Related papers: Optimal E-Values for Exponential Families: the Sim…
The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the…
We study exponential families of distributions that are multivariate totally positive of order 2 (MTP2), show that these are convex exponential families, and derive conditions for existence of the MLE. Quadratic exponential familes of MTP2…
A recurring debate in the philosophy of statistics concerns what, exactly, should count as a measure of evidence for or against a given hypothesis. P-values, likelihood ratios, and Bayes factors all have their defenders. In this paper we…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
We propose using a discounted version of a convex combination of the log-likelihood with the corresponding expected log-likelihood such that when they are maximized they yield a filter, predictor and smoother for time series. This paper…
We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate…
A nonparametric family of conditional distributions is introduced, which generalizes conditional exponential families using functional parameters in a suitable RKHS. An algorithm is provided for learning the generalized natural parameter,…
We derive the unique e-values with optimal (relative) growth rate in the worst case for testing the mean of a bounded random variable, hereby contributing with the first application beyond the assumption of mutually absolutely continuous…
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…
Free exponential families have been previously introduced as a special case of the q-exponential family. We show that free exponential families arise also from a procedure analogous to the definition of exponential families by using the…
The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
The exponential family of models is defined in a general setting, not relying on probability theory. Some results of information geometry are shown to remain valid. Exponential families both of classical and of quantum mechanical…
In this paper, we give a method to construct "good" exponential families systematically by representation theory. More precisely, we consider a homogeneous space $G/H$ as a sample space and construct an exponential family invariant under…
We show that a class of optimized e-value combinations, arising from a standard construction of e-processes, remains valid even when the tuning parameter is optimized based on the data. This result holds for independent e-values, and, more…
Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which…
Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses…
We propose an e-value based framework for testing arbitrary composite nulls against composite alternatives, when an $\epsilon$ fraction of the data can be arbitrarily corrupted. Our tests are inherently sequential, being valid at arbitrary…
It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…
Fitting a graphical model to a collection of random variables given sample observations is a challenging task if the observed variables are influenced by latent variables, which can induce significant confounding statistical dependencies…