Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Assessment of LD matrix measures for the analysis of biological pathway association.

Complex diseases will have multiple functional sites, and it will be invaluable to understand the cross-locus interaction in terms of linkage disequilibrium (LD) between those sites (epistasis) in addition to the haplotype-LD effects. We investigated the statistical properties of a class of matrix-based statistics to assess this epistasis. These statistical methods include two LD contrast tests (Zaykin et al., 2006) and partial least squares regression (Wang et al., 2008). To estimate Type 1 error rates and power, we simulated multiple two-variant disease models using the SIMLA software package. SIMLA allows for the joint action of up to two disease genes in the simulated data with all possible multiplicative interaction effects between them. Our goal was to detect an interaction between multiple disease-causing variants by means of their linkage disequilibrium (LD) patterns with other markers. We measured the effects of marginal disease effect size, haplotype LD, disease prevalence and minor allele frequency have on cross-locus interaction (epistasis). In the setting of strong allele effects and strong interaction, the correlation between the two disease genes was weak (r=0.2). In a complex system with multiple correlations (both marginal and interaction), it was difficult to determine the source of a significant result. Despite these complications, the partial least squares and modified LD contrast methods maintained adequate power to detect the epistatic effects; however, for many of the analyses we often could not separate interaction from a strong marginal effect. While we did not exhaust the entire parameter space of possible models, we do provide guidance on the effects that population parameters have on cross-locus interaction.

Environmental and technology policies for climate mitigation

We assess different policies for reducing carbon dioxide emissions and promoting innovation and diffusion of renewable energy. We evaluate the relative performance of policies according to incentives provided for emissions reduction, efficiency, and other outcomes. We also assess how the nature of technological progress through learning and research and development (R&D), and the degree of knowledge spillovers, affects the desirability of different policies. Due to knowledge spillovers, optimal policy involves a portfolio of different instruments targeted at emissions, learning, and R&D. Although the relative cost of individual policies in achieving reductions depends on parameter values and the emissions target, in a numerical application to the U.S. electricity sector, the ranking is roughly as follows: (1) emissions price, (2) emissions performance standard, (3) fossil power tax, (4) renewables share requirement, (5) renewables subsidy, and (6) R&D subsidy. Nonetheless, an optimal portfolio of policies achieves emissions reductions at a significantly lower cost than any single policy. © 2007 Elsevier Inc. All rights reserved.

Valuing ecosystem services from wetlands restoration in the Mississippi Alluvial Valley

This study assesses the value of restoring forested wetlands via the U.S. government's Wetlands Reserve Program (WRP) in the Mississippi Alluvial Valley by quantifying and monetizing ecosystem services. The three focal services are greenhouse gas (GHG) mitigation, nitrogen mitigation, and waterfowl recreation. Site- and region-level measurements of these ecosystem services are combined with process models to quantify their production on agricultural land, which serves as the baseline, and on restored wetlands. We adjust and transform these measures into per-hectare, valuation-ready units and monetize them with prices from emerging ecosystem markets and the environmental economics literature. By valuing three of the many ecosystem services produced, we generate lower bound estimates for the total ecosystem value of the wetlands restoration. Social welfare value is found to be between $1435 and $1486/ha/year, with GHG mitigation valued in the range of $171 to $222, nitrogen mitigation at $1248, and waterfowl recreation at $16. Limited to existing markets, the estimate for annual market value is merely $70/ha, but when fully accounting for potential markets, this estimate rises to $1035/ha. The estimated social value surpasses the public expenditure or social cost of wetlands restoration in only 1 year, indicating that the return on public investment is very attractive for the WRP. Moreover, the potential market value is substantially greater than landowner opportunity costs, showing that payments to private landowners to restore wetlands could also be profitable for individual landowners. © 2009 Elsevier B.V.

Designing Climate Mitigation Policy

This paper provides an exhaustive review of critical issues in the design of climate mitigation policy by pulling together key findings and controversies from diverse literatures on mitigation costs, damage valuation, policy instrument choice, technological innovation, and international climate policy. We begin with the broadest issue of how high assessments suggest the near and medium term price on greenhouse gases would need to be, both under cost-effective stabilization of global climate and under net benefit maximization or Pigouvian emissions pricing. The remainder of the paper focuses on the appropriate scope of regulation, issues in policy instrument choice, complementary technology policy, and international policy architectures.

Carbon mitigation costs for the commercial building sector: Discrete-continuous choice analysis of multifuel energy demand

We estimate a carbon mitigation cost curve for the U.S. commercial sector based on econometric estimation of the responsiveness of fuel demand and equipment choices to energy price changes. The model econometrically estimates fuel demand conditional on fuel choice, which is characterized by a multinomial logit model. Separate estimation of end uses (e.g., heating, cooking) using the U.S. Commercial Buildings Energy Consumption Survey allows for exceptionally detailed estimation of price responsiveness disaggregated by end use and fuel type. We then construct aggregate long-run elasticities, by fuel type, through a series of simulations; own-price elasticities range from -0.9 for district heat services to -2.9 for fuel oil. The simulations form the basis of a marginal cost curve for carbon mitigation, which suggests that a price of $20 per ton of carbon would result in an 8% reduction in commercial carbon emissions, and a price of $100 per ton would result in a 28% reduction. © 2008 Elsevier B.V. All rights reserved.

Discounting the distant future: How much do uncertain rates increase valuations?

We demonstrate that when the future path of the discount rate is uncertain and highly correlated, the distant future should be discounted at significantly lower rates than suggested by the current rate. We then use two centuries of US interest rate data to quantify this effect. Using both random walk and mean-reverting models, we compute the "certainty-equivalent rate" that summarizes the effect of uncertainty and measures the appropriate forward rate of discount in the future. Under the random walk model we find that the certainty-equivalent rate falls continuously from 4% to 2% after 100 years, 1% after 200 years, and 0.5% after 300 years. At horizons of 400 years, the discounted value increases by a factor of over 40,000 relative to conventional discounting. Applied to climate change mitigation, we find that incorporating discount rate uncertainty almost doubles the expected present value of mitigation benefits. © 2003 Elsevier Science (USA). All rights reserved.

Temporal Stability of Molecular Diversity Measures in Natural Populations of Drosophila pseudoobscura and Drosophila persimilis

Many molecular ecological and evolutionary studies sample wild populations at a single point in time, failing to consider that data they collect represents genetic variation from a potentially unrepresentative snapshot in time. Variation across time in genetic parameters may occur quickly in species that produce multiple generations of offspring per year. However, many studies of rapid contemporary microevolution examine phenotypic trait divergence as opposed to molecular evolutionary divergence. Here, we compare genetic diversity in wild caught populations of Drosophila persimilis and D. pseudoobscura collected 16 years apart at the same time of year and same site at four X-linked and two mitochondrial loci to assess genetic stability. We found no major changes in nucleotide diversity in either species, but we observed a drastic shift in Tajima’s D between D. pseudoobscura timepoints at one locus associated with the increased abundance of a set of related haplotypes. Our data also suggests that D. persimilis may have recently accelerated its demographic expansion. While the changes we observed were modest, this study reinforces the importance of considering potential temporal variation in genetic parameters within single populations over short evolutionary timescales.

Participant, rater, and computer measures of coherence in posttraumatic stress disorder.

We examined the coherence of trauma memories in a trauma-exposed community sample of 30 adults with and 30 without posttraumatic stress disorder. The groups had similar categories of traumas and were matched on multiple factors that could affect the coherence of memories. We compared the transcribed oral trauma memories of participants with their most important and most positive memories. A comprehensive set of 28 measures of coherence including 3 ratings by the participants, 7 ratings by outside raters, and 18 computer-scored measures, provided a variety of approaches to defining and measuring coherence. A multivariate analysis of variance indicated differences in coherence among the trauma, important, and positive memories, but not between the diagnostic groups or their interaction with these memory types. Most differences were small in magnitude; in some cases, the trauma memories were more, rather than less, coherent than the control memories. Where differences existed, the results agreed with the existing literature, suggesting that factors other than the incoherence of trauma memories are most likely to be central to the maintenance of posttraumatic stress disorder and thus its treatment.

Accounting for Posttraumatic Stress Disorder Symptom Severity With Pre- and Posttrauma Measures: A Longitudinal Study of Older Adults.

Using data from a longitudinal study of community-dwelling older adults, we analyzed the most extensive set of known correlates of PTSD symptoms obtained from a single sample to examine the measures' independent and combined utility in accounting for PTSD symptom severity. Fifteen measures identified as PTSD risk factors in published meta-analyses and 12 theoretically and empirically supported individual difference and health-related measures were included. Individual difference measures assessed after the trauma, including insecure attachment and factors related to the current trauma memory, such as self-rated severity, event centrality, frequency of involuntary recall, and physical reactions to the memory, accounted for symptom severity better than measures of pre-trauma factors. In an analysis restricted to prospective measures assessed before the trauma, the total variance explained decreased from 56% to 16%. Results support a model of PTSD in which characteristics of the current trauma memory promote the development and maintenance of PTSD symptoms.