Related papers: Exact Computation of Minimum Sample size for Estim…

In this paper we use a Malliavin-Stein type method to investigate Poisson and normal approximations for the measurable functions of infinitely many independent random variables. We combine Stein's method with the difference operators in…

Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…

A common approach to modelling extreme values is to consider the excesses above a high threshold as realisations of a non-homogeneous Poisson process. While this method offers the advantage of modelling using threshold-invariant extreme…

We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…

Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…

This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and the sum (or equivalently the mean) of the parameters is introduced. Under…

Compound Poisson distributions have been employed by many authors to fit experimental data, typically via the method of moments or maximum likelihood estimation. We propose a new technique and apply it to several sets of published data. It…

It is well-known that assumptions of monotonicity in size-bias couplings may be used to prove simple, yet powerful, Poisson approximation results. Here we show how these assumptions may be relaxed, establishing explicit Poisson…

Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…

We revisit the problem of constructing predictive confidence sets for which we wish to obtain some type of conditional validity. We provide new arguments showing how ``split conformal'' methods achieve near desired coverage levels with high…

Protection against disclosure is a legal and ethical obligation for agencies releasing microdata files for public use. Consider a microdata sample of size $n$ from a finite population of size $\bar{n}=n+\lambda n$, with $\lambda>0$, such…

This paper develops a theory and methodology for estimation of Gini index such that both cost of sampling and estimation error are minimum. Methods in which sample size is fixed in advance, cannot minimize estimation error and sampling cost…

Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…

Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling…

It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$…

Approximate Bayesian computation (ABC) is an approach for sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model,…

We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly…

Models often need to be constrained to a certain size for them to be considered interpretable. For example, a decision tree of depth 5 is much easier to understand than one of depth 50. Limiting model size, however, often reduces accuracy.…

For all $n, \epsilon >0$, we show that the set of Poisson Binomial distributions on $n$ variables admits a proper $\epsilon$-cover in total variation distance of size $n^2+n \cdot (1/\epsilon)^{O(\log^2 (1/\epsilon))}$, which can also be…