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We lay out novel foundations for the computer-aided verification of guaranteed bounds on expected outcomes of imperative probabilistic programs featuring (i) general loops, (ii) continuous distributions, and (iii) conditioning. To handle…
A common approach to synthetic data is to sample from a fitted model. We show that under general assumptions, this approach results in a sample with inefficient estimators and whose joint distribution is inconsistent with the true…
We develop conservative tests for the mean of a bounded population under stratified sampling and apply them to risk-limiting post-election audits. The tests are ``anytime valid'' under sequential sampling, allowing optional stopping in each…
Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Many existing network inference solutions focus on global testing of entire networks, without comparing individual network…
The mitigation of false positives is an important issue when conducting multiple hypothesis testing. The most popular paradigm for false positives mitigation in high-dimensional applications is via the control of the false discovery rate…
Monte Carlo (MC) permutation test is considered the gold standard for statistical hypothesis testing, especially when standard parametric assumptions are not clear or likely to fail. However, in modern data science settings where a large…
The circular uniform distribution on the unit circle is closed under summation, that is, the sum of independent circular uniformly distributed random variables is also circular uniformly distributed. In this study, it is shown that a family…
Conventional multiple testing procedures often assume hypotheses for different features are exchangeable. However, in many scientific applications, additional covariate information regarding the patterns of signals and nulls are available.…
Statistical hypothesis testing and effect size measurement are routine parts of quantitative research. Advancements in computer processing power have greatly improved the capability of statistical inference through the availability of…
We study the sample complexity of the Sign-Perturbed Sums (SPS) method, which constructs exact, non-asymptotic confidence regions for the true system parameters under mild statistical assumptions, such as independent and symmetric noise…
A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…
We consider the problem of inference on the signs of $n>1$ parameters. We aim to provide $1-\alpha$ post-hoc confidence bounds on the number of positive and negative (or non-positive) parameters. The guarantee is simultaneous, for all…
In this article, we propose a generalized weighted version of the well-known Benjamini-Hochberg (BH) procedure. The rigorous weighting scheme used by our method enables it to encode structural information from simultaneous multi-way…
Continuous POMDPs with general belief-dependent rewards are notoriously difficult to solve online. In this paper, we present a complete provable theory of adaptive multilevel simplification for the setting of a given externally constructed…
Hypothesis tests under order restrictions arise in a wide range of scientific applications. By exploiting inequality constraints, such tests can achieve substantial gains in power and interpretability. However, these gains come at a cost:…
Consider the problem of simultaneously testing null hypotheses H_1,...,H_s. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of…
We describe group sequential tests which efficiently incorporate information from multiple endpoints allowing for early stopping at pre-planned interim analyses. We formulate a testing procedure where several outcomes are examined, and…
Online decision making under uncertainty in partially observable domains, also known as Belief Space Planning, is a fundamental problem in robotics and Artificial Intelligence. Due to an abundance of plausible future unravelings,…
Assessing goodness of fit to a given distribution plays an important role in computational statistics. The Probability integral transformation (PIT) can be used to convert the question of whether a given sample originates from a reference…
This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…