Likelihood-Free Parameter Estimation with Neural Bayes Estimators

Empirical Bayes Estimators with Uncertainty Measures for NEF-QVF Populations

The paper proposes empirical Bayes (EB) estimators for simultaneous estimation of means in the natural exponential family (NEF) with quadratic variance functions (QVF) models. Morris (1982, 1983a) characterized the NEF-QVF distributions which include among others the binomial, Poisson and normal distributions. In addition to the EB estimators, we provide approximations to the MSE’s of t...

Maximum Likelihood Parameter Estimation

The problem of estimating the parameters for continuous-time partially observed systems is discussed. New exact lters for obtaining Maximum Likelihood (ML) parameter estimates via the Expectation Maximization algorithm are derived. The methodology exploits relations between incomplete and complete data likelihood and gradient of likelihood functions, which are derived using Girsanov's measure t...

Bayes Parameter Estimation for the Bivariate

Parameter estimation of ODE’s via nonparametric estimators

Ordinary differential equations (ODE’s) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the sets of interactions and the evolution of complex systems and it might consist of high-dimensional sets of coupled nonlinear differential equations. In this setting, we propose a general method for estimating the parameters indexi...

Variational Bayes with synthetic likelihood

Synthetic likelihood is an attractive approach to likelihood-free inference when an approximately Gaussian summary statistic for the data, informative for inference about the parameters, is available. The synthetic likelihood method derives an approximate likelihood function from a plug-in normal density estimate for the summary statistic, with plug-in mean and covariance matrix obtained by Mon...