Apply prior on a simple linear regression

Hello everyone !
I am both a beginner in bayesian stats and probabilistic programming,

I am trying to do simple linear regression with a toy dataset with a predefined prior on the bias.
So far I have found several ways of doing bayesian linear regressions with TFP (correct me if I'm wrong) including: using a shallow neural network with one Dense flipout layer, GLMs, STS models, Edward2 models.

Let's say my dataset is the linear relationship 3x + 1 + noise, what would be the best method to fit a linear regression saying explicity my prior was distributed on a Normal distribution centered in 10 (to force the bias posterior to be a compromise between 1 and 10).

So far I found that maybe the DenseFlipout option was the best with a simple architecture as such:

model = tf.keras.Sequential([
    tfp.layers.DenseFlipout(
        1,
        activation = "linear",
        bias_prior_fn = tfp.layers.default_mean_field_normal_fn()
    )
])

model.compile(optimizer = "adam",loss = "mse")

But do I define a custom prior on the bias ? The documentation around the default_mean_field_normal_fn() is obscure.

Also my goal is to be the more generalizable as possible, with custom distributions for the priors, or priors on the coefficients as well.

Thanks a lot !
Theo

The issue provides a tf.keras.Sequential example using tfp.layers.DenseFlipout and default_mean_field_normal_fn(), but names no repository file or test. Start by locating the relevant DenseFlipout and prior-function documentation or examples, then determine whether the request needs documentation clarification or an API change and define acceptance criteria for custom bias and coefficient priors.