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Kolyan Ray 与 Botond Szabo 对“鞅后验分布”的讨论AI 解读

We congratulate the authors for their thought-provoking article, which includes proposing a copula-based update for the predictive density and establishing its frequentist consistency under relatively mild assumptions. In this contribution, we further explore the frequentist properties of (Bayesian) predictive densities and illustrate through a simple example that, similarly to the posterior distribution, the predictive distribution can also be inconsistent. One therefore…

Isadora Antoniano Villalobos 对《鞅后验分布》的讨论AI 解读

I thank the authors for their refreshing ideas, providing many insights and intuitions on the process of statistical learning. For years, Bayesians have considered two levels of uncertainty, the likelihood and the prior. By shifting the focus to the predictive distribution as a single expression of uncertainty about a future observation (given data), the sequential nature of statistical learning is made explicit, together with some of its limitations. If each observation…

Mena Chavez 对《鞅后验分布》的讨论AI 解读

I congratulate the authors for introducing a novel approach for Bayesian inference, which avoids directly using the posterior distribution, often not available or computationally expensive. In addition to opening several lines of thinking about the foundations of Bayesian statistics, their proposal unveils many interesting directions to be explored and applied within the world of statistics. With an infinite population and the epistemic view of uncertainty (see, e.g.…

Wijayatunga对《鞅后验分布》的讨论意见AI 解读

Statistical uncertainty in (an estimate of) a parameter of a probability distribution is due to missing (unseen) observations (when it is estimated), as authors have noted. We can think that an estimate of the parameter has the maximal uncertainty when no observation is used for it, and no uncertainty when all possible observations are used for it. For example, in Bayesian sense, for a Bernoulli parameter, Beta distribution with parameter values α=1 and β=1 represents the…

布莱克·莫亚对《鞅后验分布》的讨论意见AI 解读

I would like to congratulate the authors on an expository and intuitive representation of statistical uncertainty. To assist in the further investigation of predictive resampling techniques, I have developed a software package for R (R Core Team, 2022) which implements some of the algorithms presented here as well as from subsequent work (Moya & Walker, 2023). The CopRe package (Moya, 2022), named for the copula resampling technique described in Section 4, can be installed…

贾琦顾与郭胜尹对《鞅后验分布》的讨论AI 解读

We congratulate the authors for their thought-provoking paper, especially in the three aspects as follows. Instead of imposing a prior π(θ) on the parameter θ of a likelihood function fθ(y)⁠, where both π and fθ are elicited subjectively, the authors proposed the framework of martingale posterior to directly model the predictive p(yn+1:∞∣y1:n) for which only the prior predictive p(y) needs to be specified. As a result, Bayesian inference can be conducted on any parameter (or…

Catalano、Fasano 与 Rebaudo 对《鞅后验分布》的讨论AI 解读

We congratulate the authors for an insightful foundational contribution to the statistical literature. This work builds on well-established methodologies, such as predictive inference, Doob’s theorem, and conditional independent sequences, providing a unifying framework and a novel understanding of Bayesian uncertainty. A central role is played by the predictive characterisation of the random parameter in terms of observable (yet unobserved) quantities, which are regarded as…

Pietro Rigo 对《鞅后验分布》的讨论AI 解读

This paper is really interesting and offers a number of intriguing hints. Here, I just make a few isolated remarks without any claim of being exhaustive. I would give more emphasis to the Ionescu-Tulcea theorem (ITT). This theorem is quoted only in passing, but it is the cornerstone of this paper. By ITT, the distribution of Y1:∞=(Y1,Y2,…) is completely determined by the assignment of {Pn:n≥0}⁠, where P0(⋅)=P(Y1∈⋅) and Pn(⋅)=P(Yn+1∈⋅∣Y1:n)⁠. Exploiting ITT has at least two…

Bertrand Clarke 对《鞅后验分布》的讨论AI 解读

To see the effect of the paper on statistical practice, consider the following hypothetical dialogue between a Quantitative Scientist (QS) and a Predictive Statistician (PS). QS: I’ve been thinking about the data generating mechanism and what we can safely assume pre-experimentally. PS: Actually, I’m more interested in what you think your n+1 data point would be. If you were going to predict your n+1 measurement, how would you do it? QS: I’d guess what the true model is and…

Ascolani、Lijoi与Prünster对《鞅后验分布》的讨论AI 解读

We would like to congratulate the authors on their fine and insightful contribution, which provides an original perspective on Bayesian inference and opens up new exciting research directions. The key point is a novel interpretation of the role of prediction: in a Bayesian framework all the uncertainty lies in the unobserved data Yn+1,∞ and, once they are imputed through the predictive distributions, inference is straightforward. Therefore, prediction rules, besides allowing…

对《鞅后验分布》的致谢提议与讨论AI 解读

Philip Dawid; Proposal of Vote of Thanks for “Martingale Posterior Distributions” by Edwin Fong, Chris Holmes and Stephen G. Walker, Journal of the Royal Statis

Ben Swallow对《鞅后验分布》的讨论意见AI 解读

Fong et al. (2023) present an interesting and novel approach to conducting Bayesian posterior estimation utilising a joint predictive distribution over missing potential observations and justify how this approach of generating one-step-ahead predictive distributions naturally aligns with the Bayesian likelihood-prior paradigm. The authors mention time series and hierarchical data as areas of potential future development. However, one of the major topics in Bayesian…

高维矩阵值时间序列的双向动态因子模型AI 解读

Abstract In this article, we introduce a two-way dynamic factor model (2w-DFM) for high-dimensional matrix-valued time series and study some of the basic theoretical properties in terms of identifiability and estimation accuracy. The proposed model aims to capture separable and low-dimensional effects of row and column attributes and their correlations across rows, columns, and time points. Complementary to other dynamic factor models for high-dimensional data, the 2w-DFM…

超越尖锐零假设的随机化推断：有界零假设与个体处理效应分位数AI 解读

Abstract Randomisation inference (RI) is typically interpreted as testing Fisher’s ‘sharp’ null hypothesis that all unit-level effects are exactly zero. This hypothesis is often criticised as restrictive and implausible, making its rejection scientifically uninteresting. We show, however, that many randomisation tests are also valid for a ‘bounded’ null hypothesis under which the unit-level effects are all non-positive (or all non-negative) but are otherwise heterogeneous.…

Maxway CRT：提高 model-X 推断的稳健性AI 解读

Abstract The model-X conditional randomisation test (CRT) is a flexible and powerful testing procedure for testing the hypothesis X⫫Y∣Z. However, it requires perfect knowledge of X∣Z and may lose its validity when there is an error in modelling X∣Z. This problem is even more severe when Z is of high dimensionality. In response to this, we propose the Maxway CRT, which learns the distribution of Y∣Z and uses it to calibrate the resampling distribution of X to gain robustness…

基于回归秩得分的异质分位数处理效应去偏推断AI 解读

Abstract Understanding treatment effect heterogeneity is vital to many scientific fields because the same treatment may affect different individuals differently. Quantile regression provides a natural framework for modelling such heterogeneity. We propose a new method for inference on heterogeneous quantile treatment effects (HQTE) in the presence of high-dimensional covariates. Our estimator combines an ℓ1-penalised regression adjustment with a quantile-specific bias…

基于 l₁ 球先验的贝叶斯推断：用精确零值求解组合问题AI 解读

Abstract The l1-regularisation is very popular in high-dimensional statistics—it changes a combinatorial problem of choosing which subset of the parameter is zero, into a simple continuous optimisation. Using a continuous prior concentrated near zero, the Bayesian counterparts are successful in quantifying the uncertainty in the variable selection problems; nevertheless, the lack of exact zeros makes it difficult for broader problems such as change-point detection and rank…

基于深度神经网络的图像响应回归AI 解读

Abstract Delineating associations between images and covariates is a central aim of imaging studies. To tackle this problem, we propose a novel non-parametric approach in the framework of spatially varying coefficient models, where the spatially varying functions are estimated through deep neural networks. Our method incorporates spatial smoothness, handles subject heterogeneity, and provides straightforward interpretations. It is also highly flexible and accurate, making it…

矩阵值数据的核心收缩协方差估计AI 解读

Abstract A separable covariance model can describe the among-row and among-column correlations of a random matrix and permits likelihood-based inference with a very small sample size. However, if the assumption of separability is not met, data analysis with a separable model may misrepresent important dependence patterns in the data. As a compromise between separable and unstructured covariance estimation, we decompose a covariance matrix into a separable component and a…

随机实验中处理效应的半参数估计AI 解读

Abstract We develop new semi-parametric methods for estimating treatment effects. We focus on settings where the outcome distributions may be thick tailed, where treatment effects may be small, where sample sizes are large, and where assignment is completely random. This setting is of particular interest in recent online experimentation. We propose using parametric models for the treatment effects, leading to semi-parametric models for the outcome distributions. We derive…

适应未知协变量分布漂移的预测集AI 解读

Abstract Predicting sets of outcomes—instead of unique outcomes—is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to unknown covariate shift—a prevalent issue in practice—poses a serious unsolved challenge. In this article, we show that prediction sets with finite-sample coverage guarantee are uninformative and propose a novel flexible…

DeCAMFounder：存在隐藏变量时的非线性因果发现AI 解读

Abstract Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical scenarios. Without additional assumptions about the unobserved variables, it is not possible to recover any causal relationships from observational data. Fortunately, in many applied settings, additional structure among the confounders…

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分位数自回归条件异方差模型AI 解读

Abstract This article proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(∞) form of the GARCH model. This model can provide varying structures for conditional quantiles of the time series across different quantile levels, while including the commonly used GARCH model as a special case. The strict stationarity of the model is discussed. For robustness against heavy-tailed distributions, a…