Related papers: Improving Wald's (approximate) sequential probabil…
This paper revisits the classical problem of determining the bias of a weighted coin, where the bias is known to be either $p = 1/2 + \varepsilon$ or $p = 1/2 - \varepsilon$, while minimizing the expected number of coin tosses and the error…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
Recent advancements in large language models (LLMs) integrating explicit reasoning, such as OpenAI's o3-mini, DeepSeek-R1, and QWQ-32B, enable smaller models to solve complex tasks by generating intermediate reasoning steps prior to…
The sequential probability ratio test (SPRT) from statistics is known to have the least mean decision time compared to other sequential or fixed-time tests for given error rates. In some circumstances, cells need to make decisions…
Classifying sequential data as early and as accurately as possible is a challenging yet critical problem, especially when a sampling cost is high. One algorithm that achieves this goal is the sequential probability ratio test (SPRT), which…
Post-approval safety surveillance of medical products using observational healthcare data can help identify safety issues beyond those found in pre-approval trials. When testing sequentially as data accrue, maximum sequential probability…
In this paper, we develop a simple approach for testing multiple statistical hypotheses based on the observations of a number of probability ratios enumerated consecutively with respect to the index of hypotheses. Explicit and tight bounds…
We consider Wald's sequential probability ratio test for deciding whether a sequence of independent and identically distributed observations comes from a specified phase-type distribution or from an exponentially tilted alternative…
Time-sensitive machine learning benefits from Sequential Probability Ratio Test (SPRT), which provides an optimal stopping time for early classification of time series. However, in finite horizon scenarios, where input lengths are finite,…
We provide a novel analysis of Wald's sequential probability ratio test based on information theoretic measures for symmetric thresholds, symmetric noise, and equally likely hypotheses under the assumption that the test exactly terminates…
While many statistical procedures rely on a fixed sample size, sequential methods allow a decision-maker to adapt the sample size to achieve a given precision. In this way, sequential tests reduce the average number of observations required…
Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure…
This paper deals with the issue of testing hypothesis in symmetric and log-symmetric linear regression models in small and moderate-sized samples. We focus on four tests, namely the Wald, likelihood ratio, score, and gradient tests. These…
Background: Sequential positivity is often a necessary assumption for drawing causal inferences, such as through marginal structural modeling. Unfortunately, verification of this assumption can be challenging because it usually relies on…
Given a fixed-sample-size test that controls the error probabilities under two specific, but arbitrary, distributions, a 3-stage and two 4-stage tests are proposed and analyzed. For each of them, a novel, concrete, non-asymptotic,…
Variational quantum algorithms face a fundamental trainability crisis: barren plateaus render optimization exponentially difficult as system size grows. While recent Lie algebraic theory precisely characterizes when and why these plateaus…
We propose an adaptive sequential framework for testing two simple hypotheses that analytically ensures finite exposure to the less effective treatment. Our proposed procedure employs a likelihood ratio-driven adaptive allocation rule,…
The inflated beta regression model aims to enable the modeling of responses in the intervals $(0,1]$, $[0,1)$ or $[0,1]$. In this model, hypothesis testing is often performed based on the likelihood ratio statistic. The critical values are…
The article proposes a method of designing a statistically distinguishable rating scale that is not excessive in relation to the existing observation statistics. This allows for more stable validation with a fixed maximum number of…
Stochastic approximation (SA) is a classical approach for stochastic convex optimization. Previous studies have demonstrated that the convergence rate of SA can be improved by introducing either smoothness or strong convexity condition. In…