Related papers: On the Proofs of the Predictive Synthesis Formula
Program synthesis is the task of constructing a program conforming to a given specification. We focus on deductive synthesis, and in particular on synthesis problems with specifications given as $\forall\exists$-formulas, expressing the…
Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…
Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…
In this contribution we investigate how to describe the results and usage of evolutionary synthesis models. In particular, we look for an explicit and quantitative description of the parameter space of synthesis models and the evaluation of…
The sheer scale of high-resolution raw data generated by simulation has motivated non-conventional approaches for data exploration referred as `immersive' and `in situ' query processing of the raw simulation data. Another step towards…
The Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in analysis of cosmological models has been limited by difficulties in calculating it, with current…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…
The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple…
Across the empirical sciences, few statistical procedures rival the popularity of the frequentist t-test. In contrast, the Bayesian versions of the t-test have languished in obscurity. In recent years, however, the theoretical and practical…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
The macroeconomy is a sophisticated dynamic system involving significant uncertainties that complicate modelling. In response, decision-makers consider multiple models that provide different predictions and policy recommendations which are…
Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous,…
In this fact sheet we give some preliminary research results on the Bayesian Decision Theory. This theory has been under construction for the past two years. But what started as an intuitive enough idea, now seems to have the makings of…
We propose novel controller synthesis techniques for probabilistic systems modelled using stochastic two-player games: one player acts as a controller, the second represents its environment, and probability is used to capture uncertainty…
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,…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in…
Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…