Arman Oganisian

Bayesian nonparametric models allow flexibility in regions w/ lots of data, while allowing priors about sensitivity parameters drive inference in regions w/o data (see bottom-right plot).

Uncertainty about *all* unknowns flow into a single posterior for the causal quantity!

Are some patients missing outcome info? Condition on data, make inferences about unknown {regression lines & missing values}.

Think the missingness is not at-random? Condition on data, making inferences about unknown {regression lines, missing values, & sensitivity parameters}

Why I find Bayesian nonparametric causal inference compelling in one figure.

The key distinction is btwn (1) "known" vs (2) "unknown" quantities: Make inferences about (2) conditional on (1).

Want cond. avg trt effects? Condition on data, make inferences about regression lines

Arman Oganisian: Untangling Sample and Population Level Estimands in Bayesian Causal Inference https://arxiv.org/abs/2508.15016 https://arxiv.org/pdf/2508.15016 https://arxiv.org/html/2508.15016

We also discuss differences and similarities with methods for irregular visit processes that inverse-weight by the visit process intensity.

... and how identifiability conditions may be read off a Single World Intervention Graph (SWIG) template for the implicit DTR.

We discuss formalize connections between g-methods that use discrete-time versus continuous-time models adjustment models and the relative pros/cons of each...

Progress can be made by (1) casting waiting times between decisions as potential outcomes of previous treatments and (2) framing subsequent decisions as outputs of an implicit dynamic Treatment Rule (DTR).

In causal inference problems w/ sequential treatments, long stretches of time may elapse between treatment decisions

This paper, in press at Epidemiology, was really fun to write: it discusses biases that may arise & corresponding adjustment via g-methods
arxiv.org/abs/2508.21804

ChatGPT explains double robustness to gen z crowd.

I hope it’s helpful to others as they build Bayesian methods into their causal inference work.

I originally wrote to share with trainees but was encouraged to post it online. I address a lot of subtleties:

Why does sample-level inference need stronger assumptions? When should/n’t we impute counterfactuals? How does this differ from g-computation? Do we really need to Bayesian bootstrap?

Another distinction between imputation of counterfactuals versus monte carlo simulations used to approximate expectations in the g-formula: In the latter, you want the variance across sims (ie approx. error) to be ≈0. In the former, variance imputation should propagate to reflect uncertainty.

The “E” in the e g-formula represents expectations over the population distribution of the outcome. Whereas in Rubin’s Bayesian imputations, “E” represent expectations over the joint posterior distribution of the counterfactuals. These are different distributions in general.

I see what you’re saying. But the “filled in” values are just monte carlo simulations for approximating the integrals over the time-varying confounder distributions because the integrals have no closed form solns in general. MC approximation of integrals is distinct from imputation imo

I see yeah. Imposing common betas is such a pet peeve.

Under additional cross-world assumptions implicitly made in this paper (e.g. assuming Y^1 & Y^0 are independent), drawing the POs and averaging the differences may recover the PATE for large n. But these draws are more like Monte Carlo sims that approximate the cond. expectations than imputations.

Thanks for the reference! I'm not convinced the g-formula can be seen as an imputation-based estimator. For one thing, Rubin's imputation-based approach targets the sample ATE. the G-formula on the other hand identifies the population ATE. These have different variances & interpretations.

Just curious in what sense is this “imputation”- based. To me this is just estimating the conditional expectation at empirically observed values of X. It’s not like values of Y are being drawn or multiply imputed from some distribution.

Such a “check” is a strong yet implicit prior belief that “if PT holds in the pre-period, it must also hold in the post-period”

When estimating the effect of the Philadelphia beverage tax, Seong makes this explicit via a prior process on sensitivity parameters encoding departures from PT.

New paper on Bayesian Diff-in-Diff methods:

www.arxiv.org/abs/2508.02970

When doing DiD, many inspect the difference in trends in the pre-period to “check” whether parallel trends (PT) holds.

But PT is fundamentally uncheckable since it must hold in the post-period as well.

What’s going on?

As you suggested in the post, in my experience the situation is a lot better in biostatistics vs pure statistics departments at least at the places i’ve been at. I could also just be lucky - I have a great group of collaborators and can afford to be selective in the work I take on.

If someone raises this concern, then the burden is on them to bring forward even a single plausible covariate - that is sufficiently unrelated with all the other covariates controlled for - with a realistic dual effect on treatment and outcomes. Otherwise they shouldn’t bring it up.

On the other hand: we have causal critiques of the sort “this is wrong because there may be unmeasured confounding.”

Such critiques without solutions are intellectually lazy and do not add scientific value - after all unmeasured confounding is an issue in all obs causal studies.

GitHub - stablemarkets/cci_institute_2025: Materials for Bayesian Causal Inference Sessions @ University of Pennsylvania's Center for Causal Inference (CCI)'s summer institute. May 29, 2025 Materials for Bayesian Causal Inference Sessions @ University of Pennsylvania's Center for Causal Inference (CCI)'s summer institute. May 29, 2025 - stablemarkets/cci_institute_2025

Thanks for linking! I also have a set of slides with Stan code from a recent half-day short course:

Slide deck 1 is just a primer on Bayesian inference. Slide deck 2 is on the Bayesian causal stuff.

github.com/stablemarket...

Possibly there’s a computational component to “performance.” But i’m not sure if that’s what is being talked about in that excerpt. I try to avoid posterior approximations if at all possible and just do full mcmc - which is feasible in most stuff I do.

GitHub - stablemarkets/cci_institute_2025: Materials for Bayesian Causal Inference Sessions @ University of Pennsylvania's Center for Causal Inference (CCI)'s summer institute. May 29, 2025 Materials for Bayesian Causal Inference Sessions @ University of Pennsylvania's Center for Causal Inference (CCI)'s summer institute. May 29, 2025 - stablemarkets/cci_institute_2025

Thanks for linking! I also have a set of slides with Stan code from a recent half-day short course:

Slide deck 1 is just a primer on Bayesian inference. Slide deck 2 is on the Bayesian causal stuff.

github.com/stablemarket...

“when the quasi-Bayesian method outperforms…”

A point of contention is typically the choice of metric. Many Bayesians feel annoyed at having to demonstrate good frequentist properties to be “worthy”. Because it implicitly casts frequentism as the home court they’re compelling you to play on.

I’ve seen so many instances of conflating sample and population estimands when doing Bayesian causal inference in conference talks, papers on arxiv, papers i’ve reviewed, and even published papers. People often claim to be doing one when actually doing the other.

2) the binning seems to complicate the causal interpretation as there are many versions a bin treatment (all the possible values within the bin). Or maybe some implicit SUTVA assumption is being made ?