Related papers: Nested sampling for frequentist computation: fast …
We propose a nonparametric estimator of multivariate joint entropy based on partitioned sample spacing (PSS). The method extends univariate spacing ideas to $\mathbb{R}^{d}$ by partitioning into localized cells and aggregating within-cell…
Nested simulation is a natural approach to tackle nested estimation problems in operations research and financial engineering. The outer-level simulation generates outer scenarios and the inner-level simulations are run in each outer…
This paper focuses on utilizing two different Bayesian methods to deal with a variety of toy problems which occur in data analysis. In particular we implement the Variational Bayesian and Nested Sampling methods to tackle the problems of…
We investigate the problem of computing a nested expectation of the form $\mathbb{P}[\mathbb{E}[X|Y] \!\geq\!0]\!=\!\mathbb{E}[\textrm{H}(\mathbb{E}[X|Y])]$ where $\textrm{H}$ is the Heaviside function. This nested expectation appears, for…
Inferring parameters and testing hypotheses from gravitational wave signals is a computationally intensive task central to modern astrophysics. Nested sampling, a Bayesian inference technique, has become an established standard for this in…
The problem of estimating the probability p=P(g(X<0) is considered when X represents a multivariate stochastic input of a monotone function g. First, a heuristic method to bound p is formally described, involving a specialized design of…
Nested sampling is a Bayesian sampling technique developed to explore probability distributions lo- calised in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence…
Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…
Likelihood ratio tests are a widely used method in global analyses in particle physics. The computation of the statistical significance (p-value) of these tests is usually done with a simple formula that relies on Wilks' theorem. There are,…
Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the step-by-step exploration of the parameter space by Monte Carlo sampling with a…
The nested sampling algorithm has been shown to be a general method for calculating the pressure-temperature-composition phase diagrams of materials. While the previous implementation used single-particle Monte Carlo moves, these are…
Hypothesis tests calibrated by (re)sampling methods (such as permutation, rank and bootstrap tests) are useful tools for statistical analysis, at the computational cost of requiring Monte-Carlo sampling for calibration. It is common and…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
We present a systematic study of the nested sampling algorithm based on the example of the Potts model. This model, which exhibits a first order phase transition for $q>4$, exemplifies a generic numerical challenge in statistical physics:…
Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…
Estimating the p-th frequency moment of data stream is a very heavily studied problem. The problem is actually trivial when p = 1, assuming the strict Turnstile model. The sample complexity of our proposed algorithm is essentially O(1) near…
Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new…
We analyze the computational efficiency of approximate Bayesian computation (ABC), which approximates a likelihood function by drawing pseudo-samples from the associated model. For the rejection sampling version of ABC, it is known that…
This paper introduces an open-ended sequential algorithm for computing the p-value of a test using Monte Carlo simulation. It guarantees that the resampling risk, the probability of a different decision than the one based on the theoretical…
We are concerned with testing replicability hypotheses for many endpoints simultaneously. This constitutes a multiple test problem with composite null hypotheses. Traditional $p$-values, which are computed under least favourable parameter…