Related papers: Estimating the selection efficiency
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…
In Bayesian meta-analysis, the specification of prior probabilities for the between-study heterogeneity is commonly required, and is of particular benefit in situations where only few studies are included. Among the considerations in the…
We consider situations in Bayesian analysis where we have a family of priors $\nu_h$ on the parameter $\theta$, where $h$ varies continuously over a space $\mathcal{H}$, and we deal with two related problems. The first involves sensitivity…
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…
Regression plays a key role in many research areas and its variable selection is a classic and major problem. This study emphasizes cost of predictors to be purchased for future use, when we select a subset of them. Its economic aspect is…
We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…
The goal of this paper is to compare several widely used Bayesian model selection methods in practical model selection problems, highlight their differences and give recommendations about the preferred approaches. We focus on the variable…
This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
Nested sampling has emerged as a valuable tool for Bayesian analysis, in particular for determining the Bayesian evidence. The method is based on a specific type of random sampling of the likelihood function and prior volume of the…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
State-of-the-art multi-objective optimization often assumes a known utility function, learns it interactively, or computes the full Pareto front-each requiring costly expert input.~Real-world problems, however, involve implicit preferences…
In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, we compare the risk functions of the Bayes estimators based on the…
Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…
A general challenge in statistics is prediction in the presence of multiple candidate models or learning algorithms. Model aggregation tries to combine all predictive distributions from individual models, which is more stable and flexible…
A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…