Documenting the Contextualization and Implementation of mhGAP-HIG in Post-earthquake Nepal

Background: The burden of mental health is increased in humanitarian settings, and needs to be addressed in emergency situations. The World Health Organization has recently released the mental health Global Action Programme Humanitarian Intervention Guide (mhGAP-HIG) in order to scale up mental health service delivery in humanitarian settings through task-shifting. This study aims to evaluate, contextualize and identify possible barriers and challenges to mhGAP-HIG manual content, training and implementation in post-earthquake Nepal.

Methods: This qualitative study was conducted in Kathmandu, Nepal. Key informant interviews were conducted with fourteen psychiatrists involved in a mhGAP-HIG Training of Trainers and Supervisors (ToTS) in order to assess the mhGAP-HIG, ToTS training, and the potential challenges and barriers to mhGAP-HIG implementation. Themes identified by informants were supplemented by process notes taken by the researcher during observed training sessions and meetings.

Results: Key themes emerging from key informant interviews include the need to take three factors into account in manual contextualization: culture, health systems and the humanitarian setting. This includes translation of the manual into the local language, adding or expanding upon conditions prevalent in Nepal, and more consideration to improving feasibility of manual use by non-specialists.

Conclusion: The mhGAP-HIG must be tailored to specific humanitarian settings for effective implementation. This study shows the importance of conducting a manual contextualization workshop prior to training in order to maximize the feasibility and success in training health care workers in mhGAP.

Predicting Forest Responses to Changing Environmental Conditions

Forests change with changes in their environment based on the physiological responses of individual trees. These short-term reactions have cumulative impacts on long-term demographic performance. For a tree in a forest community, success depends on biomass growth to capture above- and belowground resources and reproductive output to establish future generations. Here we examine aspects of how forests respond to changes in moisture and light availability and how these responses are related to tree demography and physiology.

First we address the long-term pattern of tree decline before death and its connection with drought. Increasing drought stress and chronic morbidity could have pervasive impacts on forest composition in many regions. We use long-term, whole-stand inventory data from southeastern U.S. forests to show that trees exposed to drought experience multiyear declines in growth prior to mortality. Following a severe, multiyear drought, 72% of trees that did not recover their pre-drought growth rates died within 10 years. This pattern was mediated by local moisture availability. As an index of morbidity prior to death, we calculated the difference in cumulative growth after drought relative to surviving conspecifics. The strength of drought-induced morbidity varied among species and was correlated with species drought tolerance.

Next, we investigate differences among tree species in reproductive output relative to biomass growth with changes in light availability. Previous studies reach conflicting conclusions about the constraints on reproductive allocation relative to growth and how they vary through time, across species, and between environments. We test the hypothesis that canopy exposure to light, a critical resource, limits reproductive allocation by comparing long-term relationships between reproduction and growth for trees from 21 species in forests throughout the southeastern U.S. We found that species had divergent responses to light availability, with shade-intolerant species experiencing an alleviation of trade-offs between growth and reproduction at high light. Shade-tolerant species showed no changes in reproductive output across light environments.

Given that the above patterns depend on the maintenance of transpiration, we next developed an approach for predicting whole-tree water use from sap flux observations. Accurately scaling these observations to tree- or stand-levels requires accounting for variation in sap flux between wood types and with depth into the tree. We compared different models with sap flux data to test the hypotheses that radial sap flux profiles differ by wood type and tree size. We show that radial variation in sap flux is dependent on wood type but independent of tree size for a range of temperate trees. The best-fitting model predicted out-of-sample sap flux observations and independent estimates of sapwood area with small errors, suggesting robustness in new settings. We outline a method for predicting whole-tree water use with this model and include computer code for simple implementation in other studies.

Finally, we estimated tree water balances during drought with a statistical time-series analysis. Moisture limitation in forest stands comes predominantly from water use by the trees themselves, a drought-stand feedback. We show that drought impacts on tree fitness and forest composition can be predicted by tracking the moisture reservoir available to each tree in a mass balance. We apply this model to multiple seasonal droughts in a temperate forest with measurements of tree water use to demonstrate how species and size differences modulate moisture availability across landscapes. As trees deplete their soil moisture reservoir during droughts, a transpiration deficit develops, leading to reduced biomass growth and reproductive output.

This dissertation draws connections between the physiological condition of individual trees and their behavior in crowded, diverse, and continually-changing forest stands. The analyses take advantage of growing data sets on both the physiology and demography of trees as well as novel statistical techniques that allow us to link these observations to realistic quantitative models. The results can be used to scale up tree measurements to entire stands and address questions about the future composition of forests and the land’s balance of water and carbon.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Bridging the Scale Gap from Leaf to Canopy in Biosphere-Atmosphere Gas and Particle Exchanges

Terrestrial ecosystems, occupying more than 25% of the Earth's surface, can serve as

`biological valves' in regulating the anthropogenic emissions of atmospheric aerosol

particles and greenhouse gases (GHGs) as responses to their surrounding environments.

While the signicance of quantifying the exchange rates of GHGs and atmospheric

aerosol particles between the terrestrial biosphere and the atmosphere is

hardly questioned in many scientic elds, the progress in improving model predictability,

data interpretation or the combination of the two remains impeded by

the lack of precise framework elucidating their dynamic transport processes over a

wide range of spatiotemporal scales. The diculty in developing prognostic modeling

tools to quantify the source or sink strength of these atmospheric substances

can be further magnied by the fact that the climate system is also sensitive to the

feedback from terrestrial ecosystems forming the so-called `feedback cycle'. Hence,

the emergent need is to reduce uncertainties when assessing this complex and dynamic

feedback cycle that is necessary to support the decisions of mitigation and

adaptation policies associated with human activities (e.g., anthropogenic emission

controls and land use managements) under current and future climate regimes.

With the goal to improve the predictions for the biosphere-atmosphere exchange

of biologically active gases and atmospheric aerosol particles, the main focus of this

dissertation is on revising and up-scaling the biotic and abiotic transport processes

from leaf to canopy scales. The validity of previous modeling studies in determining

iv

the exchange rate of gases and particles is evaluated with detailed descriptions of their

limitations. Mechanistic-based modeling approaches along with empirical studies

across dierent scales are employed to rene the mathematical descriptions of surface

conductance responsible for gas and particle exchanges as commonly adopted by all

operational models. Specically, how variation in horizontal leaf area density within

the vegetated medium, leaf size and leaf microroughness impact the aerodynamic attributes

and thereby the ultrane particle collection eciency at the leaf/branch scale

is explored using wind tunnel experiments with interpretations by a porous media

model and a scaling analysis. A multi-layered and size-resolved second-order closure

model combined with particle

uxes and concentration measurements within and

above a forest is used to explore the particle transport processes within the canopy

sub-layer and the partitioning of particle deposition onto canopy medium and forest

oor. For gases, a modeling framework accounting for the leaf-level boundary layer

eects on the stomatal pathway for gas exchange is proposed and combined with sap

ux measurements in a wind tunnel to assess how leaf-level transpiration varies with

increasing wind speed. How exogenous environmental conditions and endogenous

soil-root-stem-leaf hydraulic and eco-physiological properties impact the above- and

below-ground water dynamics in the soil-plant system and shape plant responses

to droughts is assessed by a porous media model that accommodates the transient

water

ow within the plant vascular system and is coupled with the aforementioned

leaf-level gas exchange model and soil-root interaction model. It should be noted

that tackling all aspects of potential issues causing uncertainties in forecasting the

feedback cycle between terrestrial ecosystem and the climate is unrealistic in a single

dissertation but further research questions and opportunities based on the foundation

derived from this dissertation are also brie

y discussed.