Daily Summary for 2026-11-01

Introduction to the show: ident: Statistics. The day in statistics: methods, theory and the inference under them.

Tom: It's the first of November, twenty twenty-six, and this is the day's research.

Jane: 9 new papers came out today.

Tom: I'm Tom.

Jane: And I'm Jane, here with Lu, Meng and our in-house large language model, Lalam.

Tom: We'll take the day in one pass, then pull out the papers we're staying with.

Jane: Start us off with Characteristic function-based tests for spatial randomness.

The day's research: Tom: Population adjusted indirect comparisons help make sense of evidence when different patient groups are involved.

Jane: But these comparisons are not automatically transportable to the populations that matter most.

Lu: The main problem is that adjusting for differences across trials does not guarantee effects hold for our target group.

Meng: We examine this by looking at estimands to distinguish conditional and marginal treatment effect estimates where transportability fails.

Lalam: Some effects on the linear predictor scale are more transportable while hazard ratios often remain dependent on population even with shared effect modifiers.

Tom: This relates to how we compare data from subgroups, right?

Jane: Consistent Bayesian meta-analysis on subgroup specific effects and interactions shows a way to adjust for variation in relative subgroup contribution when combining results.

Lu: That process helps ensure inferences about interactions remain strong no matter which published subgroup data are used.

Meng: On a computational level, least squares variational inference provides a gradient-free method for finding solutions for exponential families.

Lalam: This method can achieve efficient complexity for Gaussian distributions and performs competitively with other methods even without gradients.

Tom: That is what the paper on Reframing Population-Adjusted Indirect Comparisons as a Transportability Problem addresses.

Jane: And we have the work on Consistent Bayesian meta-analysis on subgroup specific effects and interactions too.

Lu: What about the work on Leave-One-Out Neighborhood Smoothing for Graphons?

Meng: That investigates entrywise uncertainty quantification in graphon models by introducing a leave-one-out neighborhood.

Lalam: The paper on Differentially Private Covariate Balancing Causal Inference deals with covariate balancing using observational data.

Tom: And we have the work on Subgroup comparisons within and across studies in meta-analysis summarizing treatment effects for patient subgroups.

Jane: What about Characteristic function-based tests for spatial randomness?

Lu: That introduces a new type of test for complete spatial randomness that applies to mapped point patterns in a rectangle or more.

Meng: Finally, we have the work on Least squares variational inference which introduces LSVI as a gradient-free scheme for fixed-point recursion in exponential families.

Lucky paper: 2504.07946: Jane: So we are looking at the paper titled Characteristic function-based tests for spatial randomness today.

Tom: It introduces a new test for complete spatial randomness that uses characteristic functions and a weighted L2-distance between empirical and uniform characteristic functions.

Lu: The paper says this test is the first of its kind based on characteristic functions that also uses a weighted L2-distance, scaled by n.

Jane: That distance is defined as Delta equals the integral from D over one over n times sigma j equals one to n exp of i t transpose x j minus phi hat X (t) times w (t) d t.

Meng: The weight function w (t) can be chosen in several ways, like the squared modulus of the characteristic function phi zero (t) squared, or a centered Gaussian weight function.

Tom: The paper specifically explores choices like a Bessel-like weight function, which produces a simple rectangular phi r.

Jane: It also mentions that the expectation of the test statistic under the null hypothesis for that Bessel-like weight is E0 (Delta r) equals one minus E0(phi r (xone minus xtwo)).

Lu: And they show that using the Cauchy weight function gives a specific statistic Delta r equal to one over n summed over j and k from one to n exp of negative one over r summed over d equals one to d x j minus x k d factorial minus two summed over j equals one to n ö D d equals one to r n squared minus e of negative x j d divided by r minus e of negative (one minus x j d) over r plus n over n 2r.

Meng: That Cauchy-weighted CF test is chosen because it has a much lower computational cost than the isotropicedge-corrected L-test.

Tom: The simulation results show that the two-tailed test using either method has a type I error rate very close to the theoretical value of zero point zero five, which is good for controlling false discovery rates.

Jane: They compare its power against tests like Zimmerman’s w2-test and Clark Evans test, and the CF test outperforms them in most simulation settings of heterogeneity and aggregation when the sample size is large.

Lu: Theoretically, the asymptotic distribution of Delta converges in distribution to a limit involving infinity times j equals one to infinity lambda j Z two j where Z j is a sequence of independent standard normal variables and lambda j are the eigenvalues of the linear operator T.

Tom: They also derive efficient algorithms for the asymptotic and small-sample null distributions in Section four which is helpful for practical application.

Jane: The paper concludes that while the exact relationship between weight function choice and test power is still unclear, the empirical CF has a unified formula even for non-rectangular study regions like disks or polygons.

Lu: They also noted that the three-dimensional CF statistic can be used to test for space-time CSR, but testing for space-time interaction is usually more interesting in practice than just testing for CSR.

Meng: So, what would we actually deploy with this test? Would it work well on real traffic data where we have non-rectangular regions?

Tom: It seems the computational cost is low enough that it could be viable for large-scale application when dealing with these spatial point patterns.

Lucky paper: 2501.02703: Tom: Let's talk about Full-conformal novelty detection, this is paper number two of two and it focuses on making novelty detection robust with distribution-free FDR control guarantees.

Jane: The core idea seems to be using all reference data during both the fitting and the inference stages to get a more solid measure of evidence.

Lu: Exactly. The paper introduces K-block full conformal novelty detection, or K-FC ND, which mandates using *all* reference data for those full conformal e-values.

Meng: So how does this handle when we only have limited reference datasets? Is there a trade-off in power versus the guaranteed FDR control level?

Tom: They address that with a data-driven model selection strategy that adapts the scoring function, which should help maintain FDR control even when reference datasets are small.

Lalam: The paper also boosts the detection power by using the conditionally calibrated eBH framework, computing a boost exactly without relying on Monte Carlo samples.

Jane: That sounds like a big win for computational stability and statistical rigor. What about extending this method to handle distribution shift?

Lu: They generalize K-FC ND to accommodate distribution shift, which is when the inliers in your test set have a known shift relative to the reference data.

Tom: That extension uses a weighted variant that keeps the finite-sample FDR control while empirically improving power under those shifting conditions.

Meng: When we look at implementation, what are the specific parameters they suggest for K? Is it always K=one for efficiency?

Lu: They mention canonical instantiations like K=one for computational efficiency and K=m to facilitate that data-driven model selection strategy.

Jane: It sounds like they are trying to make a very practical tool here, moving beyond just theoretical guarantees on the e-values.

Tom: The paper also introduces null proportion correction estimators based on Gao two thousand twenty-three which lets you increase the achieved FDR control level to alpha.

Lalam: That modification allows for an increase in the achieved FDR control level up to alpha, which is useful when you need a higher confidence threshold.