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7

There are only two "principled" ways you can get out of your posited model that operate within the framework of the Bayesian paradigm. Once is to initially set a broader class of models, and give some non-zero prior probability for the alternative models in that class (i.e., have a prior probability less than one for your posited model class). The other is ...

3

Ok let's do it in one way, according to the vignette (?roc.curve): scores.class0: the classification scores of i) all data points or ii) only the data points belonging to the positive class. In the first case, scores.class1 should not be assigned an explicit value, but left at the default (scores.class1=scores.class0). In ...

2

Prior predictive and posterior predictive checks may be helpful in here. In both cases you sample the predictions from the model (the "fake data"), in first case from the prior, in the second case from the posterior distribution, and then compare the distributions of the fake data, with the distribution of the observed data. Prior predictive checks are aimed ...

2

EDIT: innisfree is right. Bayes factors seem like a better approach than what I have provided here. I'm leaving it up for posterity, but it isn't the right approach. Because this problem really relies on a single assertion (namely, that $c$ has some value), we can simply estimate the following model $$y \sim \mathcal{N}(b_0 + b_1x, \sigma)$$ and ...

1

I'm not a Bayesian expert and I'm happy to stand corrected, but to me the most straightforward & principled way to test this would be to define region of practical equivalence (ROPE) around c and then estimate how much posterior density falls inside this region. For example, let's say that, based on theory and domain knowledge, you know that for all ...

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