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State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and…
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
Misclassified variables used in regression models, either as a covariate or as the response, may lead to biased estimators and incorrect inference. Even though Bayesian models to adjust for misclassification error exist, it has not been…
The exact estimation of latent variable models with big data is known to be challenging. The latents have to be integrated out numerically, and the dimension of the latent variables increases with the sample size. This paper develops a…
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…
Local projections (LPs) are widely used for impulse response analysis, but Bayesian methods face challenges due to the absence of a likelihood function. Existing approaches rely on pseudo-likelihoods, which often result in poorly calibrated…
The Laplace approximation provides a closed-form model selection objective for neural networks (NN). Online variants, which optimise NN parameters jointly with hyperparameters, like weight decay strength, have seen renewed interest in the…
Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…
Bayesian inference requires approximation methods to become computable, but for most of them it is impossible to quantify how close the approximation is to the true posterior. In this work, we present a theorem upper-bounding the KL…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
The Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM-algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be…
Complex models used to describe biological processes in epidemiology and ecology often have computationally intractable or expensive likelihoods. This poses significant challenges in terms of Bayesian inference but more significantly in the…
Integral transform method (Fourier or Laplace transform, etc) is more often effective to do the theoretical analysis for the stochastic processes. However, for the time-space coupled cases, e.g., L\'evy walk or nonlinear cases, integral…
Self-Exciting models are statistical models of count data where the probability of an event occurring is influenced by the history of the process. In particular, self-exciting spatio-temporal models allow for spatial dependence as well as…
Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge…
For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…
We define a novel class of additive models, called Extended Latent Gaussian Models, that allow for a wide range of response distributions and flexible relationships between the additive predictor and mean response. The new class covers a…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…