Team Theory and Person-by-Person Optimization with Binary Decisions.

In this paper, we extend the notion of person-by-person (pbp) optimization to binary decision spaces. The novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo-boolean optimization field as completely local-global or unimodal functions and submodularity. We also generalize the concept of pbp optimization to the case where groups of $m$ decisions makers make joint decisions sequentially, which we refer to as $m$b$m$ optimization. The main contribution is a description of sufficient conditions, verifiable in polynomial time, under which a pbp or an $m$b$m$ optimization algorithm converges to the team-optimum. As a second contribution, we present a local and greedy algorithm characterized by approximate decision strategies (i.e., strategies based on a local state vector) that return the same decisions as in the complete information framework (where strategies are based on full state vector). As a last contribution, we also show that there exists a subclass of submodular team problems, recognizable in polynomial time, for which the pbp optimization converges for at least an opportune initialization of the algorithm

Bayesian Design of Tandem Networks for Distributed Detection With Multi-bit Sensor Decisions

We consider the problem of decentralized hypothesis testing under communication constraints in a topology where several peripheral nodes are arranged in tandem. Each node receives an observation and transmits a message to its successor, and the last node then decides which hypothesis is true. We assume that the observations at different nodes are, conditioned on the true hypothesis, independent and the channel between any two successive nodes is considered error-free but rate-constrained. We propose a cyclic numerical design algorithm for the design of nodes using a person-by-person methodology with the minimum expected error probability as a design criterion, where the number of communicated messages is not necessarily equal to the number of hypotheses. The number of peripheral nodes in the proposed method is in principle arbitrary and the information rate constraints are satisfied by quantizing the input of each node. The performance of the proposed method for different information rate constraints, in a binary hypothesis test, is compared to the optimum rate-one solution due to Swaszek and a method proposed by Cover, and it is shown numerically that increasing the channel rate can significantly enhance the performance of the tandem network. Simulation results for $M$-ary hypothesis tests also show that by increasing the channel rates the performance of the tandem network significantly improves

Optimal monetary policy committee size: Theory and cross country evidence

Theoretical and empirical studies of different sciences suggest that an optimal committee consists of roughly 5-9 members, although it can swell mildly under specific circumstances. This paper develops a conceptual model in order to analyze the issue in case of monetary policy formulation. The optimal monetary policy committee (MPC) size varies according to the uncertainty of MPC members’ information influenced by the size of the monetary zone and overall economic stability. Our conceptual model is backed up with econometric evidence using a 2006 survey of 85 countries. The survey is available for further research and published on the web. The MPC size of large monetary zones (EMU, USA, Japan) is close to the estimated optimal level, but there exist several smaller countries with too many or too few MPC members.monetary policy committe, mpc size, decision making.

Determinants of the size of a monetary policy committee: Theory and cross country evidence

Theoretical and empirical studies of different sciences suggest that an optimal committee consists of roughly 5-9 members, although it can swell mildly under specific circumstances. This paper develops a conceptual model in order to analyze the issue in case of monetary policy formulation. The number of monetary policy committee (MPC) size varies according to the size of the monetary zone and overall economic stability. Our conceptual model is backed up with econometric evidence using a 2006 survey of 85 countries. The survey is available for further research and published on the web. The MPC size of large monetary zones (EMU, USA, Japan) is close to the estimated optimal level, but there exist several smaller countries with too many or too few MPC members.Monetary policy.

Bayesian Item Response Modeling in R with brms and Stan

Item Response Theory (IRT) is widely applied in the human sciences to model persons' responses on a set of items measuring one or more latent constructs. While several R packages have been developed that implement IRT models, they tend to be restricted to respective prespecified classes of models. Further, most implementations are frequentist while the availability of Bayesian methods remains comparably limited. We demonstrate how to use the R package brms together with the probabilistic programming language Stan to specify and fit a wide range of Bayesian IRT models using flexible and intuitive multilevel formula syntax. Further, item and person parameters can be related in both a linear or non-linear manner. Various distributions for categorical, ordinal, and continuous responses are supported. Users may even define their own custom response distribution for use in the presented framework. Common IRT model classes that can be specified natively in the presented framework include 1PL and 2PL logistic models optionally also containing guessing parameters, graded response and partial credit ordinal models, as well as drift diffusion models of response times coupled with binary decisions. Posterior distributions of item and person parameters can be conveniently extracted and post-processed. Model fit can be evaluated and compared using Bayes factors and efficient cross-validation procedures.Comment: 54 pages, 16 figures, 3 table