Reliability and Identifiability in Persona-Trained Monte Carlo: Variance Decomposition, Stability Bounds, and the Identifiability of Heterogeneous News Reaction

Jul 16, 2026

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Persona-Trained Monte Carlo (PTMC) estimates market-outcome distribution functionals via repeated simulations of limit-order-book interactions among K neural policy bots whose personas come from a learned heterogeneity distribution P. The work formalizes “reliability” by decomposing estimator variance into persona-draw and within-run terms, providing unbiased ANOVA estimators and a compute-budget allocation that minimizes variance. Stability bounds track how errors in P and training propagate into total estimands, including a uniform-in-horizon result under a Doeblin condition.

LanguageEnglish

CategoryResearch & Report

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Pages29

Reading Time1 h 13 min

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Introduction

Error and compute allocation

Propagated error from misestimation

Identifiability of heterogeneous news reaction

arXiv :2607 .04627v 1 [ cs .LG] 6 Jul 2026 Reliability and Identifiability in Persona-Trained Monte Carlo: Variance Decomposition, Stability Bounds, and the Identifiability of Heterogeneous News Reaction Salavat Ishbulatov Independent researcher [salavat@doplan. ai](salavat@doplan. ai) 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 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 σ2P and a within-run component σ2w, 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 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) = EQ [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 √ 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) . Companion papers. Framework specification: Persona- Trained Monte Carlo: Estimating MarketOutcome Distributions via Swarms of Persona- Conditioned Neural Policy Bots in a Limit Order Book (arXiv:2606.29556) . This paper contains the theory; nothing here depends on simulation output. 1 Introduction Agent-based market simulators promise distributions of outcomes—crash probabilities, drawdowns, spread dynamics—generated endogenously by interacting traders rather than imposed by a parametric price process. Persona-Trained Monte Carlo (PTMC) makes the promise statistical: each simulation run draws a population of K trader personas from a distribution P, instantiates K copies of one trained policy network π ϕ conditioned on those personas, lets them trade in a continuous double auction for T steps, and records a functional F of the resulting path; averaging over N independent runs gives a Monte Carlo estimator ˆµN of EP[F ] . Three questions decide whether such an estimator deserves to be called reliable, and they are the subject of this paper. First, what does the estimator’s error look like, and how should a compute budget be spent? Section 4 decomposes the estimator’s variance into a between-population component σ2P (the variance of the conditional mean across persona draws) and a within-run component σ2w, exhibits unbiased ANOVA estimators of both from a two-stage design (Theorem 1), and derives the varianceminimizing allocation between outer persona draws and inner replications under a cost model (Theorem 2) . These results are mathematically standard—they are the input-uncertainty decomposition of the stochastic-simulation literature (Cheng and Holland, 1997; Barton et al., 2014; Songet al., 2014) and the nested-simulation allocation of Sun et al. (2011) transplanted to populations of interacting learned agents—and we present them as preli

FAQs

What is Persona-Trained Monte Carlo (PTMC) used for in this paper?

PTMC estimates distributions of market-outcome functionals by simulating limit-order-book interactions among multiple trained policy bots whose personas are sampled from a learned heterogeneity distribution P, then averaging functional values across independent runs.

How does the paper define and analyze estimator reliability?

Reliability is made precise by decomposing estimator variance into a between-persona component and a within-run component, giving unbiased ANOVA estimators for both, and deriving a variance-optimal way to allocate a fixed compute budget between outer persona draws and inner replications.

How are errors from an incorrect persona distribution P and policy training errors handled?

The paper proves coupling-based stability bounds that quantify how misestimation of P and training error propagate into the estimand, yielding a multi-term total-error budget, with a uniform-in-horizon version under a Doeblin condition on the market chain.

Jul 16, 2026

Upload by Noah