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A rich set of frequentist model averaging methods has been developed, but their applications have largely been limited to point prediction, as measuring prediction uncertainty in general settings remains an open problem. In this paper we…
Recovering and distinguishing between the strict-preference, indifference and/or indecisiveness parts of a decision maker's preferences is a challenging task but also important for testing theory and conducting welfare analysis. This paper…
Generative models frequently suffer miscalibration, wherein statistics of the sampling distribution, such as the fraction of generations in a given class, deviate from desired values. We frame calibration as a constrained optimization…
In this note we prove the dual representation formula of the divergence between two distributions in a parametric model. Resulting estimators for the divergence as for the parameter are derived. These estimators do not make use of any…
Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
There is a fundamental disconnect between what is tested in a model adequacy test, and what we would like to test. The usual approach is to test the null hypothesis "Model M is the true model." However, Model M is never the true model. A…
The ability to understand and solve high-dimensional inference problems is essential for modern data science. This article examines high-dimensional inference problems through the lens of information theory and focuses on the standard…
Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high…
King and Roberts (2015, KR) claim that a disagreement between robust and classical standard errors exposes model misspecification. We emphasize that KR's claim only generally applies to parametric models: models that assume a restrictive…
We seek to find normative criteria of adequacy for nonmonotonic logic similar to the criterion of validity for deductive logic. Rather than stipulating that the conclusion of an inference be true in all models in which the premises are…
Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…
In a recent paper (Phys. Rev. A 105, 042220 (2022)), Daley et al claim that some superdeterministic models are disfavoured against standard quantum mechanics, because such models overfit the statistics of a Bell-type experiment which the…
We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large…
The problem of characterising the accuracy of, and disturbance caused by a joint measurement of position and momentum is investigated. In a previous paper the problem was discussed in the context of the unbiased measurements considered by…
Statistical and structural modeling represent two distinct approaches to data analysis. In this paper, we propose a set of novel methods for combining statistical and structural models for improved prediction and causal inference. Our first…
The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…
In this paper, we propose some estimators for the parameters of a statistical model based on Kullback-Leibler divergence of the survival function in continuous setting. We prove that the proposed estimators are subclass of "generalized…
Data scarcity drives the need for more sample-efficient large language models. In this work, we use the double descent phenomenon to holistically compare the sample efficiency of discrete diffusion and autoregressive models. We show that…
As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…