Bayesian nonlinear meta regression for benefit transfer

In recent years numerous meta-regression models for benefit transfer in the context of environmental quality changes have been proposed by the academic literature and used by government agencies for policy making. We examine a set of popular specifications in terms of consistency with some basic utility-theoretic considerations, including the adding-up condition that is currently under much scrutiny by benefit transfer practitioners. We also compare these models based on econometric fit with underlying data, and ability to generate meaningful and efficient benefit transfer distributions. We find that our preferred Bayesian Nonlinear Meta-Regression Model (BNL-MRM) satisfies all theoretical requirements. Using a built-in nonlinear model search algorithm we show that it produces benefit estimates that are comparable or superior in efficiency to those flowing from better fitting, but theoretically flawed linear models that do not satisfy adding-up.     

Ensemble Bayesian model averaging using Markov Chain Monte Carlo sampling

Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery et al. Mon Weather Rev 133:1155–1174, 2005) has recommended the Expectation–Maximization (EM) algorithm for BMA model training, even though global convergence of this algorithm cannot be guaranteed. In this paper, we compare the performance of the EM algorithm and the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm for estimating the BMA weights and variances. Simulation experiments using 48-hour ensemble data of surface temperature and multi-model streamflow forecasts show that both methods produce similar results, and that their performance is unaffected by the length of the training data set. However, MCMC simulation with DREAM is capable of efficiently handling a wide variety of BMA predictive distributions, and provides useful information about the uncertainty associated with the estimated BMA weights and variances.     

Income inequality and willingness to pay for environmental public goods

We study how the distribution of income among members of society, and income inequality in particular, affects social willingness to pay (WTP) for environmental public goods. We find that social WTP for environmental goods decreases (increases) with income inequality if and only if environmental goods and manufactured goods are substitutes (complements). We derive adjustment factors for benefit transfer to control for differences in income distributions between a study site and a policy site. For illustration, we quantify how social WTP for environmental public goods depends on the respective income distributions for empirical case studies in Sweden and the World at large. We find that the adjustment for income inequality can be substantial.     

The Use of Bayesian Model Averaging to Better Represent Uncertainty in Ecological Models

Abstract:   In conservation biology, uncertainty about the choice of a statistical model is rarely considered. Model-selection uncertainty occurs whenever one model is chosen over plausible alternative models to represent understanding about a process and to make predictions about future observations. The standard approach to representing prediction uncertainty involves the calculation of prediction (or confidence) intervals that incorporate uncertainty about parameter estimates contingent on the choice of a "best" model chosen to represent truth. However, this approach to prediction based on statistical models tends to ignore model-selection uncertainty, resulting in overconfident predictions. Bayesian model averaging (BMA) has been promoted in a range of disciplines as a simple means of incorporating model-selection uncertainty into statistical inference and prediction. Bayesian model averaging also provides a formal framework for incorporating prior knowledge about the process being modeled. We provide an example of the application of BMA in modeling and predicting the spatial distribution of an arboreal marsupial in the Eden region of southeastern Australia. Other approaches to estimating prediction uncertainty are discussed.     

Demand for environmental policies to improve health: Evaluating community-level policy scenarios

Using a national survey and a discrete choice experiment format, we estimate demand for environmental polices to improve health. We use a richly detailed community-level approach that describes illnesses avoided, premature deaths avoided, policy duration, and the affected population size. We allow preferences for policy attributes to vary systematically with the scenario design, with the source of risk and type of health threat, and with respondent characteristics. Using a willingness to pay (WTP) framework similar to that used for studies of individual risk, we find that omission of illness information leads to an upward bias in estimates of the value of avoided premature deaths and that individuals view avoided deaths and avoided illnesses as substitutes. We also find evidence of strongly diminishing marginal utility in policy scope. Differences in marginal WTP from different sources of risk or types of illness appear very small relative to differences associated with respondent characteristics and/or perceptions. Self-interest strongly dominates altruistic considerations.     

Bayesian estimation of age-specific bird nest survival rates with categorical covariates

The populations of many North American landbirds are showing signs of declining. Gathering information on breeding productivity allows critical assessment of population performance and helps identify good habitat-management practices. He (Biometrics (2003) 59 962–973) proposed a Bayesian model to estimate the age-specific nest survival rates. The model allows irregular visiting schedule under the assumption that the observed nests have homogeneous nest survival. Because nest survival studies are often conducted in different sites and time periods, it is not realistic to assume homogeneous nest survival. In this paper, we extend He’s model by incorporating these factors as categorical covariates. The simulation results show that the Bayesian hierarchical model can produce satisfactory estimates on nest survival and capture different factor effects. Finally the model is applied to a Missouri red-winged blackbird data set.     

A robust-design formulation of the incidence function model of metapopulation dynamics applied to two species of rails

The incidence function model (IFM) uses area and connectivity to predict metapopulation dynamics. However, false absences and missing data can lead to underestimates of the number of sites contributing to connectivity, resulting in overestimates of dispersal ability and turnovers (extinctions plus colonizations). We extend estimation methods for the IFM by using a hierarchical Bayesian model to account both for false absences due to imperfect detection and for missing data due to sites not surveyed in some years. We compare parameter estimates, measures of metapopulation dynamics, and forecasts using stochastic patch occupancy models (SPOMs) among three IFM models: (1) a Bayesian formulation assuming no false absences and omitting site-year combinations with missing data; (2) a hierarchical Bayesian formulation assuming no false absences but incorporating missing data; and (3) a hierarchical Bayesian formulation allowing for imperfect detection and incorporating missing data. We fit the models to multiyear data sets of occupancy for two bird species that differ in body size and presumed dispersal ability but inhabit the same network of sites: the small Black Rail (Laterallus jamaicensis) and the medium-sized Virginia Rail (Rallus limicola). Incorporating missing data affected colonization parameters and led to lower estimates of dispersal ability for the Black Rail. Detection rates were high for the Black Rail in most years but moderate for the Virginia Rail. Incorporating imperfect detection resulted in higher occupancy and lower turnover rates for both species, with largest effects for the Virginia Rail. Forecasts using SPOMs were sensitive to both missing data and false absences; persistence in models assuming no false absences was more optimistic than from robust models. Our results suggest that incorporating false absences and missing data into the IFM can improve (1) estimates of dispersal ability and the effect of connectivity on colonization, (2) the scaling of extinction risk with patch area, and (3) forecasts of occupancy and turnover rates.     

Multimethod,multistate Bayesian hierarchical modeling approach for use in regional monitoring of wolves

In many cases, the first step in large‐carnivore management is to obtain objective, reliable, and cost‐effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical‐site‐occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost‐effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well‐coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population‐parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population parameters.     

Three reasons to use annual payments in contingent valuation surveys: Convergent validity,discount rates,and mental accounting

We present three arguments for using ongoing annual payments in contingent valuation (CV) surveys that estimate the benefit of a long-lasting environmental improvement. First, by matching the duration of the payments with the duration of the environmental benefits, survey respondents are spared from performing complicated present value calculations. Second, willingness to pay (WTP) estimates from CV surveys that include ongoing annual payments best match WTP estimates obtained using travel cost surveys. Third, respondents are less likely to face binding mental budget constraints with ongoing annual payments than with a larger one-time payment. In addition, respondents’ discount rates may be estimated by collecting non-hypothetical, individual time preference data as part of the valuation survey.     

Hierarchical Bayesian modelling of early detection surveillance for plant pest invasions

Early detection surveillance programs aim to find invasions of exotic plant pests and diseases before they are too widespread to eradicate. However, the value of these programs can be difficult to justify when no positive detections are made. To demonstrate the value of pest absence information provided by these programs, we use a hierarchical Bayesian framework to model estimates of incursion extent with and without surveillance. A model for the latent invasion process provides the baseline against which surveillance data are assessed. Ecological knowledge and pest management criteria are introduced into the model using informative priors for invasion parameters. Observation models assimilate information from spatio-temporal presence/absence data to accommodate imperfect detection and generate posterior estimates of pest extent. When applied to an early detection program operating in Queensland, Australia, the framework demonstrates that this typical surveillance regime provides a modest reduction in the estimate that a surveyed district is infested. More importantly, the model suggests that early detection surveillance programs can provide a dramatic reduction in the putative area of incursion and therefore offer a substantial benefit to incursion management. By mapping spatial estimates of the point probability of infestation, the model identifies where future surveillance resources can be most effectively deployed.     

A hedonic travel cost analysis for valuation of multiple components of site quality: The recreation value of forest management

One benefit of managing forests is that one can alter the qualities of sites. The value of changing site qualities, however, is generally not known. This paper develops a formal hedonic travel cost model which can be used to estimate the value of both marginal and non-marginal changes to sites. The approach accommodates multiple simultaneous changes in site characteristics. Estimating this model using a set of permits from wilderness areas leads to revealed preference estimates of the recreational value of clear-cuts, old-growth, and nine other wilderness attributes.     

A Bayesian approach to line-transect analysis for estimating abundance

Line-transect analysis is a widely used method of estimating plant and animal density and abundance. A Bayesian approach to a basic line-transect analysis is developed for a half-normal detection function. We extend the model of Karunamuni and Quinn [Karunamuni, R.J., Quinn II, T.J., 1995. Bayesian estimation of animal abundance for line-transect sampling. Biometrics 51, 1325–1337] by including a binomial likelihood function for the number of objects detected. The method computes a joint posterior distribution on the effective strip width and the density of objects in the sampled area. Analytical and computational methods for binned and unbinned perpendicular distance data are provided. Existing information about effective strip width and density can be brought into the analysis via prior distributions. The Bayesian approach is compared to a standard line-transect analysis using both real and simulated data. Results of the Bayesian and non-Bayesian analyses are similar when there are no prior data on effective strip width or density, but the Bayesian approach performs better when such data are available from previous or related studies. Practical methods for including prior data on effective strip width and density are suggested. A numerical example shows how the Bayesian approach can provide valid estimates when the sample size is too small for the standard approach to work reliably. The proposed Bayesian approach can form the basis for developing more advanced analyses.     

Nectar secondary compounds affect self-pollen transfer: implications for female and male reproduction

Pollen movement within and among plants affects inbreeding, plant fitness, and the spatial scale of genetic differentiation. Although a number of studies have assessed how plant and floral traits influence pollen movement via changes in pollinator behavior, few have explored how nectar chemical composition affects pollen transfer. As many as 55% of plants produce secondary compounds in their nectar, which is surprising given that nectar is typically thought to attract pollinators. We tested the hypothesis that nectar with secondary compounds may benefit plants by encouraging pollinators to leave plants after visiting only a few flowers, thus reducing self-pollen transfer. We used Gelsemium sempervirens, a plant whose nectar contains the alkaloid gelsemine, which has been shown to be a deterrent to foraging bee pollinators. We found that high nectar alkaloids reduced the total and proportion of self-pollen received by one-half and one-third, respectively. However, nectar alkaloids did not affect female reproduction when we removed the potential for self-pollination (by emasculating all flowers on plants). We then tested the assumption that self-pollen in combination with outcrossed pollen depresses seed set. We found that plants were weakly self-compatible, but self-pollen with outcrossed pollen did not reduce seed set relative to solely outcrossed flowers. Finally, an exponential model of pollen carryover suggests that high nectar alkaloids could benefit plants via increased pollen export (an estimate of male function), but only when pollinators were efficient and abundant and plants had large floral displays. Results suggest that high nectar alkaloids may benefit plants via increased pollen export under a restricted set of ecological conditions, but in general, the costs of high nectar alkaloids in reducing pollination balanced or outweighed the benefits of reducing self-pollen transfer for estimates of female and male reproduction.     

A Note on Consistent Estimation of Mean WTP Using a Misspecified Logit Contingent Valuation Model

Monte Carlo evidence has shown that simple, misspecified referendum contingent valuation (CV) models sometimes lead to good estimates of mean willingness to pay (WTP). Empirical studies have found that estimates of mean WTP derived from simple parametric models often differ little from those derived from nonparametric methods. This indicates that simple models can potentially yield WTP estimators that are relatively unbiased. This note shows that very simple logit referendum CV models will estimate mean WTP consistently if the survey bids are drawn randomly from a uniform distribution.     

Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.

Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.     

Cost-Effective Management Alternatives for Snake River Chinook Salmon: a Biological-Economic Synthesis

Abstract: The mandate to increase endangered salmon populations in the Columbia River Basin of North America has created a complex, controversial resource‐management issue. We constructed an integrated assessment model as a tool for analyzing biological‐economic trade‐offs in recovery of Snake River spring‐ and summer‐run chinook salmon (Oncorhynchus tshawytscha). We merged 3 frameworks: a salmon‐passage model to predict migration and survival of smolts; an age‐structured matrix model to predict long‐term population growth rates of salmon stocks; and a cost‐effectiveness analysis to determine a set of least‐cost management alternatives for achieving particular population growth rates. We assessed 6 individual salmon‐management measures and 76 management alternatives composed of one or more measures. To reflect uncertainty, results were derived for different assumptions of effectiveness of smolt transport around dams. Removal of an estuarine predator, the Caspian Tern (Sterna caspia), was cost‐effective and generally increased long‐term population growth rates regardless of transport effectiveness. Elimination of adult salmon harvest had a similar effect over a range of its cost estimates. The specific management alternatives in the cost‐effective set depended on assumptions about transport effectiveness. On the basis of recent estimates of smolt transport effectiveness, alternatives that discontinued transportation or breached dams were prevalent in the cost‐effective set, whereas alternatives that maximized transportation dominated if transport effectiveness was relatively high. More generally, the analysis eliminated 80–90% of management alternatives from the cost‐effective set. Application of our results to salmon management is limited by data availability and model assumptions, but these limitations can help guide research that addresses critical uncertainties and information. Our results thus demonstrate that linking biology and economics through integrated models can provide valuable tools for science‐based policy and management.     

Unintended biological invasions: Does risk vary by trading partner?

International trade is the primary conduit for unintentional and damaging species introductions. But biogeographic heterogeneity, and differences in historical trade exposure across trade partners suggest that not all imports are equally risky. We develop an analytical model linking exotic species introductions and discoveries to trade volumes. The model is estimated using a novel historical data set on global trade and species introductions by region. Our estimates support theoretical predictions that trade from different regions poses different risks and that the cumulative number of introductions from a region is a concave function of imports. For each trade region we then calculate the marginal and cumulative invasion risk from additional trade. Simple volume restrictions on imports to reduce NIS introductions are not advisable based on coarse cost–benefit calculations.     

Semi-nonparametric Distribution-Free Dichotomous Choice Contingent Valuation

We apply a semi-nonparametric distribution-free estimator for binary discrete response data to the estimation of a dichotomous choice contingent valuation model. Using this estimator, mean and median compensating and equivalent variation can be consistently estimated without making nontheoretically motivated assumptions on consumer' preferences. The approach is illustrated using a contingent valuation survey of willingness to pay for reduction of risk of premature death due to exposure to hazardous waste. We find that a conventional parametric estimator and the proposed estimator give similar estimates of unconditional WTP, but that conditional on explanatory variables the estimates are quite different.     

A Bayesian hierarchical approach to quantifying stakeholder attitudes toward conservation in the presence of reporting error

Stakeholder support is vital for achieving conservation success, yet there are few reliable mechanisms to monitor stakeholder attitudes toward conservation. Approaches used to assess attitudes rarely account for bias arising from reporting error, which can lead to falsely reporting a positive attitude toward conservation (false-positive error) or not reporting a positive attitude when the respondent has a positive attitude toward conservation (false-negative error). Borrowing from developments in applied conservation science, we used a Bayesian hierarchical model to quantify stakeholder attitudes as the probability of having a positive attitude toward wildlife notionally (or in abstract terms) and at localized scales while accounting for reporting error. We compared estimates from our model, Likert scores, and naïve estimates (i.e., proportion of respondents reporting a positive attitude in at least 1 question that was only susceptible to false-negative error) with true stakeholder attitudes through simulations. We then applied the model in a survey of tea estate staff on their attitudes toward Asian elephants (Elephas maximus) in the Kaziranga–Karbi Anglong landscape of northeast India. In simulations, Bayesian model estimates of stakeholder attitudes toward wildlife were less biased than naïve estimates or Likert scores. After accounting for reporting errors, we estimated the probability of having a positive attitude toward elephants notionally as 0.85 in the Kaziranga landscape, whereas the proportion of respondents who had positive attitudes toward elephants at a localized scale was 0.50. In comparison, without accounting for reporting errors, naïve estimates of proportions of respondents with positive attitudes toward elephants were 0.69 and 0.23 notionally and at local scales, respectively. False (positive and negative) reporting probabilities were consistently not 0 (0.22–0.68). Regular and reliable assessment of stakeholder attitudes–combined with inference on drivers of positive attitudes–can help assess the success of initiatives aimed at facilitating human behavioral change and inform conservation decision making.     

Confronting Uncertainty and Missing Values in Environmental Value Transfer as Applied to Species Conservation

Abstract: The nonuse (or passive) value of nature is important but time‐consuming and costly to quantify with direct surveys. In the absence of estimates of these values, there will likely be less investment in conservation actions that generate substantial nonuse benefits, such as conservation of native species. To help overcome decisions about the allocation of conservation dollars that reflect the lack of estimates of nonuse values, these values can be estimated indirectly by environmental value transfer (EVT). EVT uses existing data or information from a study site such that the estimated monetary value of an environmental good is transferred to another location or policy site. A major challenge in the use of EVT is the uncertainty about the sign and size of the error (i.e., the percentage by which transferred value exceeds the actual value) that results from transferring direct estimates of nonuse values from a study to a policy site, the site where the value is transferred. An EVT is most useful if the decision‐making framework does not require highly accurate information and when the conservation decision is constrained by time and financial resources. To account for uncertainty in the decision‐making process, a decision heuristic that guides the decision process and illustrates the possible decision branches, can be followed. To account for the uncertainty associated with the transfer of values from one site to another, we developed a risk and simulation approach that uses Monte Carlo simulations to evaluate the net benefits of conservation investments and takes into account different possible distributions of transfer error. This method does not reduce transfer error, but it provides a way to account for the effect of transfer error in conservation decision making. Our risk and simulation approach and decision‐based framework on when to use EVT offer better‐informed decision making in conservation.