Need help with simple asymptote model using toy data

Questions
1

Hello!

I’m trying to get accustomed to pymc3 and bayesian models in general. In particular right now I’m trying to fit a michaelis-menten-type model to my data, with a normal variance around the deterministic model for the mean with a standard deviation of ϵ:

y \sim N(\mu = \frac{x}{x+k}, \epsilon )

My own data is pretty big, ~2000 points, so here is a toy example that seems to repeat the error (I assigned k = 100 for the moment):

xx = pd.Series(range(0,3500,100))
yy_real = xx/(xx + 100)
εε = np.random.normal(0, 0.05, size=len(xx))
yy = yy_real + εε

(Image of data attached)

with pm.Model() as model_g:
    ε = pm.Normal('ε', mu=0, sd = 0.05)
    y_pred = pm.Normal('y_pred', mu= xx/(xx+100), sd=ε, observed=yy)
    trace_g = pm.sample(2000, tune=1000)

This returns a long error that boils down to the following error early while running the NUTS sampler:

RuntimeWarning: Mean of empty slice.

And finally with:

Bad initial energy, check any log probabilities that are inf or -inf, nan or very small:
y_pred -inf

So I guess I am generating negative infinity values somehow in my posterior? Picture of toy data and the curve I’d like to fit: toyboxFig

Thanks in advance.

2

The problem might be coming from your noise prior, since it can give invalid negative numbers for the standard deviation of you likelihood. Try to replace it with a positive distribution like the HalfNormal or even better a Gamma and see if your problems go away.

3

Perfect, thanks! Makes sense now that I think about, standard deviations can’t be negative. What is a “noise” prior?

4

The standard deviation parameter (epsilon). These are sometimes called noise parameters as well (not to be confused with nuisance parameters) :slight_smile:

I am glad that fixed your problems