Related papers: Backward Simulation in Bayesian Networks

Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is…

Networks underpin systems that range from finance to biology, yet their structure is often only partially observed. Current reconstruction methods typically fit the parameters of a model anew to each snapshot, thus offering no guidance to…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…

Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…

With high forward gain, a negative feedback system has the ability to perform the inverse of a linear or non-linear function that is in the feedback path. This property of negative feedback systems has been widely used in analog electronic…

The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows the formulation of expert knowledge or physical constraints in a probabilistic fashion and plays an important role for the…

Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data…

The logistic specification has been used extensively in non-Bayesian statistics to model the dependence of discrete outcomes on the values of specified covariates. Because the likelihood function is globally weakly concave estimation by…

Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of…

Current deep learning-based solutions for image analysis tasks are commonly incapable of handling problems to which multiple different plausible solutions exist. In response, posterior-based methods such as conditional Diffusion Models and…

A central challenge in many areas of science and engineering is to identify model parameters that are consistent with prior knowledge and empirical data. Bayesian inference offers a principled framework for this task, but can be…

Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an…

While backpropagation--reverse-mode automatic differentiation--has been extraordinarily successful in deep learning, it requires two passes (forward and backward) through the neural network and the storage of intermediate activations.…

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…

We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…

We discuss the Bayesian emulation approach to computational solution of multi-step portfolio studies in financial time series. "Bayesian emulation for decisions" involves mapping the technical structure of a decision analysis problem to…

The notion of confidence distributions is applied to inference about the parameter in a simple autoregressive model, allowing the parameter to take the value one. This makes it possible to compare to asymptotic approximations in both the…