How to add weights to data in bayesian linear regression

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Welcome!

There are various ways to incorporate weights into your model. Many will write custom logp functions (e.g., here and here). But I personally prefer to adjust the scale parameter of my observed variable, which allows for more heavily weighted observations to contribute more model’s logp. It’s simple and relatively transparent. Here’s a simple example:

s = pm.HalfNormal('error', sd = 1)
scaled_s = pm.Deterministic('scaled_s', s / y_weights)
obs = pm.Normal('observation',
                mu = y_pred,
                sd=scaled_s,
                observed=y)

In addition, I would strongly suggest using the defaults when calling pm.sample() until you are confident that they don’t work for you. I would particularly suggest avoiding the use of pm.find_MAP()

# nice and simple
trace = pm.sample(1000)
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