Related papers: Methods to Compute Prediction Intervals: A Review …
The goal of any estimation study is an interval estimation of a the parameter(s) of interest. These estimations are mostly expressed using empirical confidence intervals that are based on sample point estimates of the corresponding…
In this paper, we develop interval estimation methods for means of bounded random variables based on a sequential procedure such that the sampling is continued until the sample sum is no less than a prescribed threshold.
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
The problem of individualized prediction can be addressed using variants of conformal prediction, obtaining the intervals to which the actual values of the variables of interest belong. Here we present a method based on detecting the…
As machine learning models are increasingly deployed in dynamic environments, it becomes paramount to assess and quantify uncertainties associated with distribution shifts. A distribution shift occurs when the underlying data-generating…
In this paper, we propose five prediction intervals for the beta autoregressive moving average model. This model is suitable for modeling and forecasting variables that assume values in the interval $(0,1)$. Two of the proposed prediction…
Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
In regression problems where there is no known true underlying model, conformal prediction methods enable prediction intervals to be constructed without any assumptions on the distribution of the underlying data, except that the training…
A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed method is general and does not require any…
Split sample methods have recently been put forward as a way to reduce the coverage oscillations that haunt confidence intervals for parameters of lattice distributions, such as the binomial and Poisson distributions. We study split sample…
Prediction intervals in supervised Machine Learning bound the region where the true outputs of new samples may fall. They are necessary in the task of separating reliable predictions of a trained model from near random guesses, minimizing…
Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to…
In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction…
Conformal predictive systems allow forecasters to issue predictive distributions for real-valued future outcomes that have out-of-sample calibration guarantees. On a more abstract level, conformal prediction makes use of in-sample…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…
Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…
Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…
Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…