Related papers: Martingale Posteriors from Score Functions
Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents. This results in particularly interpretable models which can be used to…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…
Scenario-based testing of automated driving functions has become a promising method to reduce time and cost compared to real-world testing. In scenario-based testing automated functions are evaluated in a set of pre-defined scenarios. These…
Priors are essential for reconstructing images from noisy and/or incomplete measurements. The choice of the prior determines both the quality and uncertainty of recovered images. We propose turning score-based diffusion models into…
A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter was equal or lay close to a specified value, which may, for…
We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To…
A multivariate score-driven filter is developed to extract signals from noisy vector processes. By assuming that the conditional location vector from a multivariate Student's t distribution changes over time, we construct a robust filter…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
In many domains, we are interested in analyzing the structure of the underlying distribution, e.g., whether one variable is a direct parent of the other. Bayesian model-selection attempts to find the MAP model and use its structure to…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
This paper introduces a martingale that characterizes two properties of evolving forecast distributions. Ideal forecasts of a future event behave as martingales, sequen- tially updating the forecast to leverage the available information as…
Methods that rely on proxies, without imposing strong parametric structure, are increasingly used to deal with unobserved variables in causal inference. One influential line of this work reconstructs latent distributions used to identify…
Prior-data fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular datasets, achieving state-of-the-art performance on small to moderate data sizes without tuning. While PFNs are motivated by Bayesian…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
Compared to the nominal scale, the ordinal scale for a categorical outcome variable has the property of making a monotonicity assumption for the covariate effects meaningful. This assumption is encoded in the commonly used proportional odds…
Score-based models have achieved remarkable results in the generative modeling of many domains. By learning the gradient of smoothed data distribution, they can iteratively generate samples from complex distribution e.g. natural images.…
Model uncertainty is pervasive in real world analysis situations and is an often-neglected issue in applied statistics. However, standard approaches to the research process do not address the inherent uncertainty in model building and,…
Propensity scores are often used for stratification of treatment and control groups of subjects in observational data to remove confounding bias when estimating of causal effect of the treatment on an outcome in so-called potential outcome…