Sam Andersson | Searcharxiv

arXiv2026

Two-resolution state modelling of intermittent online gambling activity during Sweden's temporary deposit-cap period

Intermittent online gambling records create two distinct representation problems: calendar-time analyses must retain represented days with no recorded play, whereas analyses of active behaviour must preserve variation within active episodes. We pair calendar-time and active-bout models in a two-resolution analysis of 14.2 million player-days from a single operator during 2019-2023. The calendar-time layer retains assignable represented days in five observed categories and propagates a pre-period reference. The active-episode layer fits a Bayesian mixed-emission hidden semi-Markov model to turnover, playing time, approved deposits and session counts. In the reference four-regime fit, two regimes share a rounded model-implied turnover median of 153.5 EUR, while their model-implied playing-time and approved-deposit medians differ by factors of 4.6 and 5.7, respectively, and their expected total session counts by a factor of 2.8. This separation remains under an ordinary hidden Markov model, two routing perturbations and a residual-dependence sensitivity; the tested turnover-only fits were diagnostically unstable. Over the temporary Swedish deposit-cap period, deposits and turnover per represented player-day were roughly 55% below the propagated reference and active-category occupancy was 7.8% lower. The largest negative deviations in a prespecified Sweden-assigned cohort occurred among high pre-policy deposit-intensity customers. These are operator-specific descriptive comparisons, not causal policy effects.

stat.AP↗

arXiv2026

Finite-Probe Total-Variation Certificates for Finite-Basis Drifting Models

Drifting objectives compare a target and model distribution through a vector field observed noisily at finitely many locations. We ask what distributional conclusion such a frozen measurement system warrants. For integrable antisymmetric interactions and absolutely continuous laws in a declared finite density basis, the unnormalized sampled numerator satisfies $\operatorname{vec}(V_X)=Mc$, where $c$ is an antisymmetric mismatch and $M$ is probe-dependent. This identity yields an a posteriori total-variation (TV) upper confidence bound accounting for held-out field noise, estimated-operator error, and externally validated $L^1$ residual radii around normalized density approximants in the span; a nonpositive observability margin returns the trivial TV bound and abstains. The audit recomputes this numerator from held-out samples; a normalized drift statistic requires a separate joint numerator--denominator analysis. For Gaussian-RBF interactions, a global envelope supports distribution-free and empirical-Bernstein radii without truncation, with companion bounds for the Laplace similarity in the original drifting objective. We characterize random-probe observability by a population Gram matrix, identify rank and symmetry degeneracies, and prove large-bandwidth collapse toward mean matching. Synthetic studies exercise Gaussian and Laplace numerators, separately prespecified bounded-vector and variance-adaptive radii, Monte Carlo-calibrated operators, nonzero residual radii around normalized finite-basis approximants, outward-rounded observability bounds, and designed abstention. A joint basis-size/dimension stress path extends evaluation through $m=8$. The result is a conditional diagnostic for a finite density class, or for normalized finite-basis density approximants with external residual radii, not a universal guarantee from small training drift.

stat.ML↗