Related papers: Test Martingales for bounded random variables

The density hypothesis on random times becomes now a standard in modeling of risks. One of the basic reasons to introduce the density hypothesis is the desire to have a computable credit risk model. However, recent work shows that merely an…

Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known…

Suppose that $X=\{X_t, t\ge 0; \mathbb{P}_{\mu}\}$ is a supercritical superprocess in a locally compact separable metric space $E$. Let $\phi_0$ be a positive eigenfunction corresponding to the first eigenvalue $\lambda_0$ of the generator…

We extend the approach of Walker (2003, 2004) to the case of misspecified models. A sufficient condition for establishing rates of convergence is given based on a key identity involving martingales, which does not require construction of…

Consider $\mathbb{G}$ the progressive enlargement of a filtration $\mathbb{F}$ with a random time $\tau$. Assuming that, in $\mathbb{F}$, the martingale representation property holds, we examine conditions under which the martingale…

To use machine learning in high stakes applications (e.g. medicine), we need tools for building confidence in the system and evaluating whether it is reliable. Methods to improve model reliability often require new learning algorithms (e.g.…

Extant "fast" algorithms for Monte Carlo confidence sets are limited to univariate shift parameters for the one-sample and two-sample problems using the sample mean as the test statistic; moreover, some do not converge reliably and most do…

We present a data-driven approach to the quantitative verification of probabilistic programs and stochastic dynamical models. Our approach leverages neural networks to compute tight and sound bounds for the probability that a stochastic…

Randomization testing is a fundamental method in statistics, enabling inferential tasks such as testing for (conditional) independence of random variables, constructing confidence intervals in semiparametric location models, and…

Arcade processes are a class of continuous stochastic processes that interpolate in a strong sense, i.e., omega by omega, between zeros at fixed pre-specified times. Their additive randomisation allows one to match any finite sequence of…

A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead,…

In this paper we introduce the concept of conic martingales}. This class refers to stochastic processes having the martingale property, but that evolve within given (possibly time-dependent) boundaries. We first review some results about…

High-dimensional tests are applied to find relevant sets of variables and relevant models. If variables are selected by analyzing the sums of products matrices and a corresponding mean-value test is performed, there is the danger that the…

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

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…

Let $X$ be a progressively measurable, almost surely right-continuous stochastic process such that $X_\tau \in L^1$ and $E[X_\tau] = E[X_0]$ for each finite stopping time $\tau$. In 2006, Cherny showed that $X$ is then a uniformly…

We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization…

Starting with a set of weighted items, we want to create a generic sample of a certain size that we can later use to estimate the total weight of arbitrary subsets. For this purpose, we propose priority sampling which tested on Internet…

Consider a branching process $\{Z_n\}$ in a varying environment. Let $\{W_n\}$ be the natural martingale $Z_n/{\bf E}Z_n$. It converges to some random variable $W$ as $n\to\infty$. An important problem is to show that ${\bf P}(W>0)$ equals…

In quantitative finance, we often fit a parametric semimartingale model to asset prices. To ensure our model is correct, we must then perform goodness-of-fit tests. In this paper, we give a new goodness-of-fit test for volatility-like…