Parallel and Streaming Truth Discovery in Large-Scale Quantitative Crowdsourcing

ACKNOWLEDGEMENTS This research is based upon work supported in part by the U.S. ARL and U.K. Ministry of Defense under Agreement Number W911NF-06-3-0001, and by the NSF under award CNS-1213140. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views or represent the official policies of the NSF, the U.S. ARL, the U.S. Government, the U.K. Ministry of Defense or the U.K. Government. The U.S. and U.K. Governments are authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon.

Near-bed hydrodynamics and turbulence below a large-scale plunging breaking wave over a mobile barred bed profile

Funded by The research presented in this paper is part of the SINBAD project. Grant Number: STW (12058) and EPSRC (EP/J00507X/1, EP/J005541/1)

A Comparison of Anchor-Item Designs for the Concurrent Calibration of Large Banks of Likert-Type Items

Current interest in measuring quality of life is generating interest in the construction of computerized adaptive tests (CATs) with Likert-type items. Calibration of an item bank for use in CAT requires collecting responses to a large number of candidate items. However, the number is usually too large to administer to each subject in the calibration sample. The concurrent anchor-item design solves this problem by splitting the items into separate subtests, with some common items across subtests; then administering each subtest to a different sample; and finally running estimation algorithms once on the aggregated data array, from which a substantial number of responses are then missing. Although the use of anchor-item designs is widespread, the consequences of several configuration decisions on the accuracy of parameter estimates have never been studied in the polytomous case. The present study addresses this question by simulation, comparing the outcomes of several alternatives on the configuration of the anchor-item design. The factors defining variants of the anchor-item design are (a) subtest size, (b) balance of common and unique items per subtest, (c) characteristics of the common items, and (d) criteria for the distribution of unique items across subtests. The results of this study indicate that maximizing accuracy in item parameter recovery requires subtests of the largest possible number of items and the smallest possible number of common items; the characteristics of the common items and the criterion for distribution of unique items do not affect accuracy.

Parallel and Streaming Truth Discovery in Large-Scale Quantitative Crowdsourcing

ACKNOWLEDGEMENTS This research is based upon work supported in part by the U.S. ARL and U.K. Ministry of Defense under Agreement Number W911NF-06-3-0001, and by the NSF under award CNS-1213140. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views or represent the official policies of the NSF, the U.S. ARL, the U.S. Government, the U.K. Ministry of Defense or the U.K. Government. The U.S. and U.K. Governments are authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon.

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.

Distributed Feature Selection in Large n and Large p Regression Problems

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (in the sample space) or vertically (in the feature space), and the challenge arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. For sample space partitioning, I propose a MEdian Selection Subset AGgregation Estimator ({\em message}) algorithm for solving these issues. The algorithm applies feature selection in parallel for each subset using regularized regression or Bayesian variable selection method, calculates the `median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in sample size, and has theoretical guarantees. I provide extensive experiments to show excellent performance in feature selection, estimation, prediction, and computation time relative to usual competitors.

While sample space partitioning is useful in handling datasets with large sample size, feature space partitioning is more effective when the data dimension is high. Existing methods for partitioning features, however, are either vulnerable to high correlations or inefficient in reducing the model dimension. In the thesis, I propose a new embarrassingly parallel framework named {\em DECO} for distributed variable selection and parameter estimation. In {\em DECO}, variables are first partitioned and allocated to m distributed workers. The decorrelated subset data within each worker are then fitted via any algorithm designed for high-dimensional problems. We show that by incorporating the decorrelation step, DECO can achieve consistent variable selection and parameter estimation on each subset with (almost) no assumptions. In addition, the convergence rate is nearly minimax optimal for both sparse and weakly sparse models and does NOT depend on the partition number m. Extensive numerical experiments are provided to illustrate the performance of the new framework.

For datasets with both large sample sizes and high dimensionality, I propose a new "divided-and-conquer" framework {\em DEME} (DECO-message) by leveraging both the {\em DECO} and the {\em message} algorithm. The new framework first partitions the dataset in the sample space into row cubes using {\em message} and then partition the feature space of the cubes using {\em DECO}. This procedure is equivalent to partitioning the original data matrix into multiple small blocks, each with a feasible size that can be stored and fitted in a computer in parallel. The results are then synthezied via the {\em DECO} and {\em message} algorithm in a reverse order to produce the final output. The whole framework is extremely scalable.

Dynamic Programming Approaches for Estimating and Applying Large-scale Discrete Choice Models

People go through their life making all kinds of decisions, and some of these decisions affect their demand for transportation, for example, their choices of where to live and where to work, how and when to travel and which route to take. Transport related choices are typically time dependent and characterized by large number of alternatives that can be spatially correlated. This thesis deals with models that can be used to analyze and predict discrete choices in large-scale networks. The proposed models and methods are highly relevant for, but not limited to, transport applications. We model decisions as sequences of choices within the dynamic discrete choice framework, also known as parametric Markov decision processes. Such models are known to be difficult to estimate and to apply to make predictions because dynamic programming problems need to be solved in order to compute choice probabilities. In this thesis we show that it is possible to explore the network structure and the flexibility of dynamic programming so that the dynamic discrete choice modeling approach is not only useful to model time dependent choices, but also makes it easier to model large-scale static choices. The thesis consists of seven articles containing a number of models and methods for estimating, applying and testing large-scale discrete choice models. In the following we group the contributions under three themes: route choice modeling, large-scale multivariate extreme value (MEV) model estimation and nonlinear optimization algorithms. Five articles are related to route choice modeling. We propose different dynamic discrete choice models that allow paths to be correlated based on the MEV and mixed logit models. The resulting route choice models become expensive to estimate and we deal with this challenge by proposing innovative methods that allow to reduce the estimation cost. For example, we propose a decomposition method that not only opens up for possibility of mixing, but also speeds up the estimation for simple logit models, which has implications also for traffic simulation. Moreover, we compare the utility maximization and regret minimization decision rules, and we propose a misspecification test for logit-based route choice models. The second theme is related to the estimation of static discrete choice models with large choice sets. We establish that a class of MEV models can be reformulated as dynamic discrete choice models on the networks of correlation structures. These dynamic models can then be estimated quickly using dynamic programming techniques and an efficient nonlinear optimization algorithm. Finally, the third theme focuses on structured quasi-Newton techniques for estimating discrete choice models by maximum likelihood. We examine and adapt switching methods that can be easily integrated into usual optimization algorithms (line search and trust region) to accelerate the estimation process. The proposed dynamic discrete choice models and estimation methods can be used in various discrete choice applications. In the area of big data analytics, models that can deal with large choice sets and sequential choices are important. Our research can therefore be of interest in various demand analysis applications (predictive analytics) or can be integrated with optimization models (prescriptive analytics). Furthermore, our studies indicate the potential of dynamic programming techniques in this context, even for static models, which opens up a variety of future research directions.

Geochemistry of basalts from the Caribbean Large Igneous Province

Oceanic flood basalts are poorly understood, short-term expressions of highly increased heat flux and mass flow within the convecting mantle. The uniqueness of the Caribbean Large Igneous Province (CLIP, 92-74 Ma) with respect to other Cretaceous oceanic plateaus is its extensive sub-aerial exposures, providing an excellent basis to investigate the temporal and compositional relationships within a starting plume head. We present major element, trace element and initial Sr-Nd-Pb isotope composition of 40 extrusive rocks from the Caribbean Plateau, including onland sections in Costa Rica, Colombia and Curaçao as well as DSDP Sites in the Central Caribbean. Even though the lavas were erupted over an area of ~3*10**6 km**2, the majority have strikingly uniform incompatible element patterns (La/Yb=0.96+/-0.16, n=64 out of 79 samples, 2sigma) and initial Nd-Pb isotopic compositions (e.g. 143Nd/144Ndin=0.51291+/-3, epsilon-Nd i=7.3+/-0.6, 206Pb/204Pbin=18.86+/-0.12, n=54 out of 66, 2sigma). Lavas with endmember compositions have only been sampled at the DSDP Sites, Gorgona Island (Colombia) and the 65-60 Ma accreted Quepos and Osa igneous complexes (Costa Rica) of the subsequent hotspot track. Despite the relatively uniform composition of most lavas, linear correlations exist between isotope ratios and between isotope and highly incompatible trace element ratios. The Sr-Nd-Pb isotope and trace element signatures of the chemically enriched lavas are compatible with derivation from recycled oceanic crust, while the depleted lavas are derived from a highly residual source. This source could represent either oceanic lithospheric mantle left after ocean crust formation or gabbros with interlayered ultramafic cumulates of the lower oceanic crust. High 3He/4He in olivines of enriched picrites at Quepos are ~12 times higher than the atmospheric ratio suggesting that the enriched component may have once resided in the lower mantle. Evaluation of the Sm-Nd and U-Pb isotope systematics on isochron diagrams suggests that the age of separation of enriched and depleted components from the depleted MORB source mantle could have been <=500 Ma before CLIP formation and interpreted to reflect the recycling time of the CLIP source. Mantle plume heads may provide a mechanism for transporting large volumes of possibly young recycled oceanic lithosphere residing in the lower mantle back into the shallow MORB source mantle.

An Exploration of the challenges associated with software logging in large systems

Over the past few years, logging has evolved from from simple printf statements to more complex and widely used logging libraries. Today logging information is used to support various development activities such as fixing bugs, analyzing the results of load tests, monitoring performance and transferring knowledge. Recent research has examined how to improve logging practices by informing developers what to log and where to log. Furthermore, the strong dependence on logging has led to the development of logging libraries that have reduced the intricacies of logging, which has resulted in an abundance of log information. Two recent challenges have emerged as modern software systems start to treat logging as a core aspect of their software. In particular, 1) infrastructural challenges have emerged due to the plethora of logging libraries available today and 2) processing challenges have emerged due to the large number of log processing tools that ingest logs and produce useful information from them. In this thesis, we explore these two challenges. We first explore the infrastructural challenges that arise due to the plethora of logging libraries available today. As systems evolve, their logging infrastructure has to evolve (commonly this is done by migrating to new logging libraries). We explore logging library migrations within Apache Software Foundation (ASF) projects. We i find that close to 14% of the pro jects within the ASF migrate their logging libraries at least once. For processing challenges, we explore the different factors which can affect the likelihood of a logging statement changing in the future in four open source systems namely ActiveMQ, Camel, Cloudstack and Liferay. Such changes are likely to negatively impact the log processing tools that must be updated to accommodate such changes. We find that 20%-45% of the logging statements within the four systems are changed at least once. We construct random forest classifiers and Cox models to determine the likelihood of both just-introduced and long-lived logging statements changing in the future. We find that file ownership, developer experience, log density and SLOC are important factors in determining the stability of logging statements.

Genome-wide association studies in oesophageal adenocarcinoma and Barrett's oesophagus: a large-scale meta-analysis

Background: Esophageal adenocarcinoma (EA) is one of the fastest rising cancers in western countries. Barrett’s Esophagus (BE) is the premalignant precursor of EA. However, only a subset of BE patients develop EA, which complicates the clinical management in the absence of valid predictors. Genetic risk factors for BE and EA are incompletely understood. This study aimed to identify novel genetic risk factors for BE and EA.Methods: Within an international consortium of groups involved in the genetics of BE/EA, we performed the first meta-analysis of all genome-wide association studies (GWAS) available, involving 6,167 BE patients, 4,112 EA patients, and 17,159 representative controls, all of European ancestry, genotyped on Illumina high-density SNP-arrays, collected from four separate studies within North America, Europe, and Australia. Meta-analysis was conducted using the fixed-effects inverse variance-weighting approach. We used the standard genome-wide significant threshold of 5×10-8 for this study. We also conducted an association analysis following reweighting of loci using an approach that investigates annotation enrichment among the genome-wide significant loci. The entire GWAS-data set was also analyzed using bioinformatics approaches including functional annotation databases as well as gene-based and pathway-based methods in order to identify pathophysiologically relevant cellular pathways.Findings: We identified eight new associated risk loci for BE and EA, within or near the CFTR (rs17451754, P=4·8×10-10), MSRA (rs17749155, P=5·2×10-10), BLK (rs10108511, P=2·1×10-9), KHDRBS2 (rs62423175, P=3·0×10-9), TPPP/CEP72 (rs9918259, P=3·2×10-9), TMOD1 (rs7852462, P=1·5×10-8), SATB2 (rs139606545, P=2·0×10-8), and HTR3C/ABCC5 genes (rs9823696, P=1·6×10-8). A further novel risk locus at LPA (rs12207195, posteriori probability=0·925) was identified after re-weighting using significantly enriched annotations. This study thereby doubled the number of known risk loci. The strongest disease pathways identified (P<10-6) belong to muscle cell differentiation and to mesenchyme development/differentiation, which fit with current pathophysiological BE/EA concepts. To our knowledge, this study identified for the first time an EA-specific association (rs9823696, P=1·6×10-8) near HTR3C/ABCC5 which is independent of BE development (P=0·45).Interpretation: The identified disease loci and pathways reveal new insights into the etiology of BE and EA. Furthermore, the EA-specific association at HTR3C/ABCC5 may constitute a novel genetic marker for the prediction of transition from BE to EA. Mutations in CFTR, one of the new risk loci identified in this study, cause cystic fibrosis (CF), the most common recessive disorder in Europeans. Gastroesophageal reflux (GER) belongs to the phenotypic CF-spectrum and represents the main risk factor for BE/EA. Thus, the CFTR locus may trigger a common GER-mediated pathophysiology.

The large- and small-scale Ca IIK structure of the Milky Way from observations of Galactic and Magellanic sightlines

Aims. The large and small-scale (pc) structure of the Galactic interstellar medium can be investigated by utilising spectra of early-type stellar probes of known distances in the same region of the sky. This paper determines the variation in line strength of Ca ii at 3933.661 Å as a function of probe separation for a large sample of stars, including a number of sightlines in the Magellanic Clouds. 

Methods. FLAMES-GIRAFFE data taken with the Very Large Telescope towards early-type stars in 3 Galactic and 4 Magellanic open clusters in Ca ii are used to obtain the velocity, equivalent width, column density, and line width of interstellar Galactic calcium for a total of 657 stars, of which 443 are Magellanic Cloud sightlines. In each cluster there are between 43 and 111 stars observed. Additionally, FEROS and UVES Ca ii K and Na i D spectra of 21 Galactic and 154 Magellanic early-type stars are presented and combined with data from the literature to study the calcium column density - parallax relationship. 

Results. For the four Magellanic clusters studied with FLAMES, the strength of the Galactic interstellar Ca ii K equivalent width on transverse scales from ∼0.05-9 pc is found to vary by factors of ∼1.8-3.0, corresponding to column density variations of ∼0.3-0.5 dex in the optically-thin approximation. Using FLAMES, FEROS, and UVES archive spectra, the minimum and maximum reduced equivalent widths for Milky Way gas are found to lie in the range ∼35-125 mÅ and ∼30-160 mÅ for Ca ii K and Na i D, respectively. The range is consistent with a previously published simple model of the interstellar medium consisting of spherical cloudlets of filling factor ∼0.3, although other geometries are not ruled out. Finally, the derived functional form for parallax (π) and Ca ii column density (N_CaII) is found to be π(mas) = 1 / (2.39 × 10^-13 × N_CaII (cm^-2) + 0.11). Our derived parallax is ∼25 per cent lower than predicted by Megier et al. (2009, A&A, 507, 833) at a distance of ∼100 pc and ∼15 percent lower at a distance of ∼200 pc, reflecting inhomogeneity in the Ca ii distribution in the different sightlines studied.

Characterisation of Large Disturbance Rotor Angle and Voltage Stability in Interconnected Power Networks with Distributed Wind Generation

Wind generation in highly interconnected power networks creates local and centralised stability issues based on their proximity to conventional synchronous generators and load centres. This paper examines the large disturbance stability issues (i.e. rotor angle and voltage stability) in power networks with geographically distributed wind resources in the context of a number of dispatch scenarios based on profiles of historical wind generation for a real power network. Stability issues have been analysed using novel stability indices developed from dynamic characteristics of wind generation. The results of this study show that localised stability issues worsen when significant penetration of both conventional and wind generation is present due to their non-complementary characteristics. In contrast, network stability improves when either high penetration of wind and synchronous generation is present in the network. Therefore, network regions can be clustered into two distinct stability groups (i.e. superior stability and inferior stability regions). Network stability improves when a voltage control strategy is implemented at wind farms, however both stability clusters remain unchanged irrespective of change in the control strategy. Moreover, this study has shown that the enhanced fault ride-through (FRT) strategy for wind farms can improve both voltage and rotor angle stability locally, but only a marginal improvement is evident in neighbouring regions.

Energy efficiency optimization in hardware-constrained large-scale MIMO systems

Large-scale multiple-input multiple-output (MIMO) communication systems can bring substantial improvement in spectral efficiency and/or energy efficiency, due to the excessive degrees-of-freedom and huge array gain. However, large-scale MIMO is expected to deploy lower-cost radio frequency (RF) components, which are particularly prone to hardware impairments. Unfortunately, compensation schemes are not able to remove the impact of hardware impairments completely, such that a certain amount of residual impairments always exists. In this paper, we investigate the impact of residual transmit RF impairments (RTRI) on the spectral and energy efficiency of training-based point-to-point large-scale MIMO systems, and seek to determine the optimal training length and number of antennas which maximize the energy efficiency. We derive deterministic equivalents of the signal-to-noise-and-interference ratio (SINR) with zero-forcing (ZF) receivers, as well as the corresponding spectral and energy efficiency, which are shown to be accurate even for small number of antennas. Through an iterative sequential optimization, we find that the optimal training length of systems with RTRI can be smaller compared to ideal hardware systems in the moderate SNR regime, while larger in the high SNR regime. Moreover, it is observed that RTRI can significantly decrease the optimal number of transmit and receive antennas.

Second Quarter 2016: Slowdown for Large Hotels Continues; Small Hotels Have Now Slowed as Well

Our Standardized Unexpected Price (SUP) metric continues to show a decline in the price of large hotels, and now also the price of small hotels has eased—even though hotel transaction volume has increased. Although debt and equity financing for hotels remain relatively inexpensive, we are concerned that the total volatility of hotel returns is greater relative to the return volatility for other commercial real estate. If this trend continues, lenders will eventually start to tighten hotel lending standards. Our early warning indicators all continue to suggest that the downward trend in hotel prices should continue into the next quarter. This is report number 19 of the index series.