Related papers: A Comparative Review of Dimension Reduction Method…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

We consider the asymptotic properties of Approximate Bayesian Computation (ABC) for the realistic case of summary statistics with heterogeneous rates of convergence. We allow some statistics to converge faster than the ABC tolerance, other…

ABC algorithms are notoriously expensive in computing time, as they require simulating many complete artificial datasets from the model. We advocate in this paper a "divide and conquer" approach to ABC, where we split the likelihood into n…

This Chapter, "ABC Samplers", is to appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). It details the main ideas and algorithms used to sample from the ABC approximation to the posterior distribution, including…

Approximate Bayesian computation (ABC) is computationally intensive for complex model simulators. To exploit expensive simulations, data-resampling via bootstrapping can be employed to obtain many artificial datasets at little cost.…

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…

This paper addresses the ``curse of dimensionality'' in the loss valuation of credit risk models. A dimension reduction methodology based on the Bayesian filter and smoother is proposed. This methodology is designed to achieve a fast and…

Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such…

In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…

Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…

Approximate Bayesian Computation (ABC) is a framework for performing likelihood-free posterior inference for simulation models. Stochastic Variational inference (SVI) is an appealing alternative to the inefficient sampling approaches…

The power of fuzz testing lies in its random, often brute-force, generation and execution of inputs to trigger unexpected behaviors and vulnerabilities in software applications. However, given the reality of infinite possible input…

Bayesian methods provide an elegant framework for estimating parameter posteriors and quantification of uncertainty associated with probabilistic models. However, they often suffer from slow inference times. To address this challenge,…

An important problem for HCI researchers is to estimate the parameter values of a cognitive model from behavioral data. This is a difficult problem, because of the substantial complexity and variety in human behavioral strategies. We report…

In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…

Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is increasing burden placed…

We propose a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, non-Gaussian priors, and non-Gaussian observation noise. The likelihood function is approximated by a ridge function, i.e., a map…

Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly,…

"Approximate Bayesian Computation" (ABC) represents a powerful methodology for the analysis of complex stochastic systems for which the likelihood of the observed data under an arbitrary set of input parameters may be entirely…

We derive the optimal proposal density for Approximate Bayesian Computation (ABC) using Sequential Monte Carlo (SMC) (or Population Monte Carlo, PMC). The criterion for optimality is that the SMC/PMC-ABC sampler maximise the effective…