Interval and Point Estimators for the Location Parameter of the Three-Parameter Lognormal Distribution

The three-parameter lognormal distribution is the extension of the two-parameter lognormal distribution to meet the need of the biological, sociological, and other fields. Numerous research papers have been published for the parameter estimation problems for the lognormal distributions. The inclusion of the location parameter brings in some technical difficulties for the parameter estimation problems, especially for the interval estimation. This paper proposes a method for constructing exact confidence intervals and exact upper confidence limits for the location parameter of the three-parameter lognormal distribution. The point estimation problem is discussed as well. The performance of the point estimator is compared with the maximum likelihood estimator, which is widely used in practice. Simulation result shows that the proposed method is less biased in estimating the location parameter. The large sample size case is discussed in the paper.

Small sample confidence intervals for the mean of a positively skewed distribution

This thesis proposes some confidence intervals for the mean of a positively skewed distribution. The following confidence intervals are considered: Student-t, Johnson-t, median-t, mad-t, bootstrap-t, BCA, T1 , T3 and six new confidence intervals, the median bootstrap-t, mad bootstrap-t, median T1, mad T1 , median T3 and the mad T3. A simulation study has been conducted and average widths, coefficient of variation of widths, and coverage probabilities were recorded and compared across confidence intervals. To compare confidence intervals, the width and coverage probabilities were compared so that smaller widths indicated a better confidence interval when coverage probabilities were the same. Results showed that the median T1 and median T3 outperformed other confidence intervals in terms of coverage probability and the mad bootstrap-t, mad-t, and mad T3 outperformed others in terms of width. Some real life data are considered to illustrate the findings of the thesis.

Association between mean residual life (MRL) and failure rate functions for continuous and discrete lifetime distributions

The purpose of this study was to correct some mistakes in the literature and derive a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. It was also desired to find the conditions under which the discrete failure rate function has an upside-down bathtub shape if corresponding MRL function has a bathtub shape. The study showed that if discrete MRL has a bathtub shape, then under some conditions the corresponding failure rate function has an upside-down bathtub shape. Also the study corrected some mistakes in proofs of Tang, Lu and Chew (1999) and established a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. Similarly, some mistakes in Gupta and Gupta (2000) are corrected, with the ensuing results being expanded and proved thoroughly to establish the relationship between the crossing points of the failure rate and associated MRL functions. The new results derived in this study will be useful to model various lifetime data that occur in environmental studies, medical research, electronics engineering, and in many other areas of science and technology.

Diatom abundance in surface sediments of the Southern Ocean

Based on the quantitative analysis of diatom assemblages preserved in 274 surface sediment samples recovered in the Pacific, Atlantic and western Indian sectors of the Southern Ocean we have defined a new reference database for quantitative estimation of late-middle Pleistocene Antarctic sea ice fields using the transfer function technique. The Detrended Canonical Analysis (DCA) of the diatom data set points to a unimodal distribution of the diatom assemblages. Canonical Correspondence Analysis (CCA) indicates that winter sea ice (WSI) but also summer sea surface temperature (SSST) represent the most prominent environmental variables that control the spatial species distribution. To test the applicability of transfer functions for sea ice reconstruction in terms of concentration and occurrence probability we applied four different methods, the Imbrie and Kipp Method (IKM), the Modern Analog Technique (MAT), Weighted Averaging (WA), and Weighted Averaging Partial Least Squares (WAPLS), using logarithm-transformed diatom data and satellite-derived (1981-2010) sea ice data as a reference. The best performance for IKM results was obtained using a subset of 172 samples with 28 diatom taxa/taxa groups, quadratic regression and a three-factor model (IKM-D172/28/3q) resulting in root mean square errors of prediction (RMSEP) of 7.27% and 11.4% for WSI and summer sea ice (SSI) concentration, respectively. MAT estimates were calculated with different numbers of analogs (4, 6) using a 274-sample/28-taxa reference data set (MAT-D274/28/4an, -6an) resulting in RMSEP's ranging from 5.52% (4an) to 5.91% (6an) for WSI as well as 8.93% (4an) to 9.05% (6an) for SSI. WA and WAPLS performed less well with the D274 data set, compared to MAT, achieving WSI concentration RMSEP's of 9.91% with WA and 11.29% with WAPLS, recommending the use of IKM and MAT. The application of IKM and MAT to surface sediment data revealed strong relations to the satellite-derived winter and summer sea ice field. Sea ice reconstructions performed on an Atlantic- and a Pacific Southern Ocean sediment core, both documenting sea ice variability over the past 150,000 years (MIS 1 - MIS 6), resulted in similar glacial/interglacial trends of IKM and MAT-based sea-ice estimates. On the average, however, IKM estimates display smaller WSI and slightly higher SSI concentration and probability at lower variability in comparison with MAT. This pattern is a result of different estimation techniques with integration of WSI and SSI signals in one single factor assemblage by applying IKM and selecting specific single samples, thus keeping close to the original diatom database and included variability, by MAT. In contrast to the estimation of WSI, reconstructions of past SSI variability remains weaker. Combined with diatom-based estimates, the abundance and flux pattern of biogenic opal represents an additional indication for the WSI and SSI extent.

Data to Decision in a Dynamic Ocean: Robust Species Distribution Models and Spatial Decision Frameworks

Human use of the oceans is increasingly in conflict with conservation of endangered species. Methods for managing the spatial and temporal placement of industries such as military, fishing, transportation and offshore energy, have historically been post hoc; i.e. the time and place of human activity is often already determined before assessment of environmental impacts. In this dissertation, I build robust species distribution models in two case study areas, US Atlantic (Best et al. 2012) and British Columbia (Best et al. 2015), predicting presence and abundance respectively, from scientific surveys. These models are then applied to novel decision frameworks for preemptively suggesting optimal placement of human activities in space and time to minimize ecological impacts: siting for offshore wind energy development, and routing ships to minimize risk of striking whales. Both decision frameworks relate the tradeoff between conservation risk and industry profit with synchronized variable and map views as online spatial decision support systems.

For siting offshore wind energy development (OWED) in the U.S. Atlantic (chapter 4), bird density maps are combined across species with weights of OWED sensitivity to collision and displacement and 10 km2 sites are compared against OWED profitability based on average annual wind speed at 90m hub heights and distance to transmission grid. A spatial decision support system enables toggling between the map and tradeoff plot views by site. A selected site can be inspected for sensitivity to a cetaceans throughout the year, so as to capture months of the year which minimize episodic impacts of pre-operational activities such as seismic airgun surveying and pile driving.

Routing ships to avoid whale strikes (chapter 5) can be similarly viewed as a tradeoff, but is a different problem spatially. A cumulative cost surface is generated from density surface maps and conservation status of cetaceans, before applying as a resistance surface to calculate least-cost routes between start and end locations, i.e. ports and entrance locations to study areas. Varying a multiplier to the cost surface enables calculation of multiple routes with different costs to conservation of cetaceans versus cost to transportation industry, measured as distance. Similar to the siting chapter, a spatial decisions support system enables toggling between the map and tradeoff plot view of proposed routes. The user can also input arbitrary start and end locations to calculate the tradeoff on the fly.

Essential to the input of these decision frameworks are distributions of the species. The two preceding chapters comprise species distribution models from two case study areas, U.S. Atlantic (chapter 2) and British Columbia (chapter 3), predicting presence and density, respectively. Although density is preferred to estimate potential biological removal, per Marine Mammal Protection Act requirements in the U.S., all the necessary parameters, especially distance and angle of observation, are less readily available across publicly mined datasets.

In the case of predicting cetacean presence in the U.S. Atlantic (chapter 2), I extracted datasets from the online OBIS-SEAMAP geo-database, and integrated scientific surveys conducted by ship (n=36) and aircraft (n=16), weighting a Generalized Additive Model by minutes surveyed within space-time grid cells to harmonize effort between the two survey platforms. For each of 16 cetacean species guilds, I predicted the probability of occurrence from static environmental variables (water depth, distance to shore, distance to continental shelf break) and time-varying conditions (monthly sea-surface temperature). To generate maps of presence vs. absence, Receiver Operator Characteristic (ROC) curves were used to define the optimal threshold that minimizes false positive and false negative error rates. I integrated model outputs, including tables (species in guilds, input surveys) and plots (fit of environmental variables, ROC curve), into an online spatial decision support system, allowing for easy navigation of models by taxon, region, season, and data provider.

For predicting cetacean density within the inner waters of British Columbia (chapter 3), I calculated density from systematic, line-transect marine mammal surveys over multiple years and seasons (summer 2004, 2005, 2008, and spring/autumn 2007) conducted by Raincoast Conservation Foundation. Abundance estimates were calculated using two different methods: Conventional Distance Sampling (CDS) and Density Surface Modelling (DSM). CDS generates a single density estimate for each stratum, whereas DSM explicitly models spatial variation and offers potential for greater precision by incorporating environmental predictors. Although DSM yields a more relevant product for the purposes of marine spatial planning, CDS has proven to be useful in cases where there are fewer observations available for seasonal and inter-annual comparison, particularly for the scarcely observed elephant seal. Abundance estimates are provided on a stratum-specific basis. Steller sea lions and harbour seals are further differentiated by ‘hauled out’ and ‘in water’. This analysis updates previous estimates (Williams & Thomas 2007) by including additional years of effort, providing greater spatial precision with the DSM method over CDS, novel reporting for spring and autumn seasons (rather than summer alone), and providing new abundance estimates for Steller sea lion and northern elephant seal. In addition to providing a baseline of marine mammal abundance and distribution, against which future changes can be compared, this information offers the opportunity to assess the risks posed to marine mammals by existing and emerging threats, such as fisheries bycatch, ship strikes, and increased oil spill and ocean noise issues associated with increases of container ship and oil tanker traffic in British Columbia’s continental shelf waters.

Starting with marine animal observations at specific coordinates and times, I combine these data with environmental data, often satellite derived, to produce seascape predictions generalizable in space and time. These habitat-based models enable prediction of encounter rates and, in the case of density surface models, abundance that can then be applied to management scenarios. Specific human activities, OWED and shipping, are then compared within a tradeoff decision support framework, enabling interchangeable map and tradeoff plot views. These products make complex processes transparent for gaming conservation, industry and stakeholders towards optimal marine spatial management, fundamental to the tenets of marine spatial planning, ecosystem-based management and dynamic ocean management.

New Bivariate Lifetime Distributions Based on Bath-Tub Shaped Failure Rate

A class of lifetime distributions which has received considerable attention in modelling and analysis of lifetime data is the class of lifetime distributions with bath-tub shaped failure rate functions because of their extensive applications. The purpose of this thesis was to introduce a new class of bivariate lifetime distributions with bath-tub shaped failure rates (BTFRFs). In this research, first we reviewed univariate lifetime distributions with bath-tub shaped failure rates, and several multivariate extensions of a univariate failure rate function. Then we introduced a new class of bivariate distributions with bath-tub shaped failure rates (hazard gradients). Specifically, the new class of bivariate lifetime distributions were developed using the method of Morgenstern’s method of defining bivariate class of distributions with given marginals. The computer simulations and numerical computations were used to investigate the properties of these distributions.

Winter sea surface temperature reconstruction from planktic foraminiferal transfer functions in the northeastern Arabian Sea over the last two millennia

The Indian monsoon system is an important climate feature of the northern Indian Ocean. Small variations of the wind and precipitation patterns have fundamental influence on the societal, agricultural, and economic development of India and its neighboring countries. To understand current trends, sensitivity to forcing, or natural variation, records beyond the instrumental period are needed. However, high-resolution archives of past winter monsoon variability are scarce. One potential archive of such records are marine sediments deposited on the continental slope in the NE Arabian Sea, an area where present-day conditions are dominated by the winter monsoon. In this region, winter monsoon conditions lead to distinctive changes in surface water properties, affecting marine plankton communities that are deposited in the sediment. Using planktic foraminifera as a sensitive and well-preserved plankton group, we first characterize the response of their species distribution on environmental gradients from a dataset of surface sediment samples in the tropical and sub-tropical Indian Ocean. Transfer functions for quantitative paleoenvironmental reconstructions were applied to a decadal-scale record of assemblage counts from the Pakistan Margin spanning the last 2000?years. The reconstructed temperature record reveals an intensification of winter monsoon intensity near the year 100 CE. Prior to this transition, winter temperatures were >1.5°C warmer than today. Conditions similar to the present seem to have established after 450 CE, interrupted by a singular event near 950 CE with warmer temperatures and accordingly weak winter monsoon. Frequency analysis revealed significant 75-, 40-, and 37-year cycles, which are known from decadal- to centennial-scale resolution records of Indian summer monsoon variability and interpreted as solar irradiance forcing. Our first independent record of Indian winter monsoon activity confirms that winter and summer monsoons were modulated on the same frequency bands and thus indicates that both monsoon systems are likely controlled by the same driving force.

On The Dirichlet Distribution

The Dirichlet distribution is a multivariate generalization of the Beta distribution. It is an important multivariate continuous distribution in probability and statistics. In this report, we review the Dirichlet distribution and study its properties, including statistical and information-theoretic quantities involving this distribution. Also, relationships between the Dirichlet distribution and other distributions are discussed. There are some different ways to think about generating random variables with a Dirichlet distribution. The stick-breaking approach and the Pólya urn method are discussed. In Bayesian statistics, the Dirichlet distribution and the generalized Dirichlet distribution can both be a conjugate prior for the Multinomial distribution. The Dirichlet distribution has many applications in different fields. We focus on the unsupervised learning of a finite mixture model based on the Dirichlet distribution. The Initialization Algorithm and Dirichlet Mixture Estimation Algorithm are both reviewed for estimating the parameters of a Dirichlet mixture. Three experimental results are shown for the estimation of artificial histograms, summarization of image databases and human skin detection.

The VLT-FLAMES tarantula survey:X. Evidence for a bimodal distribution of rotational velocities for the single early B-type stars

Aims. Projected rotational velocities (ve sin i) have been estimated for 334 targets in the VLT-FLAMES Tarantula Survey that do not manifest significant radial velocity variations and are not supergiants. They have spectral types from approximately O9.5 to B3. The estimates have been analysed to infer the underlying rotational velocity distribution, which is critical for understanding the evolution of massive stars. Methods. Projected rotational velocities were deduced from the Fourier transforms of spectral lines, with upper limits also being obtained from profile fitting. For the narrower lined stars, metal and non-diffuse helium lines were adopted, and for the broader lined stars, both non-diffuse and diffuse helium lines; the estimates obtained using the different sets of lines are in good agreement. The uncertainty in the mean estimates is typically 4% for most targets. The iterative deconvolution procedure of Lucy has been used to deduce the probability density distribution of the rotational velocities. Results. Projected rotational velocities range up to approximately 450 kms-1 and show a bi-modal structure. This is also present in the inferred rotational velocity distribution with 25% of the sample having 0 <ve <100 km s^-1 and the high velocity component having v_e ∼ 250 km s^-1. There is no evidence from the spatial and radial velocity distributions of the two components that they represent either field and cluster populations or different episodes of star formation. Be-type stars have also been identified. Conclusions. The bi-modal rotational velocity distribution in our sample resembles that found for late-B and early-A type stars.While magnetic braking appears to be a possible mechanism for producing the low-velocity component, we can not rule out alternative explanations. © ESO 2013.

Influência dos intermediários de distribuição de produtos turísticos no processo de decisão do meio de hospedagem pelo consumidor

This study examines the complex hotel buyer decision process in front of the tourism distribution channels. Its objective is to describe the influence level of the tourism marketing intermediaries, mainly the travel agents and tour operators, over the hotel decision process by the buyer-tourist. The data collection process was done trough a survey with three hundred brazilian tourists hosted in nineteen hotels of Natal, capital of Rio Grande do Norte, Brazil. The data analysis was done using some multivariate statistic techniques as correlation analysis, multiple regression analysis, factor analysis and multiple discriminant analysis. The research characterizes the hotel services consumers profile and his trip, and identifying the distribution channels used by them. Furthermore, the research verifies the intermediaries influence exercised over hotel buyer decision process, looking for identify causality relations between the influence level and the buyer profile. Verifies that information about hotels available on internet reduces the probability that this influence can be practiced; however it was possible identifying those consumers considers this information complementary and non-substitutes than the information from intermediaries. The characteristics of the data do not allow indentifying the factors that constraint the intermediaries influence neither identifying discriminant functions of the specific distribution channel choice by consumers. The study concludes that consumers don t agree in have been influenced by intermediaries or don t know if they have, still considering important to consult them and internet doesn t substitute their function as information source

Asymptotic and structural properties of special cases of the Wright function arising in probability theory

This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish new asymptotic properties of the particular Wright function 1Ψ1(ρ, k; ρ, 0; x) = X∞ n=0 Γ(k + ρn) Γ(ρn) x n n! (|x| < ∞) when the parameter ρ ∈ (−1, 0)∪(0, ∞) and the argument x is real. In the probability theory applications, which are focused on studies of the Poisson-Tweedie mixtures, the parameter k is a non-negative integer. Several representations involving well-known special functions are given for certain particular values of ρ. The asymptotics of 1Ψ1(ρ, k; ρ, 0; x) are obtained under numerous assumptions on the behavior of the arguments k and x when the parameter ρ is both positive and negative. We also provide some integral representations and structural properties involving the ‘reduced’ Wright function 0Ψ1(−−; ρ, 0; x) with ρ ∈ (−1, 0) ∪ (0, ∞), which might be useful for the derivation of new properties of members of the power-variance family of distributions. Some of these imply a reflection principle that connects the functions 0Ψ1(−−;±ρ, 0; ·) and certain Bessel functions. Several asymptotic relationships for both particular cases of this function are also given. A few of these follow under additional constraints from probability theory results which, although previously available, were unknown to analysts.

An Estimation of Distribution Algorithm for Nurse Scheduling

Schedules can be built in a similar way to a human scheduler by using a set of rules that involve domain knowledge. This paper presents an Estimation of Distribution Algorithm (EDA) for the nurse scheduling problem, which involves choosing a suitable scheduling rule from a set for the assignment of each nurse. Unlike previous work that used Genetic Algorithms (GAs) to implement implicit learning, the learning in the proposed algorithm is explicit, i.e. we identify and mix building blocks directly. The EDA is applied to implement such explicit learning by building a Bayesian network of the joint distribution of solutions. The conditional probability of each variable in the network is computed according to an initial set of promising solutions. Subsequently, each new instance for each variable is generated by using the corresponding conditional probabilities, until all variables have been generated, i.e. in our case, a new rule string has been obtained. Another set of rule strings will be generated in this way, some of which will replace previous strings based on fitness selection. If stopping conditions are not met, the conditional probabilities for all nodes in the Bayesian network are updated again using the current set of promising rule strings. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed approach might be suitable for other scheduling problems.

Ecological drivers of a vector borne pathogen: distribution and abundance of Borrelia burgdorferi sensu lato and its vector Ixodes ricinus in Scotland

Vector-borne disease emergence in recent decades has been associated with different environmental drivers including changes in habitat, hosts and climate. Lyme borreliosis is among the most important vector-borne diseases in the Northern hemisphere and is an emerging disease in Scotland. Transmitted by Ixodid tick vectors between large numbers of wild vertebrate host species, Lyme borreliosis is caused by bacteria from the Borrelia burgdorferi sensu lato species group. Ecological studies can inform how environmental factors such as host abundance and community composition, habitat and landscape heterogeneity contribute to spatial and temporal variation in risk from B. burgdorferi s.l. In this thesis a range of approaches were used to investigate the effects of vertebrate host communities and individual host species as drivers of B. burgdorferi s.l. dynamics and its tick vector Ixodes ricinus. Host species differ in reservoir competence for B. burgdorferi s.l. and as hosts for ticks. Deer are incompetent transmission hosts for B. burgdorferi s.l. but are significant hosts of all life-stages of I. ricinus. Rodents and birds are important transmission hosts of B. burgdorferi s.l. and common hosts of immature life-stages of I. ricinus. In this thesis, surveys of woodland sites revealed variable effects of deer density on B. burgdorferi prevalence, from no effect (Chapter 2) to a possible ‘dilution’ effect resulting in lower prevalence at higher deer densities (Chapter 3). An invasive species in Scotland, the grey squirrel (Sciurus carolinensis), was found to host diverse genotypes of B. burgdorferi s.l. and may act as a spill-over host for strains maintained by native host species (Chapter 4). Habitat fragmentation may alter the dynamics of B. burgdorferi s.l. via effects on the host community and host movements. In this thesis, there was lack of persistence of the rodent associated genospecies of B. burgdorferi s.l. within a naturally fragmented landscape (Chapter 3). Rodent host biology, particularly population cycles and dispersal ability are likely to affect pathogen persistence and recolonization in fragmented habitats. Heterogeneity in disease dynamics can occur spatially and temporally due to differences in the host community, habitat and climatic factors. Higher numbers of I. ricinus nymphs, and a higher probability of detecting a nymph infected with B. burgdorferi s.l., were found in areas with warmer climates estimated by growing degree days (Chapter 2). The ground vegetation type associated with the highest number of I. ricinus nymphs varied between studies in this thesis (Chapter 2 & 3) and does not appear to be a reliable predictor across large areas. B. burgdorferi s.l. prevalence and genospecies composition was highly variable for the same sites sampled in subsequent years (Chapter 2). This suggests that dynamic variables such as reservoir host densities and deer should be measured as well as more static habitat and climatic factors to understand the drivers of B. burgdorferi s.l. infection in ticks. Heterogeneity in parasite loads amongst hosts is a common finding which has implications for disease ecology and management. Using a 17-year data set for tick infestations in a wild bird community in Scotland, different effects of age and sex on tick burdens were found among four species of passerine bird (Chapter 5). There were also different rates of decline in tick burdens among bird species in response to a long term decrease in questing tick pressure over the study. Species specific patterns may be driven by differences in behaviour and immunity and highlight the importance of comparative approaches. Combining whole genome sequencing (WGS) and population genetics approaches offers a novel approach to identify ecological drivers of pathogen populations. An initial analysis of WGS from B. burgdorferi s.s. isolates sampled 16 years apart suggests that there is a signal of measurable evolution (Chapter 6). This suggests demographic analyses may be applied to understand ecological and evolutionary processes of these bacteria. This work shows how host communities, habitat and climatic factors can affect the local transmission dynamics of B. burgdorferi s.l. and the potential risk of infection to humans. Spatial and temporal heterogeneity in pathogen dynamics poses challenges for the prediction of risk. New tools such as WGS of the pathogen (Chapter 6) and blood meal analysis techniques will add power to future studies on the ecology and evolution of B. burgdorferi s.l.

STATISTICAL METHODS FOR ADVANCED ECONOMETRIC MODELS WITH APPLICATIONS TO VEHICLE HOLDING AND SPEED QUANTILES DISTRIBUTION

This dissertation proposes statistical methods to formulate, estimate and apply complex transportation models. Two main problems are part of the analyses conducted and presented in this dissertation. The first method solves an econometric problem and is concerned with the joint estimation of models that contain both discrete and continuous decision variables. The use of ordered models along with a regression is proposed and their effectiveness is evaluated with respect to unordered models. Procedure to calculate and optimize the log-likelihood functions of both discrete-continuous approaches are derived, and difficulties associated with the estimation of unordered models explained. Numerical approximation methods based on the Genz algortithm are implemented in order to solve the multidimensional integral associated with the unordered modeling structure. The problems deriving from the lack of smoothness of the probit model around the maximum of the log-likelihood function, which makes the optimization and the calculation of standard deviations very difficult, are carefully analyzed. A methodology to perform out-of-sample validation in the context of a joint model is proposed. Comprehensive numerical experiments have been conducted on both simulated and real data. In particular, the discrete-continuous models are estimated and applied to vehicle ownership and use models on data extracted from the 2009 National Household Travel Survey. The second part of this work offers a comprehensive statistical analysis of free-flow speed distribution; the method is applied to data collected on a sample of roads in Italy. A linear mixed model that includes speed quantiles in its predictors is estimated. Results show that there is no road effect in the analysis of free-flow speeds, which is particularly important for model transferability. A very general framework to predict random effects with few observations and incomplete access to model covariates is formulated and applied to predict the distribution of free-flow speed quantiles. The speed distribution of most road sections is successfully predicted; jack-knife estimates are calculated and used to explain why some sections are poorly predicted. Eventually, this work contributes to the literature in transportation modeling by proposing econometric model formulations for discrete-continuous variables, more efficient methods for the calculation of multivariate normal probabilities, and random effects models for free-flow speed estimation that takes into account the survey design. All methods are rigorously validated on both real and simulated data.