
p = [ 0.5 ]
u0 = [ 10 ]
tspan = ( 0.0, 5.0 )
dt = 0.2
rs = @reaction_network begin
r, X--> 2X
end r
dp = DiscreteProblem( rs, u0, tspan, p )
jp = JumpProblem(rs, dp, Direct() )
jsim = solve( jp, SSAStepper(), saveat=dt )
# sample and add noise
keep = sample(1:size(jsim)[2], 20, replace = false, ordered=true)
testdata = Array(jsim[keep] )' + (0.05 * randn(20))
datatimes = jsim.t[keep]
# Plots.scatter(datatimes, testdata)
# estimate params as a Poisson process
@model function simpleExp(y, prob, N=length(y) )
# priors
r ~ Normal( 1.0, 1.0 )
y0 ~ truncated( Cauchy(0.0, 0.5), 0, Inf )
sigma ~ truncated( Cauchy(0.0, 0.5), 0, Inf )
jp2 = remake( prob, u0=[y0], tspan=tspan, p=[r] )
jsol = solve( jp2, SSAStepper() )
# likelihood
for i in 1:N
j = findall(t -> t==datatimes[i], jsol.t)
if length(j) > 0
y[i] ~ Normal( jsol.u[j[1]][1], sigma )
end
end
end
simplemodel = simpleExp(testdata, jp)
s = sample(simplemodel, MH(), 5 ) # almost works... but slow
s = sample(simplemodel, SMC(), 5 ) # fails
s = sample(simplemodel, NUTS(0.5), 5) #fails
```