On the use of the bayesian approach for the calibration, evaluation and comparison of process-based forest models

Doutoramento em Engenharia Florestal e dos Recursos Naturais - Instituto Superior de AgronomiaForest ecosystems have been experiencing fast and abrupt changes in the environmental conditions, that can increase their vulnerability to extreme events such as drought, heat waves, storms, fire. Process-based models can draw inferences about future environmental dynamics, but the reliability and robustness of vegetation models are conditional on their structure and their parametrisation. The main objective of the PhD was to implement and apply modern computational techniques, mainly based on Bayesian statistics, in the context of forest modelling. A variety of case studies was presented, spanning from growth predictions models to soil respiration models and process-based models. The great potential of the Bayesian method for reducing uncertainty in parameters and outputs and model evaluation was shown. Furthermore, a new methodology based on a combination of a Bayesian framework and a global sensitivity analysis was developed, with the aim of identifying strengths and weaknesses of process-based models and to test modifications in model structure. Finally, part of the PhD research focused on reducing the computational load to take full advantage of Bayesian statistics. It was shown how parameter screening impacts model performances and a new methodology for parameter screening, based on canonical correlation analysis, was presente

Bayesian calibration, comparison and averaging of six forest models, using data from Scots pine stands across Europe

Forest management requires prediction of forest growth, but there is no general agreement about which models best predict growth, how to quantify model parameters, and how to assess the uncertainty of model predictions. In this paper, we show how Bayesian calibration (BC), Bayesian model comparison (BMC) and Bayesian model averaging (BMA) can help address these issues. We used six models, ranging from simple parameter-sparse models to complex process-based models: 3PG, 4C, ANAFORE, BASFOR, BRIDGING and FORMIND. For each model, the initial degree of uncertainty about parameter values was expressed in a prior probability distribution. Inventory data for Scots pine on tree height and diameter, with estimates of measurement uncertainty, were assembled for twelve sites, from four countries: Austria, Belgium, Estonia and Finland. From each country, we used data from two sites of the National Forest Inventories (NFIs), and one Permanent Sample Plot (PSP). The models were calibrated using the NFI-data and tested against the PSP-data. Calibration was done both per country and for all countries simultaneously, thus yielding country-specific and generic parameter distributions. We assessed model performance by sampling from prior and posterior distributions and comparing the growth predictions of these samples to the observations at the PSPs. We found that BC reduced uncertainties strongly in all but the most complex model. Surprisingly, country-specific BC did not lead to clearly better within-country predictions than generic BC. BMC identified the BRIDGING model, which is of intermediate complexity, as the most plausible model before calibration, with 4C taking its place after calibration. In this BMC, model plausibility was quantified as the relative probability of a model being correct given the information in the PSP-data. We discuss how the method of model initialisation affects model performance. Finally, we show how BMA affords a robust way of predicting forest growth that accounts for both parametric and model structural uncertainty

Integrated Machine Learning and Optimization Frameworks with Applications in Operations Management

Incorporation of contextual inference in the optimality analysis of operational problems is a canonical characteristic of data-informed decision making that requires interdisciplinary research. In an attempt to achieve individualization in operations management, we design rigorous and yet practical mechanisms that boost efficiency, restrain uncertainty and elevate real-time decision making through integration of ideas from machine learning and operations research literature. In our first study, we investigate the decision of whether to admit a patient to a critical care unit which is a crucial operational problem that has significant influence on both hospital performance and patient outcomes. Hospitals currently lack a methodology to selectively admit patients to these units in a way that patient’s individual health metrics can be incorporated while considering the hospital’s operational constraints. We model the problem as a complex loss queueing network with a stochastic model of how long risk-stratified patients spend time in particular units and how they transition between units. A data-driven optimization methodology then approximates an optimal admission control policy for the network of units. While enforcing low levels of patient blocking, we optimize a monotonic dual-threshold admission policy. Our methodology captures utilization and accessibility in a network model of care pathways while supporting the personalized allocation of scarce care resources to the neediest patients. The interesting benefits of admission thresholds that vary by day of week are also examined. In the second study, we analyze the efficiency of surgical unit operations in the era of big data. The accuracy of surgical case duration predictions is a crucial element in hospital operational performance. We propose a comprehensive methodology that incorporates both structured and unstructured data to generate individualized predictions regarding the overall distribution of surgery durations. Consequently, we investigate methods to incorporate such individualized predictions into operational decision-making. We introduce novel prescriptive models to address optimization under uncertainty in the fundamental surgery appointment scheduling problem by utilizing the multi-dimensional data features available prior to the surgery. Electronic medical records systems provide detailed patient features that enable the prediction of individualized case time distributions; however, existing approaches in this context usually employ only limited, aggregate information, and do not take advantages of these detailed features. We show how the quantile regression forest, can be integrated into three common optimization formulations that capture the stochasticity in addressing this problem, including stochastic optimization, robust optimization and distributionally robust optimization. In the last part of this dissertation, we provide the first study on online learning problems under stochastic constraints that are "soft", i.e., need to be satisfied with high likelihood. Under a Bayesian framework, we propose and analyze a scheme that provides statistical feasibility guarantees throughout the learning horizon, by using posterior Monte Carlo samples to form sampled constraints that generalize the scenario generation approach commonly used in chance-constrained programming. We demonstrate how our scheme can be integrated into Thompson sampling and illustrate it with an application in online advertisement.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145936/1/meisami_1.pd

Bayesian inference of hydraulic properties in and around a white fir using a process-based ecohydrologic model

We present a parameter estimation study of the Soil-Tree-Atmosphere Continuum (STAC) model, a process-based model that simulates water flow through an individual tree and its surrounding root zone. Parameters are estimated to optimize the model fit to observations of sap flux, stem water potential, and soil water storage made for a white fir (Abies concolor) in the Sierra Nevada, California. Bayesian inference is applied with a likelihood function that considers temporal correlation of the model errors. Key vegetation properties are estimated, such as the tree\u27s root distribution, tolerance to drought, and hydraulic conductivity and retention functions. We find the model parameters are relatively non-identifiable when considering just soil water storage. Overall, by utilizing multiple processes (e.g. sap flow, stem water potential, and soil water storage) during the parameter estimation, we find the simulations of the soil and tree water properties to be more accurate when compared to observed data

Analytical And Decision Tools For Wildlife Population And Habitat Management

The long-term success of wildlife conservation depends on maximizing the benefits of limited funds and data in pursuit of population and habitat objectives. The ultimate currency for wildlife management is progress toward long-term preservation of ample, wild, free wildlife populations and to this end, funds must be wisely spent and maximal use made from limited data. Through simulation-based analyses, I evaluated the efficacy of various models for estimating population abundance from harvest data. Because managers have different estimators to choose from and can also elect to collect additional data, I compared the statistical performance of different estimation strategies (estimator + dataset) relative to the financial cost of data collection. I also performed a value of information analysis to measure the impact that different strategies have on a representative harvest management decision. The latter analysis is not based on the cost of data, but rather on the management benefit derived from basing decisions on different datasets. Finally, I developed a hybrid modeling framework for mapping habitat quality or suitability. This framework makes efficient use of expert opinion and empirical validation data in a single, updatable statistical structure. I illustrate this method by applying it across an entire state

Exploring robustness and uncertainties of projections with forest ecosystem models

Forests act as important CO2 sinks and might help to reduce the impacts of global and climate change. We can explore such scenarios with forest ecosystem models as their mechanistic struc- ture in principle allows forecasting into never-observed conditions. However, to make realistic projections, we have to adjust the model to fit the observed data. To do so and to assess uncer- tainties of projections, researchers use methods like a sensitivity and uncertainty analysis but also Bayesian calibration. However, the naive application and and the associated assumptions of these methods do often not reflect the empirical knowledge about forest ecosystems. To adress these issues, this doctoral thesis analyzes the robustusness of and applies these numerical meth- ods to state-of-the-art forest ecosystem models. We asked the following questions: The first one was: What are the main contributors of uncertainty in forest ecosystem models? Can we use uncertainty analysis and calibration of forest ecosystem models to analyze ecological patterns on environmental gradients? The next question deals with the remaining variance: To what ex- tent can random effects be used to represent ecological variation and how much data points are required to estimate these variations precisely? And the last question investigates if the findings above are robust when we have structural model error: What are the consequences and solutions of calibrating of and projecting with models with structural errors? The first chapter introduces the role of forest ecosystem models and their associated uncer- tainities for projecting forest dynamics under climate change and emerging challenges. In the second chapter, we explain key concepts and methods which are essential to understand our research results. In particular these are types of forest ecosystem models, their associated un- certainties (due to initial conditions, model inputs, model structure and parameters), sensitivity and uncertainty analysis and Bayesian calibration. In the third chapter, we analyze sensitivi- ties and uncertainties of carbon projections across European forests under climate change with a dynamic vegetation model (LPJ-GUESS 4.0) addressing the effect of both model parameters and environmental drivers. We find that carbon projections are most sensitive to photosynthesis- related parameters, while environmental drivers induce most uncertainty. Moreover, environ- mental drivers modify the uncertainties of other parameters. This study shows that environmen- tal drivers are strong contributors and modifiers of uncertainties in other ecosystem processes. In the fourth chapter, we analyze the consequences and possibilities to represent intraspecific variation in the calibration of a forest ecosystem model. To do so, we calibrate the 3-PG model against biomass derived from inventory data across Germany and Sweden with a hierarchical Bayesian calibration scheme. We find evidence for intraspecific variation that can be partly ex- plained by environmental conditions. This study shows the potential of using forest ecosystem models to infer not measurable ecological information. In the fifth chapter, we analyze if with a low number of levels it is better to model a grouping variable as a random or as a fixed-effect. We find with varying intercepts and slopes in the data-generating process, using a random slope and intercept model, and, in case of a singular fit switching to a fixed-effects model, avoids over- confidence in the results. This study shows how to make ecological inference with mixed-effects models more robust for a small number of levels. In the sixth chapter, we explain why model error causes bias and underestimated uncertainties, especially when calibrated against unbal- anced data, and propose a framework for robust inference with complex computer simulations. As possible solutions we discuss data rebalancing and adding bias corrections during or after the calibration procedure. We illustrate the methods in a case study, using a dynamic vegetation model. From this, we conclude that developing better methods for robust inference of complex computer simulations is essential for generating reliable predictions. The last chapter discusses the relevance and significance of our studies for forecasting and inference with forest ecosystem models and outlines further research questions