Sebastián Souyris, Jason A. Duan, Anantaram Balakrishnan +1econ.EM cs.LG stat.AP
Problem definition: Solar electricity generation is a strategic component of energy portfolios designed to meet growing demand and reduce carbon emissions. Governments and municipalities encourage household photovoltaic (PV) adoption through upfront rebates and tax credits. Limited budgets require principled, data-driven policies that account for the drivers of adoption and the effects of incentives on adoption rates. Methodology/results: We develop a dynamic structural model of residential PV diffusion based on adoption decisions by forward-looking households that weigh the economic trade-offs between installing now and later. Adoption depends on return on investment and influence from neighboring adopters. The model segments households by home value and urbanization level, incorporates unobserved heterogeneity, and captures spatiotemporal installation dynamics. We estimate the model using Bayesian methods and detailed household-level data from Austin, Texas. In out-of-sample tests, it predicts installations more accurately than contemporary alternatives. We simulate counterfactual policies within the dynamic equilibrium of PV diffusion to evaluate rebate designs. The framework can also be adapted to study the adoption of other durable technologies. Managerial implications: A rebate offered for a limited period generates more adoption and emissions reductions than a prolonged, costlier program. This counterintuitive result arises from forward-looking behavior, neighbor influence, and accelerated adoption before the rebate expires. We also evaluate phased reductions and rebates differentiated by household segment. A two-step reduction outperforms multiple small reductions. Geographic differentiation improves policy performance, whereas differentiation by home value offers little advantage over a uniform rebate.
Vector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the parametrization is identified only up to equivalence, and every evaluation costs a pass over the entire series. Yet their moving-average term captures with a few parameters what a pure autoregression matches only with many lags. We introduce an estimation framework that removes this computational barrier: each optimization iteration is independent of the series length $T$. The framework combines a partial-autocorrelation reparametrization that guarantees stationarity and invertibility by construction, Gaussian priors on the reparametrized coefficients with separate scales for diagonal and off-diagonal entries, and losses that depend on the data only through fixed-size sufficient statistics, evaluated by a Parseval (Fourier) identity at near-linear cost in the truncation length. This yields two point estimators: a regularized least-squares fit and a covariance-marginalized maximum-a-posteriori estimator. We prove that both recover the infinite-autoregressive representation of the true process at a near-parametric rate in fixed dimension, so the truncation introduces no asymptotic bias. The same machinery extends, at the same leading cost, to seasonal dynamics, exogenous regressors (VARMAX), and rolling-window refits. Empirically, the estimators stay close to the oracle forecast error from $d=10$ to $d=40$ (where classical conditional MLE returns non-invertible fits whose forecasts diverge) and match or beat VAR, Bayesian-VAR, component-wise ARMA, and sparse-VARMA baselines on retail-demand, meteorological, and air-quality data. This brings likelihood-based VARMA estimation, at a per-iteration cost independent of the series length, to the problem sizes where practitioners have so far relied on VAR models.
Interleaving mitigates burst errors but introduces decoding delay and removes temporal error structure that a channel-aware decoder could exploit. We consider packet-level selection between a random linear code and the same code used with cross-codeword interleaving, over a channel with an unknown number of on/off interferers. The receiver uses Guessing Random Additive Noise Decoding (GRAND) with a replaceable noise model and feeds aggregate channel statistics back to a Bayesian estimator at the transmitter. Once the interference amplitudes and timing parameters are estimated, the receiver's noise model is replaced: it computes hidden-Markov-model posterior bit-flip probabilities and uses them to order GRAND queries. A discounted Thompson sampler selects between the two transmission modes using a goodput-minus-latency reward whose distribution is endogenously nonstationary: receiver adaptation, rather than channel change, alters the value of each mode. Across five simulation seeds, the interleaved mode is preferred before channel estimation converges. After the learned decoder is activated, the non-interleaved mode becomes preferable because it achieves lower block error rate without interleaving delay. In the reference configuration, the learned noise model reduces block error rate by approximately one order of magnitude relative to ORBGRAND. Using partial channel estimates before full convergence reduces pre-convergence block error rate by up to $4.5\times$. Adding model-predicted utilities as confidence-weighted pseudo-observations reduces post-transition selection of the inferior arm by approximately $65\%$. Under an idealized airtime conversion at a 100~MHz 5G~NR-like symbol rate, the learning transient corresponds to a few milliseconds of occupied symbol time.
This paper presents a nonlinear parameter estimator for Wiener-type state-space models obtained as a fixed-point architecture that couples two affine minimum mean-squared error (MMSE) estimators: one for the unknown parameters and one for latent variables. The architecture retains the functional structure of the optimal affine MMSE parameter estimator while incorporating Dynamic Basis Statistics (DBS) estimates that summarize nonlinear basis-function evaluations. Two DBS construction strategies are developed, leading to two nonlinear estimator frameworks. The dual basis-parameter estimator combines an affine basis estimator with the affine parameter estimator, whereas the dual state-parameter estimator first computes affine state estimates and their covariances, then maps these state-estimate statistics through a Gaussian DBS operator to obtain DBS estimates. Both dual estimators admit fixed-point characterizations that alternate between estimating each component using the updated prior of the other, obtained from that component's plug-in estimate statistics from the previous iteration. The efficacy of the proposed methods is examined via extensive Monte Carlo experiments, showing that the dual basis-parameter estimator attains parameter mean-squared errors comparable to those of the purely affine parameter estimator, while the dual state-parameter estimator achieves the lowest parameter mean-squared error, outperforming both the dual basis-parameter and purely affine parameter estimators, as well as sequential Monte Carlo variants of classical Particle Gibbs and Expectation-Maximization schemes.