We use a Bayesian Markov Chain Monte Carlo algorithm jointly to estimate the parameters of a ‘true’ data generating mechanism and those of a sequence of approximating models that a monetary authority uses to guide its decisions. Gaps between a true expectational Phillips curve and the monetary authority’s approximating non-expectational Phillips curve models unleash inflation that a monetary au...

In a Markov decision problem with hidden state variables, a posterior distribution serves as a state variable and Bayes’ law under the approximating model gives its law of motion. A decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby as measured by their expected log likelihood ratios (entropies). Sets of martingales represen...

In a Markov decision problem with hidden state variables, a posterior distribution serves as a state variable and Bayes’ law under an approximating model gives its law of motion. A decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby when measured by their expected log likelihood ratios (entropies). Martingales represent alter...

Given a finite collection of functions defined on a common domain, the paper describes an algorithm that constructs a vector valued approximating martingale sequence. The orthonomal basis functions used to construct the martingale approximation are optimally selected, in each greedy step, from a large dictionary. The resulting approximations are characterized as generalized Hsystems and provide...

We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of the so-called Canadization procedure suggested by P. Carr in [2] for the fast computation of American put option prices. In addition to the original applicati...

We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, variational boosting, iteratively refines an existing variational approximation by solving a sequence of optimization problems, allowing a trade-off between computation time and accuracy. We expand the variational approximating class by incorpor...

Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using single-qubit gates and the controlled-not (cnot). Our approach uses the decomposition of the single-qubit channel into a convex combination of "quasiextreme" chan...

In this article, multivariable derivative-free optimization algorithms for unconstrained problems are developed. A novel procedure approximating the gradient of objective functions based on noncommutative maps is introduced. The construction an exploration sequence to specify where function evaluated and definition so-called generating which composed with function, such that mimics a descent al...

Abstract In this paper, we introduce an inertial Halpern-type iterative algorithm for approximating a zero of the sum two monotone operators in setting real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence sequence generated by our proposed is established means some new geometric inequalities proved paper independent interest. Furthermore, numerical simulations...