Related papers: Inferring Evidence from Nested Sampling Data via I…
The main idea of nested sampling is to substitute the high-dimensional likelihood integral over the parameter space $\Omega$ by an integral over the unit line $[0,1]$ by employing a push-forward with respect to a suitable transformation.…
Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…
We revisit empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to…
In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…
A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small…
We propose a novel method ($floZ$), based on normalizing flows, to estimate the Bayesian evidence (and its numerical uncertainty) from a pre-existing set of samples drawn from the unnormalized posterior distribution. We validate it on…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…
In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
While particle trajectories encode information on their governing potentials, potentials can be challenging to robustly extract from trajectories. Measurement errors may corrupt a particle's position, and sparse sampling of the potential…
Weighted Updating generalizes Bayesian updating, allowing for biased beliefs by weighting the likelihood function and prior distribution with positive real exponents. I provide a rigorous foundation for the model by showing that…
Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…
Bayesian inference involves two main computational challenges. First, in estimating the parameters of some model for the data, the posterior distribution may well be highly multi-modal: a regime in which the convergence to stationarity of…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
We demonstrate that the Bayesian evidence can be used to find a good approximation of the ground truth likelihood function of a dataset, a goal of the likelihood-free inference (LFI) paradigm. As a concrete example, we use forward modelled…
Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…
In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a…
In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with…
Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…