Related papers: La Baguette Math\'emagique
Many models require integrals of high-dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The…
The coefficient of restitution $\epsilon$ characterizes the energy retained when a ball bounces, and can easily be measured in an ``at home'' experiment. For thin-walled gas-filled balls such as basketballs, we construct a simple two…
We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and…
We study inference with a small labeled sample, a large unlabeled sample, and high-quality predictions from an external model. We link prediction-powered inference with empirical likelihood by stacking supervised estimating equations based…
A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…
Fr\'echet means, conceptually appealing, generalize the Euclidean expectation to general metric spaces. We explore how well Fr\'echet means can be estimated from independent and identically distributed samples and uncover a fundamental…
Fine-tuning studies whether some physical parameters, or relevant ratios between them, are located within so-called life-permitting intervals of small probability outside of which carbon-based life would not be possible. Recent developments…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
Familiar statistical tests and estimates are obtained by the direct observation of cases of interest: a clinical trial of a new drug, for instance, will compare the drug's effects on a relevant set of patients and controls. Sometimes,…
"No two rainbows are the same. Neither are two packs of Skittles. Enjoy an odd mix!". Using an interpretation via spatial random walks, we quantify the probability that two randomly selected packs of Skittles candy are identical and…
This paper presents necessary and sufficient conditions for on- and off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the…
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a…
The probability distribution p(l) of an atom to return to a step at distance l from the detachment site, with a random walk in between, is exactly enumerated. In particular, we study the dependence of p(l) on step roughness, presence of…
The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean rate for a Poisson model. Other…
Parameter inference is essential when interpreting observational data using mathematical models. Standard inference methods for differential equation models typically rely on obtaining repeated numerical solutions of the differential…
We extend the empirical likelihood of Owen [Ann. Statist. 18 (1990) 90-120] by partitioning its domain into the collection of its contours and mapping the contours through a continuous sequence of similarity transformations onto the full…
Because the stochastic calculus yields rarely random variables with laws defined by explicit closed formulas, probabilistic numerical computations are done most often by simulation. The simulation by the shift, whose field of application is…
Given an unconditional diffusion model targeting a joint model $\pi(x, y)$, using it to perform conditional simulation $\pi(x \mid y)$ is still largely an open question and is typically achieved by learning conditional drifts to the…
For the space of functions that can be approximated by linear chirps, we prove a reconstruction theorem by random sampling at arbitrary rates.
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…