{"ID":5937217,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-09T03:17:38.775576136Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.04627","arxiv_id":"2607.04627","title":"Reliability and Identifiability in Persona-Trained Monte Carlo: Variance Decomposition, Stability Bounds, and the Identifiability of Heterogeneous News Reaction","abstract":"Persona-Trained Monte Carlo (PTMC) estimates distributions of market-outcome functionals by repeatedly simulating limit-order-book interaction among $K$ neural policy bots whose behavioral personas are drawn from a learned heterogeneity distribution $\\mathcal{P}$. This paper develops the statistical theory that makes the word \"reliable\" precise for such estimators. We decompose estimator variance into a persona-draw component $σ_P^2$ and a within-run component $σ_w^2$, give unbiased ANOVA estimators of both, and derive the variance-optimal allocation of a fixed compute budget between outer persona draws and inner replications. A coupling-based stability bound quantifies how misestimation of $\\mathcal{P}$ and error in the trained policy propagate into the estimand, yielding a three-term total-error budget whose terms are separately estimable; a uniform-in-horizon version holds under a Doeblin condition on the market chain. The main contribution is an identification theory for heterogeneous news reaction: under a fixed response nonlinearity, the aggregate impact curve $A(z)=\\mathbb{E}_Q[g(ηz)]$ detects heterogeneous news sensitivity through a strict Jensen gap and identifies the distribution $Q$ locally via odd moments and Hausdorff determinacy, with sharp failure when the response family is unknown. We provide $\\sqrt{n}$-consistent estimators and a boundary-corrected test of homogeneous news reaction. Two separation theorems delimit when PTMC is provably preferable to homogeneous-population simulators and reduced-form forecasters, formalizing an irreducible Jensen bias floor and the Lucas critique as a minimax limit on intervention extrapolation. All proofs are given in full; guarantees are classified as unconditional (Monte Carlo convergence), conditional worst-case (the error budget), or open (the large-$K$ mean-field limit).","short_abstract":"Persona-Trained Monte Carlo (PTMC) estimates distributions of market-outcome functionals by repeatedly simulating limit-order-book interaction among $K$ neural policy bots whose behavioral personas are drawn from a learned heterogeneity distribution $\\mathcal{P}$. This paper develops the statistical theory that makes t...","url_abs":"https://arxiv.org/abs/2607.04627","url_pdf":"https://arxiv.org/pdf/2607.04627v1","authors":"[\"Salavat Ishbulatov\"]","published":"2026-07-06T03:22:05Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CE\"]","methods":"[]","has_code":false}