Schedule for: 17w5107 - Challenges in the Statistical Modeling of Stochastic Processes for the Natural Sciences

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

The increasing availability of precipitation observations from the Global Precipitation Measuring (GPM) Mission constellation of satellites, has fueled renewed interest in developing frameworks for accurate estimation of precipitation extremes especially over land, ungauged mountainous terrains and coastal regions to improve hydro-geological hazard prediction and control. Our recent research has shown that treating precipitation retrieval and data fusion/assimilation as inverse problems and using a regularized variational approach with the regularization term(s) selected to impose desired smoothness in the solution, leads to improved representation of extremes. Here we present some new theoretical and computational developments, which extend the ideas to a model-agnostic framework of retrieval via a regularized search within properly constructed data bases. We test the framework in several tropical storms and over the Himalayas and compare the results with the standard retrieval algorithms currently used for operational purposes. We also present a global multi-scale diagnostic evaluation of the current satellite passive microwave retrievals and point shortcomings for future developments.

This talk will describe a system named 4-Dimensional Visual Delivery (4DVD) for big climate data recently developed at San Diego State University (SDSU). The 4DVD system is a cloud-based data visualization and delivery technology that harnesses resources from browser, database, and server. This technology optimizes computing resources and distributes the visualization computing completely on the user end’s browser. The 4DVD system allows the NOAA data to be visualized in classrooms, museums, and households, and can support the NOAA big data project (BDP) in partnership with Amazon and other big data platform providers. Thus, the 4DVD can serve as an effective delivery tool for climate data to the general public, including school students. The talk will demonstrate the usage of 4DVD using real climate datasets, including NOAAGlobalTemp, NCEP/NCAR Reanalysis, SDSU Weather History Time Machine, and SOG-Reconstructed Global Oceanic Temperate. The reconstruction method is a multivariate regression guided by climate model data. Uncertainty quantifications are made based on the existing theory of multivariate regression and statistical inference. This research is joint with Julien Pierret, and Greg Behm, San Diego State University, and Scripps Institution of Oceanography.

Weather-related climate is the long-term distribution of weather. Climate change means that this distribution is nonstationary. Climate scientists like to study anomalies, and we outline some problems relating to how this is done. Comparison of climate models to weather data can use empirical process tools, but may need some new developments. Regional climate models, or dynamic downscaling, illustrates clearly some problems with current climate models.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

Weather-related climate is the long-term distribution of weather. Climate change means that this distribution is nonstationary. Climate scientists like to study anomalies, and we outline some problems relating to how this is done. Comparison of climate models to weather data can use empirical process tools, but may need some new developments. Regional climate models, or dynamic downscaling, illustrates clearly some problems with current climate models.

To ensure future food security, a key objective of crop breeding programs is to effectively identify which genetic and physiological characteristics of the plant are associated with high yield and/or resistance to environmental stressors. Regarding physiology, the part of the plant that is above-ground is easily observed and thus commonly emphasized. However, the root system is perceivably more sensitive to soil-related stressors yet notoriously challenging to (a) measure and (b) characterize. For (a), recent imaging technology can evaluate the number of roots at regular depths along soil cores that are sampled from the crop field. This method results in 1-dimensional spatial data on within-core root counts. For (b), we develop a modelling framework (http://doi.org/10.3389/fpls.2017.00282) that regards the spatial count data as longitudinal in nature, exhibiting a parametric trend that depends on the plant’s genotype (or “breed”). Under our framework, we define new measures of heritability — the variability among cores that is due to genetics as opposed to noise. The novelty of our methodology lies in the ability to reflect root architecture as a whole by accounting for within-core root counts collectively. Applied to a field study in Australia, our approach indicates an overall heritability of 0.52-0.71 (95% credible interval), which is substantially higher than previous methods. This suggests that our approach is much more effective in discerning root architecture as captured by soil core data.

In the study of biological, ecological, or environmental dynamical processes, many theoretical models have been developed but it is not common practice to estimate model parameters using statistical functions of observed data. In this talk we present an overview of methods that have been proposed to enable statistical inference for parameters of dynamical models such as ordinary differential equation, continuous-time Markov chain, and stochastic differential equation models. A challenge for statisticians is to develop methods to address the issue of the computationally intensive or intractable likelihoods required for these problems.

This informal talk will review some of the many types of variation for environmental processes in space-time. For example, statistical models for purely temporal variation may need to consider seasonal and diurnal effects in both marginal distributions and dependence structure. Purely spatial variation may need to take account of differences in zonal and meridional variation, differences between horizontal and vertical variation and effects due to geographic features such as mountains. Spatial-temporal variation requires considering not just purely spatial and purely temporal variation, but their interaction. I will discuss some simple settings in which one can get misleading results by not properly thinking about these various sources of variation and propose strategies for avoiding such errors.

In the early spatial point process literature, point patterns were typically small, observed in 2D, had quite simple interaction structures, and there were no repetitions available. The observed point patterns were assumed to be realizations of stationary and isotropic point processes, and e.g. clustered patterns were typically modelled by assuming conditional independence between the cluster points given the Poisson distributed parents. However, large data sets (with repetitions) observed both in 2D and in 3D have become more and more common and it is less likely that stationarity and/or isotropy assumptions hold and that simple interaction structures are enough for realistic modelling of the data. In this talk, I will describe two examples of more complicated data sets where such a simple set-up is not enough. The first example concerns nerve fibre patterns on the epidermis, the outermost living layer of the skin. The spatial structure of nerves plays an important role in understanding how the nerve structure changes due to some small fibre neuropathy. The termination points of the nerve fibres form clusters around the base points of the nerves and even the parent (base) points tend to be clustered. In addition, the daughter points may not be located independently of each other, nor of the other parent points. The second example concerns air bubbles in polar ice. The air bubble patterns deep down in the ice are not isotropic (and some noise bubbles may occur in the data). Being able to estimate the deformation (anisotropy) can help physicists to determine the age of the ice at different depths.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Hematopoiesis is the process by which stem cells that reside in the bone marrow differentiate into mature and functional blood cells. Whether an individual hematopoietic stem cell differentiates, replicates (self-renews), or dies is determined by its unique genetic, epigenetic and environmental inputs. These cues cannot be directly observed. Thus, stem cell fates cannot be suitably predicted deterministically, but are very amenable to stochastic modeling and simulation. The many insights derived from 25 years of collaborative studies with Peter Guttorp will be reviewed. As examples, we showed that hematopoiesis is maintained by the successive contributions of different hematopoietic stem cell clones and that the rate at which hematopoietic stem cells replicate differs greatly among mammalian species (from once per 2.5 to once per 40 weeks) although the numbers of stem cells per animal and numbers of stem divisions per lifetime are relatively constant. These insights are crucial for understanding how normal blood cells develop, why diseases like aplastic anemia and leukemia occur, and why close collaborations between biology and statistics are needed to optimize discovery.

Stochastic compartmental models have played a crucial role in statistical studies of biological processes. Inference can be challenging when the data are only partially informative or largely missing, which is almost always the case in experimental and observational studies. We present recent methodology for estimation in challenging missing data settings based on branching process techniques. These methods enable likelihood-based inference in previously intractable settings, but face computational limitations for extremely large systems, which present an open challenge for future work. Applications we consider throughout the talk include molecular epidemiology, hematopoietic lineage tracking, and SIR models of infectious disease from prevalence data.

Compartmental models describe dynamics of populations, where individuals can be assigned types, and individuals are allowed to switch types as time goes by. I will review statistical challenges that arise when analyzing such models and will highlight how different research communities proposed to tackle these challenges. My main focus will be describing statistics of compartmental models under realistically complicated observation schemes with noisy observations and large fractions of missing data.

In the analysis of most spatio-temporal processes in environmental studies, observations present skewed distributions, with a heavy right or left tail. Usually, a single transformation of the data is used to approximate normality, and stationary Gaussian processes are assumed to model the transformed data. Spatial interpolation and/or temporal prediction are routinely performed by transforming the predictions back to the original scale. The choice of a distribution for the data is key for spatial interpolation and temporal prediction. Initially we will discuss advantages and disadvantages of using a single transformation to model such processes. Then we will focus on some recent advances in the modeling of non-Gaussian spatial and spatio-temporal processes.

The EUSTACE project will give publicly available daily estimates of surface air temperature since 1850 across the globe for the first time by combining surface and satellite data using novel statistical techniques." To fulfil this ambitious mission, a spatio-temporal multiscale statistical Gaussian random field model is constructed, with a hierarchy of spatio-temporal dependence structures, ranging from weather on a daily timescale to climate on a multidecadal timescale. Connections between SPDEs and Markov random fields are used to obtain sparse matrices for the practical computation of point estimates, uncertainty estimates, and posterior samples. The extreme size of the problem necessitates the use of iterative solvers, which requires using the multiscale structure of the model to design an effective preconditioner. We raise questions about how to leverage domain specific knowledge and merge traditional statistical techniques with modern numerical methods.

Non-Gaussian random fields can offer increased flexibility over Gaussian random fields for modeling complex spatial surfaces. We extend the concept of Gaussian Markov random fields (GMRF) to allow the kth-order increments to follow non-Gaussian distributions. In particular, we show that placing shrinkage priors such as the horseshoe prior on the kth-order increments can result in a combination of global smoothing and local control. This fully Bayesian formulation allows adaptation to local changes in smoothness of a surface, including abrupt changes or jumps, without compromising smoothness across the rest of the surface. We call the resulting processes shrinkage prior Markov random fields (SPMRFs). We compare the performance of SPRMFs to GMRFs using simulated data, and show that SPRMF models result in reduced bias and increased precision. We also apply the method to two real spatial data sets. This is joint work with Vladimir N. Minin, University of Washington.

In the analysis of climate it is common to build non-stationary spatio-temporal processes, often based on assuming a random walk behavior over time for the error process. Random walk models may be a poor description for the temporal dynamics, leading to inaccurate uncertainty quantification. Likewise, assuming stationarity in time may also not be a reasonable assumption, especially under climate change. In our ongoing research, we present a class of time-varying autoregressive processes that are stationary in space, but locally stationary in time. We demonstrate how to parameterize the time-varying model parameters in terms of a transformation of basis functions. We present some properties of parameter estimates when the process is observed at a finite collection of spatial locations, and apply our methodology to a spatio-temporal analysis of temperature.

Local factors like orographic effects and temperature, and processes that create remote dependence like the El Nino-Southern Oscillation (ENSO) teleconnection both impact local and regional weather patterns. Many statistical methods, however, can only account for either local or remote covariates when analyzing this data. While existing methods can model important phenomena like rainfall and temperature, improvements are possible by introducing new methods that simultaneously account for the effects of local and remote covariates. We propose a geostatistical model that uses covariates observed on a spatially remote domain to improve locally-driven models of a spatial process. Our model draws on ideas from spatially varying coefficient models, spatial basis functions, and predictive processes to allow several interpretations of effects and to overcome modeling challenges in for teleconnections. We adopt a hierarchical Bayesian framework to conduct inference and make predictions to demonstrate how precipitation in Colorado is more accurately modeled by accounting for teleconnection effects with Pacific Ocean sea surface temperatures. We also discuss physical motivations and interpretations for our model.

Argo floats measure sea water temperature and salinity in the upper 2 km of the global ocean. The statistical analysis of the resulting spatio-temporal dataset is challenging due to its non-stationary structure and large size. We propose mapping these data using locally stationary Gaussian process regression where covariance parameter estimation and spatio-temporal prediction are carried out in a moving-window fashion. This yields computationally tractable non-stationary anomaly fields without the need to explicitly model the non-stationary covariance structure. The approach also provides local estimates of the ocean covariance parameters which may be of scientific interest in their own right. We demonstrate using a cross-validation study that the approach yields improved point predictions and uncertainty quantification of Argo anomaly fields and study the structure of the estimated spatial and temporal dependence scales. Joint work with Michael Stein.

In spite of the fact that studies have found substantial risk of a magnitude 9.0 earthquake on the Cascadia Subduction Zone (CSZ) in the next 50 years, few fully likelihood-based spatial models have been developed to explore them. Although they represent important steps in the study of Cascadia, many studies use only a handful of predetermined earthquakes to represent the full range of those possible. While Levy Processes have been used to model slips due to their convenient stability properties, they are heavy-tailed to the point of having all moments infinite, which is unrealistic. This work combines paleoseismic subsidence data collected along the US and Canadian west coast with GPS-based fault locking rate estimates over the CSZ megathrust to fit a fully stochastic spatial-statistical model for earthquake slips. To match observations, slips are tapered off in deeper parts of the fault, but the rate of tapering varies as a function of latitude and is estimated empirically. Multiple distributions for Cascadia slips are tested, including normal, truncated (positive) normal, and lognormal distributions, and error inflations for subsidence estimates are computed empirically. We also obtain predictive distributions of past earthquakes and infer how historical earthquake slips may have been distributed across the fault. We find that subsidence data uncertainties are on average higher than reported, and that the normal and truncated normal models fit the data better than the lognormal model. This study demonstrates that historical subsidence and GPS data can be used to help understand variation in earthquake slip across the CSZ, and the inferred historical earthquake slips can help us better understand the range of possible CSZ earthquakes.

Union of Intersections for Vector Autoregression (UoI-VAR) is a method under development for estimating sparse graphs with both temporal and instantaneous edges. The method is presented with performance results on synthetic datasets, and its application to graphical representation of temporal functional connectivity in neural electrocorticography recordings is considered. The graphical estimation problem is formulated as a regression to which common regularized estimation methods can be applied. While sparse estimation in regression with dependent data is a comparatively underdeveloped area relative to the iid setting, the subject has been studied more recently, including as a special case regularized transition matrix estimation in vector autoregressions. The LASSO is the primary regularization method currently used in this context; the UoI-VAR method aims to deliver improved performance for estimation problems involving high-dimensional time series.

A Spatially-Varying Parameters Point Process Model of Earthquake Occurrence in the Pacific Northwest Abstract: A major component of the earthquake risk in the Pacific Northwest comes from onshore faults under population centers. Mitigating and reducing this risk requires earthquake occurrence modeling that not only has optimal fit to earthquake catalogs but also quantifiable measures of uncertainty that can be presented to diverse audiences. Furthermore, characterizing the spatial nonstationary in earthquake occurrence data is crucial to properly model such a tectonically heterogenous region. To reach this aim, we implement a series of earthquake occurrence models based on the hierarchical space-time Epidemic Type Aftershock Sequence (HIST-ETAS) method. ETAS is a space-time point process model where the conditional intensity is governed by a set of parameters such as background seismicity and aftershock productivity that are directly related to earthquake risk. The HIST-ETAS version allows for the estimated parameters to vary over the spatial domain. We combine three catalogs for the region, incorporating error estimates for reported magnitudes and locations. We present preliminary results for several HIST-ETAS models for a subregion centered around the Puget Sound in western Washington. Methods for model comparison and uncertainty quantification (both from the catalog data and model estimations) will be solicited and discussed.

This poster describes the Snow-Man toolkit for snow and ice coverage calculation and display (SACD) based on the Interactive Multisensor Snow and Ice Mapping System (IMS). Snow-Man generates time series of snow and ice coverage for any area over the Northern Hemisphere from 4 February 1997 to today. IMS is a well-used system for monitoring the snow and ice cover and supported by National Snow and Ice Data Center. The Tibetan Plateau region is selected as an example to describe the toolkit's method, results, and use. Snow-Man novel feature calculates areas using the shoelace formula for a sphere projected on a 2d surface. Snow-Man's main feature obtains Snow coverage for a given day and region by summing up the pixel areas reported as snow or ice. The IMS products include 24, 4, and 1 km nominal resolution data over the northern hemisphere. Although the current version of Snow-Man utilizes only the 24 and 4km data sets, recent developments have the data parsed into a MongoDB database for easy querying and scalable storage, and allowing the addition of the 1km data set. The Tibetan Plateau (TP) region bounded by 25-45 latitude by 65-105 longitude is used as an example to demonstrate our work on SACD. Grid areas calculated by Snow-Man were compared with spherical triangle areas and are shown to have a difference 0.046% for the 24 km grid and 0.033% for the 4 km grid. The differences in the snow-cover area reported by the 24 km and 4 km grids vary between -2.34 and 6.24%. Climate averaged anomalies were calculated and was shown to have a mean of -309.9 km^2. With a standard deviation of 342599.71 km^2, a skew of 1.0006 and a kurtosis of 4.351. Further developments for this product include a website coupled with the database, where the data can be easily obtained easily and without programming experience.

A new class of non-Gaussian multivariate random fields is formulated using systems of stochastic partial differential equations (SPDEs) with additive spatial type-G noise. We show how to formulate the system to get solutions with marginal Matérn co-variance functions for each dimension and derive a parametrization that allows for separate control of cross-covariance and other dependence between the dimensions. Four different constructions of the type-G noise based on normal-variance mixtures are examined. The different constructions result in random fields with increasing flexibility. The fields are incorporated in a geostatistical model with measurement errors and covariates, for which a computationally efficient likelihood-based parameter estimation method is derived.

Contour maps are widely used to display estimates of spatial fields. Instead of showing the estimated field, a contour map only shows a fixed number of contour lines for different levels. However, despite the ubiquitous use of these maps, the uncertainty associated with them has been given a surprisingly small amount of attention. We derive measures of the statistical uncertainty, or quality, of contour maps, and use these to decide an appropriate number of contour lines, that relates to the uncertainty in the estimated spatial field. For practical use in geostatistics and medical imaging, computational methods are constructed, that can be applied to Gaussian Markov random fields, and in particular be used in combination with integrated nested Laplace approximations for latent Gaussian models. The methods are demonstrated on simulated data and an application to temperature estimation is presented.

It is well established by now that the earth system is a highly interconnected system across processes (atmospheric, oceanic, and eco-hydrologic) and across scales (cloud microphysics to large scale dynamics). Improving modeling and prediction relies on using state-of-the-art methodologies for extracting from available data relevant information and hidden relationships, merging observations at different scales, advancing data assimilation methodologies, and identifying trends and patterns. Here we will focus on two main topics: (1) Modern spatial data analysis and reconstruction methods: from EOF regression to random forests, and dictionary learning; and (2) Stochastic modeling approaches for the next generation of climate models: from self-similarity to connections between microscopic scales and global circulations scales.

Long-term planning and decision-making regarding fundamental societal infrastructure such as transportation, energy supply and water and drainage systems must account for a changing climate. However, we still lack a better understanding of climate change and the associated impacts. Furthermore, these factors are typically associated with severe inherent uncertainty and it is critical that the decision-making appropriately accounts for this. An additional complication of the decision-making process is the involvement of multiple different actors with different backgrounds and expertise. We present the outcomes of a workshop that brought together representatives from science and practice to discuss the practical and methodological challenges of climate change adaptation. Aiming to address some of the challenges identified at the workshop, we further present a case study on local adaptation to sea level rise in Bergen, Norway. Adapting to sea level rise requires comparing different possible adaptation strategies, comparing the cost of different actions (including no action), and assessing where and at what point in time the chosen strategy should be implemented. All these decisions must be made under considerable uncertainty. We demonstrate the value of uncertainties and show for example that failing to take uncertainty into account can result in the median projected damage costs being an order of magnitude smaller.

The rise in technology has led science into the new world of `postnormal science' which is characterized by great uncertainty, high risk, a key role for societal values and large groups of stake-holders with legitimate perspectives. Formulating scientific conclusions can involve large groups of experts with different and legitimate perspectives e.g. the IPCC panel on climate change & the EPA's CASAC panels on setting air quality standards, surrounded by policy makers, research funding organizations and advocates for societal interest groups. The paradigm of "truth" has lost its value as an objective. In this new world, the effective communication of scientific discovery and knowledge is assuming a more important role than ever. Yet most would be scientific researchers and appliers of scientific knowledge have little or no training in this important skill. This talk will discuss aspects of the problem relating specifically to the characterization of uncertainty in postnormal science and it would include something that is not much discussed in statistical science, qualitative uncertainty.

The title of the talk alludes to one of the most popular plays by Oscar Wilde. Wilde told [Wikipedia] Robert Ross [a friend of Wildes’] that the play's theme was "That we should treat all trivial things in life very seriously, and all serious things of life with a sincere and studied triviality." In the play, Wilde "refuses to play the game" of other dramatists of the period, for instance Bernard Shaw, who used their characters to draw audiences to grander ideals. Grander ideals or Trivial things: How is it at all possible to ”communicate advances in and applications of stochastic modeling in the natural sciences” to ”the public”. Grand ideals is what guides scientists, Trivial (but important) things is what (we think) guides the public. The talk will deal with the link between the Grander ideals – what the scientist calls ”the facts”, including all the uncertainties a statistician regards as ”a fact” – and the ”Trivial things” that the public is assumed to relate to. To find those links is perhaps the most important question of the following breakout. Thus: In Banff in July, the title of the talk will probably be: The importance of being relevant.

Statistical modeling of data collected in the natural sciences has often been tackled with the help of transformations such as Fourier transforms, wavelet transforms and deformations. The basic premise is that the transformed data are easier to model because of certain properties associated with the transformation (e.g., decorrelation or realignment of a covariance structure). In this talk we give an overview of modeling in transformed domains and comment on generalizations of this approach intended to handle data collected under nonstandard sampling schemes. We then pose some questions (to be discussed in the associated breakout session) intended to identify fruitful directions for future research in the area of transformations.

A 2010 BIRS workshop which was co-organized by Peter Guttorp inspired Rick Katz and me to write a paper “Design Life Level: Quantifying risk in a changing climate”. The paper was published 2013 in Water Resources Research, and has since attracted some interest from hydrologists. The thesis of the paper was that in the past the concepts of return levels and return periods have been the standard tools for engineering design, but that these concepts are based on the assumption of a stationary climate and do not apply to a changing climate. Instead, we proposed a refined concept, Design Life Level, which quantifies risk in a nonstationary climate and can serve as the basis for communication. However, current design methodology, and also our paper, mainly considers each structure, say a dike, dam, or bridge, separately. A next step in risk handling for environmental loads is to instead consider several structures, say all levees in a river network or even all dams in a country, simultaneously. This is an important challenge for Extreme Value Statistics.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.