Related papers: Admissible anytime-valid sequential inference must…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo…
We introduce a new class of reflected backward stochastic differential equations with two c\`adl\`ag barriers, which need not satisfy any separation conditions. For that reason, in general, the solutions are not semimartingales. We prove…
Distinguishing two candidate models is a fundamental and practically important statistical problem. Error rate control is crucial to the testing logic but, in complex nonparametric settings, can be difficult to achieve, especially when the…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete…
We prove inequalities involving noncommutative differentially subordinate martingales. More precisely, we prove that if $x$ is a self-adjoint noncommutative martingale and $y$ is weakly differentially subordinate to $x$ then $y$ admits a…
Adaptive clinical trials rely on interim analyses, flexible stopping, and data-dependent design modifications that complicate statistical guarantees when fixed-horizon test statistics are repeatedly inspected or reused after adaptations.…
We show the first unconditional pseudo-determinism result for all of search-BPP. Specifically, we show that every BPP search problem can be computed pseudo-deterministically on average for infinitely many input lengths. In other words, for…
Inference metaprogramming enables effective probabilistic programming by supporting the decomposition of executions of probabilistic programs into subproblems and the deployment of hybrid probabilistic inference algorithms that apply…
Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number…
A nonnegative martingale with initial value equal to one measures evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. If we exaggerate the evidence by considering…
We study class of L\'{e}vy processes having distributions being indentifiable by moments. We define system of polynomial martingales \newline $\left\{ M_{n}(X_{t},t),\mathcal{F}_{\leq t}\right\} _{n\geq 1},$ where $% \mathcal{F}_{\leq t}$…
In this paper we extend the notion of ``filtration-consistent nonlinear expectation" (or "${\cal F}$-consistent nonlinear expectation") to the case when it is allowed to be dominated by a $g$-expectation that may have a quadratic growth. We…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
This paper studies causal discovery in irregularly sampled time series-a key challenge in risk-sensitive domains like finance, healthcare, and climate science, where missing data and inconsistent sampling frequencies distort causal…
A subvector of predictor that satisfies the ignorability assumption, whose index set is called a sufficient adjustment set, is crucial for conducting reliable causal inference based on observational data. In this paper, we propose a general…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…