arXiv subjects

Kosaku Takanashi

Publications and source records attributed to Kosaku Takanashi.

7 recordsLinked to original sources

arXiv2025

Bayesian Spatial Predictive Synthesis

Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous, typical model selection and ensemble methods that assume homogeneity are not suitable. We address the issue of model uncertainty for spatial data by proposing a novel Bayesian ensemble methodology that captures spatially-varying model uncertainty and performance heterogeneity of multiple spatial predictions, and synthesizes them for improved predictions, which we call Bayesian spatial predictive synthesis. Our proposal is defined by specifying a latent factor spatially-varying coefficient model as the synthesis function, which enables spatial characteristics of each model to be learned and ensemble coefficients to vary over regions to achieve flexible predictions. We derive our method from the theoretically best approximation of the data generating process, and show that it provides a finite sample theoretical guarantee for its predictive performance, specifically that the predictions are exact minimax. Two MCMC strategies are implemented for full uncertainty quantification, as well as a variational inference strategy for fast point inference. We also extend the estimation strategy for general responses. Through simulation examples and two real data applications in real estate and ecology, our proposed Bayesian spatial predictive synthesis outperforms standard spatial models and ensemble methods, and advanced machine learning methods, in terms of predictive accuracy and uncertainty quantification, while maintaining interpretability of the prediction mechanism.

stat.ME↗

arXiv2024

Ensemble Doubly Robust Bayesian Inference via Regression Synthesis

The doubly robust estimator, which models both the propensity score and outcomes, is a popular approach to estimate the average treatment effect in the potential outcome setting. The primary appeal of this estimator is its theoretical property, wherein the estimator achieves consistency as long as either the propensity score or outcomes is correctly specified. In most applications, however, both are misspecified, leading to considerable bias that cannot be checked. In this paper, we propose a Bayesian ensemble approach that synthesizes multiple models for both the propensity score and outcomes, which we call doubly robust Bayesian regression synthesis. Our approach applies Bayesian updating to the ensemble model weights that adapt at the unit level, incorporating data heterogeneity, to significantly mitigate misspecification bias. Theoretically, we show that our proposed approach is consistent regarding the estimation of both the propensity score and outcomes, ensuring that the doubly robust estimator is consistent, even if no single model is correctly specified. An efficient algorithm for posterior computation facilitates the characterization of uncertainty regarding the treatment effect. Our proposed approach is compared against standard and state-of-the-art methods through two comprehensive simulation studies, where we find that our approach is superior in all cases. An empirical study on the impact of maternal smoking on birth weight highlights the practical applicability of our proposed method.

stat.ME↗

arXiv2024

Bayesian Causal Synthesis for Meta-Inference on Heterogeneous Treatment Effects

The estimation of heterogeneous treatment effects in the potential outcome setting is biased when there exists model misspecification or unobserved confounding. As these biases are unobservable, what model to use when remains a critical open question. In this paper, we propose a novel Bayesian methodology to mitigate misspecification and improve estimation via a synthesis of multiple causal estimates, which we call Bayesian causal synthesis. Our development is built upon identifying a synthesis function that correctly specifies the heterogeneous treatment effect under no unobserved confounding, and achieves the irreducible bias under unobserved confounding. We show that our proposed method results in consistent estimates of the heterogeneous treatment effect; either with no bias or with irreducible bias. We provide a computational algorithm for fast posterior sampling. Several benchmark simulations and an empirical study highlight the efficacy of the proposed approach compared to existing methodologies, providing improved point and density estimation of the heterogeneous treatment effect, even under unobserved confounding.

stat.ME↗

arXiv2023

Inadmissibility and Transience

We discuss the relation between the statistical question of inadmissibility and the probabilistic question of transience. Brown (1971) proved the mathematical link between the admissibility of the mean of a Gaussian distribution and the recurrence of a Brownian motion, which holds for $\mathbb{R}^{2}$ but not for $\mathbb{R}^{3}$ in Euclidean space. We extend this result to symmetric, non-Gaussian distributions, without assuming the existence of moments. As an application, we prove that the relation between the inadmissibility of the predictive density of a Cauchy distribution under a uniform prior and the transience of the Cauchy process differs from dimensions $\mathbb{R}^{1}$ to $\mathbb{R}^{2}$. We also show that there exists an extreme model that is inadmissible in $\mathbb{R}^{1}$.

math.ST↗

arXiv2021

Convergence of Computed Dynamic Models with Unbounded Shock

This paper studies the asymptotic convergence of computed dynamic models when the shock is unbounded. Most dynamic economic models lack a closed-form solution. As such, approximate solutions by numerical methods are utilized. Since the researcher cannot directly evaluate the exact policy function and the associated exact likelihood, it is imperative that the approximate likelihood asymptotically converges -- as well as to know the conditions of convergence -- to the exact likelihood, in order to justify and validate its usage. In this regard, Fernandez-Villaverde, Rubio-Ramirez, and Santos (2006) show convergence of the likelihood, when the shock has compact support. However, compact support implies that the shock is bounded, which is not an assumption met in most dynamic economic models, e.g., with normally distributed shocks. This paper provides theoretical justification for most dynamic models used in the literature by showing the conditions for convergence of the approximate invariant measure obtained from numerical simulations to the exact invariant measure, thus providing the conditions for convergence of the likelihood.

econ.EM↗

arXiv2019

Mean-shift least squares model averaging

This paper proposes a new estimator for selecting weights to average over least squares estimates obtained from a set of models. Our proposed estimator builds on the Mallows model average (MMA) estimator of Hansen (2007), but, unlike MMA, simultaneously controls for location bias and regression error through a common constant. We show that our proposed estimator-- the mean-shift Mallows model average (MSA) estimator-- is asymptotically optimal to the original MMA estimator in terms of mean squared error. A simulation study is presented, where we show that our proposed estimator uniformly outperforms the MMA estimator.

econ.EM↗

arXiv2017

Local Asymptotic Normality of Infinite-Dimensional Concave Extended Linear Models

We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In the above circumstance, narrow convergence with respect to uniform convergence fails to hold, because of the strength of it's topology. A new approach we propose to the lack-of-uniform-convergence is based on Mosco-convergence that is weaker topology than uniform convergence. By applying narrow convergence with respect to Mosco topology, we develop an infinite-dimensional version of the convexity argument and provide a proof of a local asymptotic normality. Our new technique also provides a proof of an asymptotic distribution of the likelihood ratio test statistic defined on real separable Hilbert spaces.

math.ST↗