As indicated in PyMC doc, HERE :

“*Prior predictive checks […] allow you to check whether you are indeed incorporating scientific knowledge into your model – in short, they help you check how credible your assumptions before seeing the data are.*”

The most important point, in my opinion, is the assumption “*before seeing the data*”, which seems logical.

However, it gives me a modeling problem, which I explain below:

Let `B`

be a certain random variable following a Bernoulli law, where the parameter involved is, say, `θ`

. Suppose I plan an experiment consisting of `n`

`i.i.d`

realizations of `B`

; the number `x∈[[0,n]]`

of successes follows a binomial distribution `X~Binom(n,θ)`

and the likelihood of `x`

knowing `θ`

is, unless I err:

f(x|θ)= \begin{pmatrix}n\\x \end{pmatrix} θ^x (1-θ)^{(n-x)}

Previous knowledge on that particular `B`

suggest me that `θ`

must be close to `0`

or `1`

. I then take as prior the beta distribution `Beta(1⁄2,1⁄2)`

and write:

import pymc as pm

with pm.Model() as model:

`p = pm.Beta("p", alpha=0.5, beta=0.5) idata = pm.sample() pm.sample_prior_predictive(return_inferencedata=True) idata.extend(pm.sample_prior_predictive())`

Note that, for the moment, neither `n`

nor `x`

have been defined and I have no data yet…

My first miscomprehension comes from the fact that both groups `idata.posterior`

and `idata.prior`

contain the same variable `p`

with different values and shapes: `idata.posterior ["p"].shape= (4, 1000)`

and `idata.prior ["p"].shape= (1, 500)`

.

- How can this be explained to someone new to Bayesian inference?

My second miscomprehension comes from the `PyMC doc`

sentence: “*help you check how credible your assumptions before seeing the data are*”.

The only assumption made so far is to include the beta distribution `Beta(1⁄2,1⁄2)`

in the model, so…

- How can someone new to Bayesian inference check if this assumption is credible, knowing that
`idata`

contains only the groups`posterior`

,`sample_stats`

and`prior`

?

I know something still escapes me in the logic of all this… But could my two questions be answered, as basic as they are, to help me progress?

I hope I have been understandable and not excessively tedious.