pm.HalfStudentT.dist() failing to give correct shape

Questions v5
1

Runing on PyMC v4.4.0

df_penguins=pd.read_csv(r'https://raw.githubusercontent.com/BayesianModelingandComputationInPython/BookCode_Edition1/main/data/penguins.csv')
df=df_penguins.dropna(how = 'any').reset_index(drop=True) #drop if any of the values in a row is missing

data=df_adelie.loc[:,'body_mass_g'].values

with pm.Model() as model_adelie_penguin_mass:
   
    μ = pm.Normal("μ", 4000, 3000)
    σ = pm.HalfStudentT("σ", nu=30, sigma=2000)
    #σ=pm.Exponential('σ', 1/30)+1
    y = pm.Normal("y", mu=μ, sigma=σ, observed=data) 
    idata = pm.sample(2000,chains=2) 
    idata.extend(pm.sample_prior_predictive())
    idata.extend(pm.sample_posterior_predictive(idata))
az.plot_posterior(idata.prior, var_names=["σ"]) # This plot gives a symmetric approx normal shape around "σ"=2000 for the prior.   The shape of the prior from idata.prior["σ"] should be approx. pymc.HalfStudentT shape, instead its approximately symmetric normal centred on 2000. Has the parameterization of the pymc.HalfStudentT in the latest version of PYMC changed in some way.

I tried the following: rv = pm.HalfStudentT.dist(nu=10,sigma=20)

rv = pm.HalfStudentT.dist(nu=30,sigma=3000)
x = np.linspace(-1000, 7000, 50)
pdf = pm.logp(rv,x).exp().eval()

fig,ax=plt.subplots(1,1,figsize=(4 ,3),sharex=True)
plt.plot(x, pdf, label='Half-Student-t', lw=2)

which showed a graph of the correct shape but

rv = pm.HalfStudentT.dist(nu=10,sigma=5)
sns.histplot(pm.draw(rv,10000))

again did not give the pymc.HalfStudentT shape. It would be very helpful if anybody can spot the flaw in the parameterisation or in the way I am attempting to parameterize the HalfStudentT prior. the example is taken from ‘Bayesian Moddelling and Computation’ in python by Osvaldo Martin page69 but he is using pymc3. I also tried instead setting prior to : σ=pm.Exponential('σ', 1/30)+1 which worked perfectly but would very much like to know why σ = pm.HalfStudentT("σ", nu=30, sigma=2000) fails to give correct shape when plotted with az.plot_posterior(idata.prior, var_names=["σ"]). Thanking you in advance. Declan.

2

continued… σ=pm.HalfNormal(“σ”,2000,dims=‘species’) also works.

3

@Nn_Nnn Thanks for reporting, it seems there is a bug in how we generate random draws for the HalfStudentT distribution!

sigma should be passed by keyword as scale, otherwise it’s used for loc

4

Opened an issue here: Bug in `rng_fn` of `HalfStudentT` · Issue #6657 · pymc-devs/pymc · GitHub

5

Thank you Ricardo for taking the time to look at the puzzling code.
Runing on PyMC v4.4.0 Just to follow up: if I run the code for σ = pm.HalfStudentT(“σ”, nu=30,scale=2000) using 'scale as mentioned does not seem to work, it gives:-
error:TypeError: make_node() got an unexpected keyword argument ‘scale’ .
Also σ = pm.HalfNormal(“σ”,sigma=2000) seems to work.
I think I might be wise to avoid σ = pm.HalfStudentT(“σ”, nu=30,scale=2000) and just use pm.HalfNormal(“σ”,sigma=2000). I Am assuming its ok to parameterizing normal distribution with mu and sigma and half-normal with sigma. thanks again for helping with these challenging puzzles. declan

6

Yes, unfortunately you can’t pass scale to the PyMC distribution yourself, we need to fix it in the codebase.

7

Thanks delan