Related papers: A conservation law for posterior predictive varian…
We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the…
We give a decomposition of the posterior predictive variance using the law of total variance and conditioning on a finite dimensional discrete random variable. This random variable summarizes various features of modeling that are used to…
A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…
The law of total probability may be deployed in binary classification exercises to estimate the unconditional class probabilities if the class proportions in the training set are not representative of the population class proportions. We…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the solutions is exhibited, even for smooth initial data. The…
Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…
Well known biological approximations are universal, i.e. invariant to transformations from one species to another. With no other experimental data, such invariance yields exact conservation (with respect to biological diversity and…
Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action…
Because of the finiteness of the life span and boundedness of the physical space, the more reasonable or physical choice is the tempered power-law instead of pure power-law for the CTRW model in characterizing the waiting time and jump…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
A common problem in Machine Learning and statistics consists in detecting whether the current sample in a stream of data belongs to the same distribution as previous ones, is an isolated outlier or inaugurates a new distribution of data. We…
This note generalizes the notion of conditional probability to Riesz spaces using the order-theoretic approach. With the aid of this concept, we establish the law of total probability and Bayes' theorem in Riesz spaces; we also prove an…
In this paper we obtain some possibilistic variants of the probabilistic laws of large numbers, different from those obtained by other authors, but very natural extensions of the corresponding ones in probability theory. Our results are…
Most of the consistency analyses of Bayesian procedures for variable selection in regression refer to pairwise consistency, that is, consistency of Bayes factors. However, variable selection in regression is carried out in a given class of…
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
A Bayesian hierarchical model for total variation regularisation is presented in this paper. All the parameters of an inverse problem, including the "regularisation parameter", are estimated simultaneously from the data in the model. The…
We study high-dimensional Bayesian linear regression with product priors. Using the nascent theory of non-linear large deviations (Chatterjee and Dembo,2016), we derive sufficient conditions for the leading-order correctness of the naive…