Related papers: Bounds on Bayes Factors for Binomial A/B Testing
Large-scale multiple testing problems require the simultaneous assessment of many p-values. This paper compares several methods to assess the evidence in multiple binomial counts of p-values: the maximum of the binomial counts after…
When developing a new networking algorithm, it is established practice to run a randomized experiment, or A/B test, to evaluate its performance. In an A/B test, traffic is randomly allocated between a treatment group, which uses the new…
We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions,…
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
Tolerance limits have received considerable attention in the statistical literature, with applications reaching far beyond their initial role in quality control. The well-known formula of Scheff\'e and Tukey (1944) establishes a simple,…
Bayesian methods are increasingly applied in these days in the theory and practice of statistics. Any Bayesian inference depends on a likelihood and a prior. Ideally one would like to elicit a prior from related sources of information or…
We investigate moment sequences of probability measures on $E\subset\mathbb{R}$ under constraints of certain moments being fixed. This corresponds to studying sections of $n$-th moment spaces, i.e. the spaces of moment sequences of order…
Scientific theories can often be formulated using equality and order constraints on the relative effects in a linear regression model. For example, it may be expected that the effect of the first predictor is larger than the effect of the…
Bayesian model selection poses two main challenges: the specification of parameter priors for all models, and the computation of the resulting Bayes factors between models. There is now a large literature on automatic and objective…
The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…
Priors in which a large number of parameters are specified to be independent are dangerous; they make it hard to learn from data. I present a couple of examples from the literature and work through a bit of large sample theory to show what…
We study the Besov regularity of wavelet series on $\mathbb{R}^d$ with randomly chosen coefficients. More precisely, each coefficient is a product of a random factor and a parameterized deterministic factor (decaying with the scale $j$ and…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
Businesses frequently run online controlled experiments (i.e., A/B tests) to learn about the effect of an intervention on multiple business metrics. To account for multiple hypothesis testing, multiple metrics are commonly aggregated into a…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
We develop a method to perform model averaging in two-stage linear regression systems subject to endogeneity. Our method extends an existing Gibbs sampler for instrumental variables to incorporate a component of model uncertainty. Direct…
When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most…
Bayesian hypothesis testing is investigated when the prior probabilities of the hypotheses, taken as a random vector, are quantized. Nearest neighbor and centroid conditions are derived using mean Bayes risk error as a distortion measure…
We generalise the known fact that for binomial $X_{n,k} \sim \mathrm{Bin}(n, k/n)$ one has $\inf_{k>1,n} \mathrm{P}(X_{n,k} \geq k) \geq \lim_{k \to 1+}\mathrm{P}(X_{2,k} \geq k) = 1/4$ to cover probabilities of exceeding a constant shift…
In this work, we undertake a comprehensive reformulation, modification, and extension of Smith and Spiegelhalter's (1980) and (1982) Bayes Factor work within the evolving subject of Objective Bayes Factors. Our primary focus centers on…