7 citations · 12 across the 15 of their papers we have counts for
15 papers
Loeb Equivalence for General Internal Probability Spaces
Haosui Duanmu, Xinyu Liu, David Schrittesser
Loeb measure theory stands as one of the most influential concepts in nonstandard analysis, underpinning nearly all applications in probability, stochastic processes, and mathemati…
Existence of Equilibria in Large Competitive Markets with Bads, Production and Comprehensive Externalities
Robert M. Anderson, Haosui Duanmu, M. Ali Khan +1
This paper establishes existence of equilibrium in a measure-theoretic general equilibrium (MGE) model with production, bads, and comprehensive externalities. These features are jo…
General Equilibrium Theory for Climate Change
Robert M. Anderson, Haosui Duanmu
We propose two general equilibrium models, quota equilibrium and emission tax equilibrium. The government specifies quotas or taxes on emissions, then refrains from further action.…
Statistical minimax theorems via nonstandard analysis
Haosui Duanmu, Daniel M. Roy, David Schrittesser
For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a gener…
On Existence of Berk-Nash Equilibria in Misspecified Markov Decision Processes with Infinite Spaces
Robert M. Anderson, Haosui Duanmu, Aniruddha Ghosh +1
Model misspecification is a critical issue in many areas of theoretical and empirical economics. In the specific context of misspecified Markov Decision Processes, Esponda and Pouz…
Admissibility is Bayes optimality with infinitesimals
Haosui Duanmu, Daniel M. Roy, David Schrittesser
We give an exact characterization of admissibility in statistical decision problems in terms of Bayes optimality in a so-called nonstandard extension of the original decision probl…
Loeb Extension and Loeb Equivalence II
Duanmu Haosui, David Schrittesser, William Weiss
The paper answers two open questions that were raised in by Keisler and Sun. The first question asks, if we have two Loeb equivalent spaces and $(Ω, \mathcal G…
Existence of matching priors on compact spaces
Haosui Duanmu, Daniel M. Roy, Aaron Smith
A matching prior at level is a prior such that an associated credible set is also a confidence set. We study the existence of matching priors for general families…
Finitely-additive, countably-additive and internal probability measures
Haosui Duanmu, William Weiss
We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an inte…
Nonstandard Representation of the Dirichlet Form
Robert M. Anderson, Haosui Duanmu, Aaron Smith
The Dirichlet form is a generalization of the Laplacian, heavily used in the study of many diffusion-like processes. In this paper we present a nonstandard representation theorem f…
Loeb Extension and Loeb Equivalence
Robert M. Anderson, Haosui Duanmu, David Schrittesser +1
In Keisler and Sun (2004), the authors raise several open problems on Loeb equivalences between various internal probability spaces. We provide counter-examples for the first two o…
Drift, Minorization, and Hitting Times
Robert M. Anderson, Haosui Duanmu, Aaron Smith +1
The "drift-and-minorization" method, introduced and popularized in (Rosenthal, 1995; Meyn and Tweedie, 1994; Meyn and Tweedie, 2012), remains the most popular approach for bounding…
Mixing Times and Hitting Times for General Markov Processes
Robert M. Anderson, Haosui Duanmu, Aaron Smith
The hitting and mixing times are two fundamental quantities associated with Markov chains. In Peres and Sousi[PS2015] and Oliveira[Oli2012], the authors show that the mixing times…
On Extended Admissible Procedures and their Nonstandard Bayes Risk
Haosui Duanmu, Daniel M. Roy
For finite parameter spaces under finite loss, every Bayes procedure derived from a prior with full support is admissible, and every admissible procedure is Bayes. This relationshi…
Productively Lindelof and Indestructibly Lindelof Spaces
Haosui Duanmu, Franklin D. Tall, Lyubomyr Zdomskyy
There has recently been considerable interest in productively Lindelof spaces, i.e. spaces such that their product with every Lindelof space is Lindelof. Here we make several relat…