Exact goodness-of-fit testing for the Ising model

The Ising model is one of the simplest and most famous models of interacting systems. It was originally proposed to model ferromagnetic interactions in statistical physics and is now widely used to model spatial processes in many areas such as ecology, sociology, and genetics, usually without testing its goodness of fit. Here, we propose various test statistics and an exact goodness-of-fit test for the finite-lattice Ising model. The theory of Markov bases has been developed in algebraic statistics for exact goodness-of-fit testing using a Monte Carlo approach. However, finding a Markov basis is often computationally intractable. Thus, we develop a Monte Carlo method for exact goodness-of-fit testing for the Ising model which avoids computing a Markov basis and also leads to a better connectivity of the Markov chain and hence to a faster convergence. We show how this method can be applied to analyze the spatial organization of receptors on the cell membrane.Comment: 20 page

Numerical Modelling of Satellite Downlink Signals in a Finslerian-Perturbed Schwarzschild Spacetime

The work presented in this paper aims to contribute to the problem of testing Finsler gravity theories by means of experiments and observations in the solar system. Within a class of spherically symmetric static Finsler spacetimes we consider a satellite with an on-board atomic clock, orbiting in the Finslerian-perturbed gravitational field of the earth, whose time signal is transmitted to a ground station, where its receive time and frequency are measured with respect to another atomic clock. This configuration is realized by the Galileo 5 and 6 satellites that have gone astray and are now on non-circular orbits. Our method consists in the numerical integration of the satellite's orbit, followed by an iterative procedure which provides the numerically integrated signals, i.e., null geodesics, from the satellite to the ground station. One of our main findings is that for orbits that are considerably more eccentric than the Galileo 5 and 6 satellite orbits, Finslerian effects can be separated from effects of perturbations of the Schwarzschild spacetime within the Lorentzian geometry. We also discuss the separation from effects of non-gravitational perturbations. This leads us to the conclusion that observations of this kind combined with appropriate numerical modelling can provide suitable tests of Finslerian modifications of general relativity

Entry and Competition in Local Hospital Markets

There has been considerable consolidation in the hospital industry in recent years. Over 900 deals occurred from 1994-2000, and many local markets, even in large urban areas, have been reduced to monopolies, duopolies or triopolies. This surge in consolidation has led to concern about its effect on competition in local markets for hospital services. In this paper we examine the impact of market structure on competition in local hospital markets – specifically, does competition increase with the number of firms? We extend the entry model developed by Bresnahan and Reiss to make use of quantity information and apply it to data on the US hospital industry. The results from the estimation are striking. In the hospital markets we examine, entry leads to markets quickly becoming competitive. Entry reduces variable profits and increases quality. Indeed, most of the effects of entry come from having a second and possibly a third firm enter the market. The use of quantity information allows us to infer that entry is welfare increasing.analysis of health care markets

Household Demand for Employer-Based Health Insurance

We use the 1996 Medical Expenditure Panel Survey to estimate a model of household demand for employer-based health insurance, explicitly investigating differences in behavior between households with two potential sources of coverage and those with one source. Own and cross-price elasticities are estimated for three types of health plans, including exclusive provider organizations, any provider organizations, and mixed provider organizations. We find that the premium, family size, income, and wealth significantly affect demand. Our elasticity estimates reveal an overall, small behavioral response to changes in price with respect to health plan switching and take-up. Finally, we discuss the implications of our findings with respect to employer benefit design.

Entry and Competition in Local Hospital Markets

There has been considerable consolidation in the hospital industry in recent years. Over 900 deals occurred from 1994-2000, and many local markets, even in large urban areas, have been reduced to monopolies, duopolies, or triopolies. This surge in consolidation has led to concern about competition in local markets for hospital services. We examine the effect of market structure on competition in local hospital markets -- specifically, does the hardness of competition increase with the number of firms? We extend the entry model developed by Bresnahan and Reiss to make use of quantity information, and apply it to data on the U.S. hospital industry. In the hospital markets we examine, entry leads to a quick convergence to competitive conduct. Entry reduces variable profits and increases quantity. Most of the effects of entry come from having a second and a third firm enter the market. The fourth entrant has little estimated effect. The use of quantity information allows us to infer that entry is consumer-surplus-increasing.

An Economic and Life Cycle Analysis of Regional Land Use and Transportation Plans, Research Report 11-25

Travel and emissions models are commonly applied to evaluate the change in passenger and commercial travel and associated greenhouse gas (GHG) emissions from land use and transportation plans. Analyses conducted by the Sacramento Area Council of Governments predict a decline in such travel and emissions from their land use and transportation plan (the “Preferred Blueprint” or PRB scenario) relative to a “Business-As-Usual” scenario (BAU). However, the lifecycle GHG effects due to changes in production and consumption associated with transportation and land use plans are rarely, if ever, conducted. An earlier study conducted by the authors, applied a spatial economic model (Sacramento PECAS) to the PRB plan and found that lower labor, transport, and rental costs increased producer and consumer surplus and production and consumption relative to the BAU. As a result, lifecycle GHG emissions from these upstream economic activities may increase. At the same time, lifecycle GHG emissions associated with the manufacture of construction materials for housing may decline due to a shift in the plan from larger luxury homes to smaller multi-family homes in the plan. To explore the net impact of these opposing GHG impacts, the current study used the economic production and consumption data from the PRB and BAU scenarios as simulated with the Sacramento PECAS model as inputs to estimate the change in lifecycle GHG emissions. The economic input-output lifecycle assessment model is applied to evaluate effects related to changes in economic production and consumption as well as housing construction. This study also builds on the findings from two previous studies, which suggest potential economic incentives for jurisdictional non-compliance with Sustainable Communities Strategies (SCSs) under Senate Bill 375 (also known as the “anti-sprawl” bill). SB 375 does not require local governments to adopt general plans that are consistent with the land use plans included in SCSs, and thus such incentives could jeopardize implementation of SCSs and achievement of GHG goals. In this study, a set of scenarios is simulated with the Sacramento PECAS model, in which multiple jurisdictions partially pursue the BAU at differing rates. The PRB is treated as a straw or example SCS. The scenarios are evaluated to understand how non-conformity may influence the supply of housing by type, and holding other factors constant, the geographic and income distribution of rents, wages, commute costs, and consumer surplus

On strongly norm attaining Lipschitz maps

We study the set $\operatorname{SNA}(M,Y)$ of those Lipschitz maps from a (complete pointed) metric space $M$ to a Banach space $Y$ which (strongly) attain their Lipschitz norm (i.e.\ the supremum defining the Lipschitz norm is a maximum). Extending previous results, we prove that this set is not norm dense when $M$ is a length space (or local) or when $M$ is a closed subset of $\mathbb{R}$ with positive Lebesgue measure, providing new examples which have very different topological properties than the previously known ones. On the other hand, we study the linear properties which are sufficient to get Lindenstrauss property A for the Lipschitz-free space $\mathcal{F}(M)$ over $M$, and show that all of them actually provide the norm density of $\operatorname{SNA}(M,Y)$ in the space of all Lipschitz maps from $M$ to any Banach space $Y$. Next, we prove that $\operatorname{SNA}(M,\mathbb{R})$ is weakly sequentially dense in the space of all Lipschitz functions for all metric spaces $M$. Finally, we show that the norm of the bidual space of $\mathcal{F}(M)$ is octahedral provided the metric space $M$ is discrete but not uniformly discrete or $M'$ is infinite.Comment: 28 pages, electronically published in the Journal of Functional Analysi