Xinjia Chen
In this paper, we develop an approach for optimizing the explicit binomial confidence interval recently derived by Chen et al. The optimization reduces conservativeness while guaranteeing prescribed coverage probability.
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In this paper, we develop an exact method for computing the minimum coverage probability of Wald interval for estimation of binomial parameters. Similar approach can be used for other type of confidence intervals.
In this paper, we derive an explicit formula for constructing the confidence interval of binomial parameter with guaranteed coverage probability. The formula overcomes the limitation of normal approximation which is asymptotic in nature and thus inevitably introduce unknown errors in applications. Moreover, the formula is very tight in comparison with classic Clopper-Pearson's approach from the perspective of interval width. Based on the rigorous formula, we also obtain approximate formulas with excellent performance of coverage probability.
We consider the classic problem of interval estimation of a proportion $p$ based on binomial sampling. The "exact" Clopper-Pearson confidence interval for $p$ is known to be unnecessarily conservative. We propose coverage-adjustments of the Clopper-Pearson interval using prior and posterior distributions of $p$. The adjusted intervals have improved coverage and are often shorter than competing intervals found in the literature. Using new heatmap-type plots for comparing confidence intervals, we find that the coverage-adjusted intervals are particularly suitable for $p$ close to 0 or 1.
When computing a confidence interval for a binomial proportion p one must choose between using an exact interval, which has a coverage probability of at least 1-α for all values of p, and a shorter approximate interval, which may have lower coverage for some p but that on average has coverage equal to 1-α. We investigate the cost of using the exact one and two-sided Clopper--Pearson confidence intervals rather than shorter approximate intervals, first in terms of increased expected length and then in terms of the increase in sample size required to obtain a desired expected length. Using asymp…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random intervals with respect to corresponding parameters are achieved at discrete finite sets and that the coverage probabilities are continuous and unimodal when parameters are varying in between interval endpoints. The theory applies to common important discrete random variables including binomial variable, Poisson variable, negative binomial variable and hypergeo…
It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such a very old but also extremely important problem and demonstrate that the difficulty for obtaining the exact solution is not insurmountable. Unlike the classical approximate sample size method based on the central limit theorem, we develop a new approach for computing the minimum sample size that does not require any approximation. Moreover, our approach over…
Well-recommended methods of forming `confidence intervals' for a binomial proportion give interval estimates that do not actually meet the definition of a confidence interval, in that their coverages are sometimes lower than the nominal confidence level. The methods are favoured because their intervals have a shorter average length than the Clopper-Pearson (gold-standard) method, whose intervals really are confidence intervals. Comparison of such methods is tricky -- the best method should perhaps be the one that gives the shortest intervals (on average), but when is the coverage of a method s…
We consider interval estimation of the difference between two binomial proportions. Several methods of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly smaller than the nominal confidence level. In this paper a new confidence interval is proposed. The construction needs only information on sample sizes and sample difference between proportions. The coverage probability of the proposed confidence interval is at least the nominal confidence level. The new confidence interval is illustrated by a medical example.
It is challenging to deal with censored data, where we only have access to the incomplete information of survival time instead of its exact value. Fortunately, under linear predictor assumption, people can obtain guaranteed coverage for the confidence band of survival time using methods like Cox Regression. However, when relaxing the linear assumption with neural networks (e.g., Cox-MLP (Katzman et al., 2018; Kvamme et al., 2019)), we lose the guaranteed coverage. To recover the guaranteed coverage without linear assumption, we propose two algorithms based on conformal inference. In the first …
Split sample methods have recently been put forward as a way to reduce the coverage oscillations that haunt confidence intervals for parameters of lattice distributions, such as the binomial and Poisson distributions. We study split sample intervals in the binomial setting, showing that these intervals can be viewed as being based on adding discrete random noise to the data. It is shown that they can be improved upon by using noise with a continuous distribution instead, regardless of whether the randomization is determined by the data or an external source of randomness. We compare split samp…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal approximation is often unreliable in one-sample inference and proposed alternative techniques. We seek to extend these methods to the problem of two-sample inference on the difference of sample means in highly dispersed Negative Binomial models. We demonstrate that the Normal approximation is considerably more robust in the two-sample setting and may often b…
There are over 55 different ways to construct a confidence respectively credible interval (CI) for the binomial proportion. Methods to compare them are necessary to decide which should be used in practice. The interval score has been suggested to compare prediction intervals. This score is a proper scoring rule that combines the coverage as a measure of calibration and the width as a measure of sharpness. We evaluate eleven CIs for the binomial proportion based on the expected interval score and propose a summary measure which can take into account different weighting of the underlying true pr…
Binomial confidence intervals for rare events: importance of defining margin of error relative to magnitude of proportion
本文针对稀有事件比例估计，提出以相对误差边际衡量置信区间精度，并评估四种常用区间方法在覆盖概率与相对误差边际下的表现，给出实践中可采用的相对误差边际取值范围。
We introduce a new framework for creating point-wise confidence intervals for the distribution of event times for current status data. Existing methods are based on asymptotics. Our framework is based on binomial properties and motivates confidence intervals that are very simple to apply and are valid, i.e., guarantee nominal coverage. Although these confidence intervals are necessarily conservative for small sample sizes, asymptotically their coverage rate approaches the nominal one. This binomial framework also motivates approximately valid confidence intervals, and simulations show that the…
Robust Confidence Intervals for a Binomial Proportion: Local Optimality and Adaptivity
本文研究了在未知污染比例下二项比例的稳健置信区间构造，通过局部最优性和适应性分析，提出了一种保证有效覆盖和高效计算的置信区间方法，并探讨了其在泊松数据和Erdős--Rényi模型中的应用。
Conformal Tradeoffs: Operational Profiles Beyond Coverage
本文提出SSBC方法，通过校准与审计机制，在有限样本下实现精确覆盖语义，并通过诱导划分揭示制度边界和权衡问题。
The Elliptically Optimal Confidence Interval: A Bivariate Extension of Wilson's Score Method
本文提出椭圆最优置信区间，通过闭式优化投影椭圆区域构造二项比例差的最短得分区间，保证覆盖且不欠覆盖，并精确量化极端比例下的过度覆盖。
The Negative Binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard Normal approximation often does not provide adequate inferences about the data's mean in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expected value. These methods were based upon Gamma and Chi Square approximations or tail probability bounds such as Bernstein's Inequality. We now propose growth estimators of the Negative Binomial mean. Under high dis…
Penalized likelihood inference for beta-binomial meta-analysis of proportions of rare events
针对罕见事件比例元分析中常用最大似然估计器存在有限样本偏差的问题，提出最大惩罚似然估计器，通过最大化Jeffreys先验惩罚增强的对数似然得到，模拟显示其在多方面优于普通MLE，还引入新置信区间，为相关元分析提供有用替代方法。
An Accurate Computational Approach for Partial Likelihood Using Poisson-Binomial Distributions
针对Cox模型偏似然近似计算不精确的问题，提出基于泊松-二项分布精确计算条件概率的方法，统一处理有结与无结数据，减少偏差和均方误差，提高置信区间覆盖率。
Robust Conformal Prediction under Distribution Shift via Physics-Informed Structural Causal Model
针对分布偏移下保形预测覆盖失效问题，利用累积密度函数与Wasserstein距离界定覆盖差异上界，并提出物理信息结构因果模型（PI-SCM）降低该上界，有效提升了多任务下的覆盖鲁棒性。
Conformal inference, cross-validation+, and the jackknife+ are hold-out methods that can be combined with virtually any machine learning algorithm to construct prediction sets with guaranteed marginal coverage. In this paper, we develop specialized versions of these techniques for categorical and unordered response labels that, in addition to providing marginal coverage, are also fully adaptive to complex data distributions, in the sense that they perform favorably in terms of approximate conditional coverage compared to alternative methods. The heart of our contribution is a novel conformity …
Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there continues to be new work on this issue and no consensus solution. Previous reviews have focused primarily on testing and the properties of validity and power, or primarily on confidence intervals, their coverage, and expected length. Here we evaluate both. For example, we consider whether a p-value and its matching confidence interval are compatible, meaning …
Signed-Perturbed Sums Estimation of ARX Systems: Exact Coverage and Strong Consistency (Extended Version)
本文研究ARX系统的符号扰动和（SPS）方法，证明其置信域在有限数据下具有用户选择的精确覆盖概率，并具备强一致性，同时渐近性能逼近传统置信椭球。
Generative Conformal Prediction with Optimized Coverage Allocation
针对传统保形预测在多维场景中不确定性集合过于保守的问题，提出基于向量化非一致性得分的生成式保形预测框架，利用生成模型采样多预测构建自适应集合，在多数据集上优于现有技术。
Though black-box predictors are state-of-the-art for many complex tasks, they often fail to properly quantify predictive uncertainty and may provide inappropriate predictions for unfamiliar data. Instead, we can learn more reliable models by letting them either output a prediction set or abstain when the uncertainty is high. We propose training these selective prediction-set models using an uncertainty-aware loss minimization framework, which unifies ideas from decision theory and robust maximum likelihood. Moreover, since black-box methods are not guaranteed to output well-calibrated predicti…
Quasi-Monte Carlo confidence intervals using quantiles of randomized nets
本文提出利用随机化网的分位数构造高维积分的渐近有效置信区间方法。
Weighted Conformal Prediction Provides Adaptive and Valid Mask-Conditional Coverage for General Missing Data Mechanisms
本文提出加权置信预测方法，通过预填补掩码并校正预测集，提供对一般缺失数据机制的边缘覆盖性和掩码条件有效性。
Exact Conditional Confidence Intervals for Cramér's V: Near-Nominal and Tight Where the Guaranteed Interval Is Wide and the Software Interval Does Not Cover
针对Cramér's V置信区间难以构造的问题，本文通过条件于观测边际计算精确分布并求逆，得到接近名义水平且宽度仅为投影区间三分之一到一半的区间，以估计目标改变为代价。
Conformal Predictions for Longitudinal Data
提出无分布的LPCI保形预测算法，通过分位数固定效应回归构造有限宽度区间，同时保证纵向数据的纵向与横截面覆盖，实验与理论均验证其优于现有方法。
We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a logarithmic factor. The corresponding support estimate enjoys control of both false negatives and false positives. Simulatio…
Existing inferential methods for small area data involve a trade-off between maintaining area-level frequentist coverage rates and improving inferential precision via the incorporation of indirect information. In this article, we propose a method to obtain an area-level prediction region for a future observation which mitigates this trade-off. The proposed method takes a conformal prediction approach in which the conformity measure is the posterior predictive density of a working model that incorporates indirect information. The resulting prediction region has guaranteed frequentist coverage r…
We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the mean with high probability for all distributions on a bounded interval, for all samples sizes, and for all confidence levels. This new method provides confidence intervals that are competitive with those produced using Student's t-statistic, but does not rely on normality assumptions. In particular, its only requirement is that the distribution be bounded on a …
Fast Conformal Prediction using Conditional Interquantile Intervals
本文提出CIR和CIR+方法，通过改进的分位数区间构建技术，实现高效且准确的符合预测，适用于处理偏斜分布和提高计算效率。
This article presents an algorithm that generates a conservative confidence interval of a specified length and coverage probability for the power of a Monte Carlo test (such as a bootstrap or permutation test). It is the first method that achieves this aim for almost any Monte Carlo test. Previous research has focused on obtaining as accurate a result as possible for a fixed computational effort, without providing a guaranteed precision in the above sense. The algorithm we propose does not have a fixed effort and runs until a confidence interval with a user-specified length and coverage probab…
Adaptive Bounding Box Uncertainties via Two-Step Conformal Prediction
针对多目标检测中边界框不确定性量化问题，提出两步保形预测方法，将类别标签预测的不确定性传播至边界框区间，并结合集成与分位数回归实现适应物体大小的均衡覆盖率，在真实数据集上验证了其满足期望覆盖率且区间紧凑。
Uncertainty Quantification over Graph with Conformalized Graph Neural Networks
本文提出共形化图神经网络（CF-GNN），将共形预测扩展到图数据，通过置换不变性条件保证覆盖率，并利用拓扑感知的输出校正模型显著减小预测集合/区间大小，在保证目标边际覆盖率的同时将集合大小最多减小74%。
Optimal Decision-Making Based on Prediction Sets
本文提出ROCP算法，通过最小化稳健风险来优化基于预测集的决策制定，适用于医疗诊断等安全关键任务。
Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression
本文提出VSPS方法，利用条件归一化流与共形校准为多目标回归构建灵活非凸预测区域，在保证覆盖概率的同时生成更小、更具信息量的预测区域，有效提升了复杂高维环境下的不确定性建模能力。
Design-based conformal prediction
本文邀请调查方法学家使用保形预测，在基于设计的有限总体推断框架下将其应用于复杂样本调查数据，并通过模拟和真实数据验证其有限样本覆盖率保证。
Conformal Thresholded Intervals for Efficient Regression
本文提出共形阈值区间（CTI）方法，利用多输出分位数回归估计条件概率密度，通过长度阈值化构建预测集，在保证边际覆盖率的同时实现最小预测集，并在多个数据集上优于现有共形回归方法。
Wasserstein-regularized Conformal Prediction under General Distribution Shift
针对一般联合分布偏移下保形预测覆盖差距难以控制的问题，提出基于Wasserstein距离的覆盖差距上界及WR-CP算法，通过分离协变量与概念偏移影响，在准确性与效率间取得平衡，实验证明覆盖差距降至3.2%，预测集平均缩小37%。
ConfEviSurrogate: A Conformalized Evidential Surrogate Model for Uncertainty Quantification
针对代理模型不确定性量化成本高、无法分离来源及缺乏覆盖率保证的问题，提出ConfEviSurrogate模型，通过学习高阶证据分布与保形预测校准，实现预测区间分离并提升可靠性。
This paper reviews two main types of prediction interval methods under a parametric framework. First, we describe methods based on an (approximate) pivotal quantity. Examples include the plug-in, pivotal, and calibration methods. Then we describe methods based on a predictive distribution (sometimes derived based on the likelihood). Examples include Bayesian, fiducial, and direct-bootstrap methods. Several examples involving continuous distributions along with simulation studies to evaluate coverage probability properties are provided. We provide specific connections among different prediction…
Enhancing Adversarial Robustness with Conformal Prediction: A Framework for Guaranteed Model Reliability
本文提出 OPSA 攻击及融合该攻击的 OPSA-AT conformal 对抗训练框架，在增大预测不确定性的同时提升模型对多种对抗攻击的鲁棒性与可靠性。
Comparing Two Survival Functions at a Fixed Timepoint
本文针对右删失下固定时间点的两条生存函数比较问题，将单样本Greenwood方差调整纳入delta法两样本应用，扩展BPCP融合区间为中p版本，经模拟发现BPCP融合可保证全场景覆盖率，中p版本覆盖率最接近名义，还提供了bpcp R包函数。
Sequential Conformal Calibration under Recursive Selection
本文针对递归选择场景提出序列共形校准方法，推导了覆盖过程规律，刻画了新鲜度与数据复用的权衡，将其应用于多级库存问题，模拟显示其覆盖达标且成本低于Bonferroni基线。
Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this gap by first defining different methods for the construction of confidence intervals, and then by their application to a binomial proportion, the mean value, and to arbitrary estimators. Beside the frequentist approach, the likelihood ratio and the highest posterior density approach are explained. Two methods to estimate the variance of general maximum likel…
Hierarchical Conformal Classification
本文提出分层保形分类（HCC），将类别层级结构融入保形预测的预测集，通过约束优化在保持覆盖保证的同时生成分层预测集，并在音频、图像和文本基准上验证了其优势。
Multi-Distribution Robust Conformal Prediction
研究在多源分布下构建一致有效的共形预测集问题，提出最大\(p\)聚合方案，证明其最优性并给出学习一致性分数算法，实验表明该方法能在多分布上提供有效覆盖率且减小集合大小。
Co-optimization for Adaptive Conformal Prediction
CoCP通过联合优化中心和半径，改进了置信区间的效率和准确性，实现了更短的区间和更精确的覆盖诊断。
Network Weighted Functional Regression: a method for modeling dependencies between functional data in a network
本文提出网络加权函数回归（NWFR）模型，通过显式建模网络结构来处理网络设定下的函数数据，并开发了函数保形预测程序生成免分布预测区间，显著提升了点预测准确度及预测区间的有效性与精确度。
Optimal Conformal Prediction under Epistemic Uncertainty
研究如何在能表达偶然和认知不确定性的信念集上最优应用共形预测，提出概率伯努利预测集及变体，处理信念集有效性无保证场景，通过共形风险控制得出PAC风格保证，并经实证验证理论发现。
Consider the observation of n iid realizations of an experiment with d>1 possible outcomes, which corresponds to a single observation of a multinomial distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}. In many applications, the construction of a confidence region for p when n is small is crucial. This concrete challenging problem has a long history. It is well known that the confidence regions built from asymptotic statistics do not have good coverage when n is small. On the other hand, most available methods providing non-asymptotic regions with controlled coverage …
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