Bayesian framework decouples inference and decision

[hyunjimoon]

In Calibrating Model-Based Inferences and Decisions, Michael Betancourt explains:

in frequentist framework, any self-consistent weighting is equivalent to the assignment of probabilities meaning from a frequentist perspective, inference and decisions are one in the same.

On the other hand, Bayesian inference broadens the interpretation of probability theory, allowing it to be used to not only model inherent variation in observations but also provide a probabilistic quantification of consistency between the data generating processes in the model configuration space and observations. Hence Bayesian frameworks allows inference and decision to be decoupled, making the assumptions underlying both more explicit and often easier to communicate.

sec. 3.4.1 and sec.3.4.2 of the paper contrasts Bayesian inference and Bayesian calibration. More recent explanation is in his blog Probabilistic Modeling and Statistical Inference which I find easier to parse.

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based on the above, I gave feedback to Tom's slide on recent Vensim update in Bayesian aspect
Fiddaman25_BayesSD_Vensim.pdf as follows:

1. p.10 Payoff elements using Poisson/Binomial family or logarithmic transform now add a large pentalty term if the model generates a value <= 0

Might the following be more generic solution? https://mc-stan.org/docs/reference-manual/transforms.html#lower-bound-transform.section

Bob Carpenter mentioned this function was a great breakthrough during Stan conference.

2. p.11 calibration

-> Bayesian calibration

3. p.15 what do you want from calibration?

-> what calibration do we want?
"detection of systemic errors" is only possible with Bayesian calibration

4. p.16 calibration

-> frequentist calibration
as prior information is not used except for rejecting out of range and parameter uncertainty doesn't exist, this is frequentist calibration

5. p.19 combine calibration optimization or MCMC with priors that capture the state of knowledge about parameters

-> combine frequentist calibration optimization or Bayesian calibration MCMC with priors ...