Plasma parameter profile inference from limited data utilizing second-order derivative priors and physic-based constraints

Constructing second-order data dependent probability matching priors from first-order probability matching priors

Second-order probability matching priors

The paper considers priors obtained by ensuring approximate frequentist validity of (a) posterior quantiles, and of (b) the posterior distribution function. It is seen that, at the second order of approximation, the two approaches do not necessarily lead to identical conclusions. Examples are given to illustrate this. The role of invariance in the context of probability matching is also discussed.

Second-order particle MCMC for Bayesian parameter inference

We propose an improved proposal distribution in the Particle Metropolis-Hastings (PMH) algorithm for Bayesian parameter inference in nonlinear state space models. This proposal incorporates second-order information about the parameter posterior distribution, which can be extracted from the particle filter already used within the PMH algorithm. The added information makes the proposal scale-inva...

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations