Related papers: Sequential inductive prediction intervals
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…
Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
Clinical trials usually involve sequential patient entry. When designing a clinical trial, it is often desirable to include a provision for interim analyses of accumulating data with the potential for stopping the trial early. We review…
Prediction sets capture uncertainty by predicting sets of labels rather than individual labels, enabling downstream decisions to conservatively account for all plausible outcomes. Conformal inference algorithms construct prediction sets…
Researchers faced with a sequence of candidate model specifications must often choose the best specification that does not violate a testable identification assumption. One option in this scenario is sequential specification tests:…
Having a regression model, we are interested in finding two-sided intervals that are guaranteed to contain at least a desired proportion of the conditional distribution of the response variable given a specific combination of predictors. We…
We introduce the notion of a stochastic probabilistic program and present a reference implementation of a probabilistic programming facility supporting specification of stochastic probabilistic programs and inference in them. Stochastic…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a…
Continuous-time event sequences, i.e., sequences consisting of continuous time stamps and associated event types ("marks"), are an important type of sequential data with many applications, e.g., in clinical medicine or user behavior…
Constructing prediction sets with coverage guarantees for unobserved outcomes is a core problem in modern statistics. Methods for predictive inference have been developed for a wide range of settings, but usually only consider test data…
We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then…
Motivated by a broad range of potential applications, we address the quantile prediction problem of real-valued time series. We present a sequential quantile forecasting model based on the combination of a set of elementary nearest…
For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…
We consider inference post-model-selection in linear regression. In this setting, Berk et al.(2013) recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain non-standard quantity of interest with a…
We investigate generically applicable and intuitively appealing prediction intervals based on $k$-fold cross validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training…
Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing…
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we…
In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast `on the fly' without the need for fully specifying a probability measure on all possible sequences of outcomes, as is the case in the…