Mathematical Statistics and Data Analysis John Rice download pdf

So Stat will start faster than Stat due to the Data 8 prerequisite , avoid approximations that are unnecessary when SciPy is at hand, and replace some of the routine calculus by symbolic math done in SymPy. This will create time for a unit on the convergence and reversibility of Markov Chains as well as added focus on conditioning and Bayes methods. Data 8 , there is considerable demand for follow-on courses that build on the skills acquired in that class.

Stat is a probability course for Data 8 graduates who have also had a year of calculus and wish to go deeper into data science. Student Learning Outcomes: Understand the difference between math and simulation, and appreciate the power of both Use a variety of approaches to problem solving Work with probability concepts algebraically, numerically, and graphically.

Further topics such as: continuous time Markov chains, queueing theory, point processes, branching processes, renewal theory, stationary processes, Gaussian processes.

Terms offered: Fall , Spring , Fall A coordinated treatment of linear and generalized linear models and their application. Linear regression, analysis of variance and covariance, random effects, design and analysis of experiments, quality improvement, log-linear models for discrete multivariate data, model selection, robustness, graphical techniques, productive use of computers, in-depth case studies.

STAT recommended. Terms offered: Spring , Spring , Spring Theory and practice of sampling from finite populations. Simple random, stratified, cluster, and double sampling. Sampling with unequal probabilities. Properties of various estimators including ratio, regression, and difference estimators. Error estimation for complex samples. Terms offered: Spring , Fall , Spring An introduction to time series analysis in the time domain and spectral domain.

Topics will include: estimation of trends and seasonal effects, autoregressive moving average models, forecasting, indicators, harmonic analysis, spectra. Terms offered: Spring , Fall , Spring Theory and practice of statistical prediction.

Contemporary methods as extensions of classical methods. Topics: optimal prediction rules, the curse of dimensionality, empirical risk, linear regression and classification, basis expansions, regularization, splines, the bootstrap, model selection, classification and regression trees, boosting, support vector machines.

Computational efficiency versus predictive performance. Emphasis on experience with real data and assessing statistical assumptions. Prerequisites: Mathematics 53 or equivalent; Mathematics 54, Electrical Engineering 16A, Statistics 89A, Mathematics or equivalent linear algebra; Statistics or equivalent; experience with some programming language.

Recommended prerequisite: Mathematics 55 or equivalent exposure to counting arguments. Terms offered: Spring , Summer 8 Week Session, Spring General theory of zero-sum, two-person games, including games in extensive form and continuous games, and illustrated by detailed study of examples. Terms offered: Fall , Fall , Fall This course will focus on approaches to causal inference using the potential outcomes framework.

It will also use causal diagrams at an intuitive level. The main topics are classical randomized experiments, observational studies, instrumental variables, principal stratification and mediation analysis. Applications are drawn from a variety of fields including political science, economics, sociology, public health, and medicine. This course is a mix of statistical theory and data analysis. Students will be exposed to statistical questions that are relevant to decision and policy making.

Terms offered: Spring , Fall , Spring Substantial student participation required. The topics to be covered each semester that the course may be offered will be announced by the middle of the preceding semester; see departmental bulletins. Recent topics include: Bayesian statistics, statistics and finance, random matrix theory, high-dimensional statistics. Prerequisites: Mathematics , Statistics , Knowledge of scientific computing environment R or Matlab often required.

Prerequisites might vary with instructor and topics. Terms offered: Spring , Spring , Spring An introduction to the design and analysis of experiments. This course covers planning, conducting, and analyzing statistically designed experiments with an emphasis on hands-on experience. Standard designs studied include factorial designs, block designs, latin square designs, and repeated measures designs.

Other topics covered include the principles of design, randomization, ANOVA, response surface methodoloy, and computer experiments.

Prerequisites: Statistics and or consent of instructor. Statistics may be taken concurrently. Statistics is recommended. Terms offered: Spring , Spring , Fall A project-based introduction to statistical data analysis.

Through case studies, computer laboratories, and a term project, students will learn practical techniques and tools for producing statistically sound and appropriate, reproducible, and verifiable computational answers to scientific questions.

Course emphasizes version control, testing, process automation, code review, and collaborative programming. Prerequisites: Statistics , Statistics , and Statistics or equivalent. Summer: 6 weeks - hours of independent study per week 8 weeks - hours of independent study per week.

Terms offered: Fall , Fall , Spring Supervised experience relevant to specific aspects of statistics in on-campus or off-campus settings. Credit Restrictions: Enrollment is restricted; see the Introduction to Courses and Curricula section of this catalog.

Summer: 6 weeks - hours of fieldwork per week 8 weeks - hours of fieldwork per week 10 weeks - hours of fieldwork per week. Terms offered: Fall , Spring , Fall Special tutorial or seminar on selected topics. Directed Study for Undergraduates: Read Less [-]. Summer: 6 weeks - hours of independent study per week 8 weeks - hours of independent study per week 10 weeks - hours of independent study per week. Peter L. Bartlett, Professor.

Statistics, machine learning, statistical learning theory, adaptive control. Research Profile. Andrew Bray, Teaching Professor. Phase transitions in computer science, structural and dynamical properties of networks, graphons, machine learning, ethical decision making, climate change.

Peng Ding, Associate Professor. Statistical causal inference, missing data, Bayesian statistics, applied statistics. Sandrine Dudoit, Professor. Genomics, classification, statistical computing, biostatistics, cross-validation, density estimation, genetic mapping, high-throughput sequencing, loss-based estimation, microarray, model selection, multiple hypothesis testing, prediction, RNA-Seq.

Noureddine El Karoui, Professor. Applied statistics, theory and applications of random matrices, large dimensional covariance estimation and properties of covariance matrices, connections with mathematical finance.

Steven N. Evans, Professor. Genetics, random matrices, superprocesses and other measure-valued processes, probability on algebraic structures -particularly local fields, applications of stochastic processes to biodemography, mathematical finance, phylogenetics and historical linguistics.

Avi Feller, Assistant Professor. Applied statistics, theoretical statistics, Bayesian statistics, machine learning, statistics in social sciences. Will Fithian, Assistant Professor. Theoretical and Applied Statistics. Shirshendu Ganguly, Assistant Professor. Probability theory, statistical mechanics.

Adityanand Guntuboyina, Associate Professor. Nonparametric and high-dimensional statistics, shape constrained statistical estimation, empirical processes, statistical information theory. Alan Hammond, Professor. Statistical mechanics. Haiyan Huang, Professor. Jiantao Jiao, Assistant Professor. Artificial intelligence, control and intelligent systems and robotics, communications and networking.

Michael I. Jordan, Professor. Computer science, artificial intelligence, bioinformatics, statistics, machine learning, electrical engineering, applied statistics, optimization.

Jon Mcauliffe, Adjunct Professor. Bioinformatics, machine learning, nonparametrics, convex optimization, statistical computing, prediction, supervised learning. Song Mei, Assistant Professor. Data science, statistics, machine learning. Rasmus Nielsen, Professor. Statistical and computational aspects of evolutionary theory and genetics. Statistics, empirical process, high-dimensional modeling, technology in education. Fernando Perez, Associate Professor.

High-level languages, interactive and literate computing, and reproducible research. Sam Pimentel, Assistant Professor. James W. Pitman, Professor. Fragmentation, statistics, mathematics, Brownian motion, distribution theory, path transformations, stochastic processes, local time, excursions, random trees, random partitions, processes of coalescence.

Elizabeth Purdom, Associate Professor. Computational biology, bioinformatics, statistics, data analysis, sequencing, cancer genomics. Jasjeet S. Sekhon, Professor. Program evaluation, statistical and computational methods, causal inference, elections, public opinion, American politics. Alistair Sinclair, Professor. Algorithms, applied probability, statistics, random walks, Markov chains, computational applications of randomness, Markov chain Monte Carlo, statistical physics, combinatorial optimization.

Yun Song, Professor. Computational biology, population genomics, applied probability and statistics. Philip B. Stark, Professor. Astrophysics, law, statistics, litigation, causal inference, inverse problems, geophysics, elections, uncertainty quantification, educational technology.

Jacob Steinhardt, Assistant Professor. Artificial intelligence, machine learning. Bernd Sturmfels, Professor. Mathematics, combinatorics, computational algebraic geometry. Mark J. Student Solution Manual for Foundation K. Solution Manual to Hydraulics in Civil and A. Cooper []. Solution Manual to Introduction to Robert V. Hogg, Joseph W. Craig []. Classical Mechanics solution manual Goldstein Herbert [].

Ingle, Stephen M. Kogon []. Solution Manual Sonntag []. Instructors Solution Manual to Artificial B. Yegnanarayana Neural Networks []. Solution manual for machine design Norton Thomas A. Cook 3e [3rd ed. West Theory, 2nd Ed. Numerical Solution of Partial Differential K.

Morton, D. Solution manual to Fundamentals of Thermal- Yunus A. Fluid Sciences Turner, John M. Cimbala []. Discrete and Combinatorial Mathematics ,5e Ralph P. Grimaldi Instructor's Solution Manual []. Principles of Communication: Systems, R. Ziemer, W. Lathi Linear Systems , []. Introduction to Graph Theory 2nd Douglas B. West Edition With Solution Manual [2 ed. Proakis Manolakis Proakis and D.

Manolakis - Instructor Solution Manual[Fourth ed. Schilling, Sandra L. West - Solution Manual []. Wakerly Edition Solution Manual [3rd ed. Introduction 8th Edition Solution Manual [8th ed. Calculations in Chemical Engineering 7th Riggs Edition [7 ed. Mechanics, 5th Edition [5 ed. Okiishi , []. Probability, Statistics, and Random Processes A. Edition [11th ed.

Giordano , []. Mechanics Berkeley Physics Course, Vol. LeVine solution manual []. Signals and Systems: Analysis of Signals M.

Roberts Through Linear Systems - Solution manual [1 ed. Solution manual of modern quantum J. Sakurai mechanics []. The and Microprocessors: Walter A. Abstract Algebra. Student's Solution Manual I.

Herstein []. Complex Variables with Applications - The A. Brown []. Principles of Foundation Engineering. Solution Braja M. Das Manual [6 ed. Wicks, Gregory L. Transfer - Solution Manual [5 ed. Essential Mathematical Methods for the Riley K. Physical Sciences: Student Solution Manual [draft ed. The chemistry maths book, with Solution Steiner E. Foundation Mathematics for the Physical Riley K. Sciences: Student Solution Manual [].

An introduction to modern astrophysics: Carroll B. Solution manual [2ed. Classical mechanics: Solution manual Gregory R. Whiting, Joseph A. Solution manual [3 ed. Electric Circuits. Solution Manual [7 ed. Introduction to graph theory 2ed. Instructor's Solution Manual for Adel S. Sedra, Kenneth C. Introduction to Probability and Statistics - B. Without examining the impact of priors through a sensitivity analysis and prior predictive checking, the researcher would not be aware of how sensitive results are to changes in the priors.

To enable reproducibility and allow others to run Bayesian statistics on the same data with different parameters, priors, models or likelihood functions for sensitivity analyses 49 , it is important that the underlying data and code used are properly documented and shared following the FAIR principles , : findability, accessibility, interoperability and reusability. Preferably, data and code should be shared in a trusted repository Registry of Research Data Repositories with their own persistent identifier such as a DOI , and tagged with metadata describing the data set or codebase.

This also allows the data set and the code to be recognized as separate research outputs and allows others to cite them accordingly As data and code require different licence options and metadata, data are generally best stored in dedicated data repositories, which can be general or discipline-specific Some journals, such as Scientific Data , have their own list of recommended data repositories.

To make depositing data and code easier for researchers, two repositories Zenodo and Dryad are exploring collaboration to allow the deposition of code and data through one interface, with data stored in Dryad and code stored in Zenodo Many scientific journals adhere to transparency and openness promotion guidelines , which specify requirements for code and data sharing.

Verification and reproducibility require access to both the data and the code used in Bayesian modelling, ideally replicating the original environment in which the code was run, with all dependencies documented either in a dependency file accompanying the code or by creating a static container image that provides a virtual environment in which to run the code Open-source software should be used as much as possible, as open sources reduce the monetary and accessibility threshold to replicating scientific results.

Moreover, it can be argued that closed-source software keeps part of the academic process hidden, including from the researchers who use the software themselves. However, open-source software is only truly accessible with proper documentation, which includes listing dependencies and configuration instructions in Readme files, commenting on code to explain functionality and including a comprehensive reference manual when releasing packages.

Ensure the prior distributions and the model or likelihood are well understood and described in detail in the text. Prior-predictive checking can help identify any prior—data conflict. Assess each parameter for convergence, using multiple convergence diagnostics if possible. Ensure that there were sufficient chain iterations to construct a meaningful posterior distribution. The posterior distribution should consist of enough samples to visually examine the shape, scale and central tendency of the distribution.

Examine the effective sample size for all parameters, checking for strong degrees of autocorrelation, which may be a sign of model or prior mis-specification. Visually examine the marginal posterior distribution for each model parameter to ensure that they do not have irregularities that could have resulted from misfit or non-convergence.

Posterior predictive distributions can be used to aid in examining the posteriors. Fully examine multivariate priors through a sensitivity analysis. These priors can be particularly influential on the posterior, even with slight modifications to the hyperparameters. To fully understand the impact of subjective priors, compare the posterior results with an analysis using diffuse priors.

This comparison can facilitate a deeper understanding of the impact the subjective priors have on findings. Next, conduct a full sensitivity analysis of all priors to gain a clearer understanding of the robustness of the results to different prior settings.

Given the subjectivity of the model, it is also important to conduct a sensitivity analysis of the model or likelihood to help uncover how robust results are to deviations in the model.

Report findings, including Bayesian interpretations. Take advantage of explaining and capturing the entire posterior rather than simply a point estimate. It may be helpful to examine the density at different quantiles to fully capture and understand the posterior distribution.

The optimization of Bayesian inference is conditional on the assumed model. Bayesian posterior probabilities are calibrated as long-term averages if parameters are drawn from the prior distribution and data are drawn from the model of the data given these parameters. Events with a stated probability occur at that frequency in the long term, when averaging over the generative model.

In practice, our models are never correct. There are two ways we would like to overcome this limitation: by identifying and fixing problems with the model; and by demonstrating that certain inferences are robust to reasonable departures from the model.

Even the simplest and most accepted Bayesian inferences can have serious limitations. This would be considered statistically indistinguishable from noise, in the sense that such an estimate could occur by chance, even if the true parameter value was zero. This makes the calibration of the probability questionable calibrated inferences or predictions are correct on average, conditional on the prediction.

In this example, the probability is calibrated if you average over the prior. In practice, studies are designed to estimate treatment effects with a reasonable level of precision.

True effects may be 1 or 2 standard errors from 0, but they are rarely 5, 10 or standard errors away. Ultimately, only a strong prior will make a big difference.

Bayesian probabilities are only calibrated when averaging over the true prior or population distribution of the parameters. The important thing about this example is not the specific numbers, which will depend on the context, but the idea that any statistical method should be evaluated over the range of problems to which it will be applied.

More generally, Bayesian models can be checked by comparing posterior predictive simulations with data and by estimating the out-of-sample predictive error There is a benefit to strong prior distributions that constrain parameters to reasonable values to allow the inclusion of more data while avoiding overfitting. More data can come from various sources, including additional data points, additional measurements on existing data and prior information summarizing other data or theories. All methods, Bayesian and otherwise, require subjective interpretation to tell a plausible story, and all models come from researcher decisions.

The widespread adoption of Bayesian statistics across disciplines is a testament to the power of the Bayesian paradigm for the construction of powerful and flexible statistical models within a rigorous and coherent probability framework. Modern Bayesian practitioners have access to a wealth of knowledge and techniques that allow the creation of bespoke models and computational approaches for particular problems.

Probabilistic programming languages, such as Stan, can take away much of the implementation details for many applications, allowing the focus to remain on the fundamentals of modelling and design.

An ongoing challenge for Bayesian statistics is the ever-growing demands posed by increasingly complex real-world applications, which are often associated with issues such as large data sets and uncertainties regarding model specification. All of this occurs within the context of rapid advances in computing hardware, the emergence of novel software development approaches and the growth of data sciences, which has attracted a larger and more heterogeneous scientific audience than ever before.

In recent years, the revision and popularization of the term artificial intelligence to encompass a broad range of ideas including statistics and computation has blurred the traditional boundaries between these disciplines.

This has been hugely successful in popularizing probabilistic modelling and Bayesian concepts outside their traditional roots in statistics, but has also seen transformations in the way Bayesian inference is being carried out and new questions about how Bayesian approaches can continue to be at the innovative forefront of research in artificial intelligence. Driven by the need to support large-scale applications involving data sets of increasing dimensionality and sample numbers, Bayesian concepts have exploited the growth of new technologies centred on deep learning.

This includes deep learning programming frameworks TensorFlow , PyTorch , which simplify the use of DNNs, permitting the construction of more expressive, data-driven models that are immediately amenable to inference techniques using off-the-shelf optimization algorithms and state-of-the-art hardware. In addition to providing a powerful tool to specify flexible and modular generative models, DNNs have been employed to develop new approaches for approximate inference and stimulated a new paradigm for Bayesian practice that sees the integration of statistical modelling and computation at its core.

An archetypal example is the variational autoencoder , which has been successfully used in various applications, including single-cell genomics , , providing a general modelling framework that has led to numerous extensions including latent factor disentanglement , , The underlying statistical model is a simple Bayesian hierarchical latent variable model, which maps high-dimensional observations to low-dimensional latent variables assumed to be normally distributed through functions defined by DNNs.

Variational inference is used to approximate the posterior distribution over the latent variables. However, in standard variational inference we would introduce a local variational parameter for each latent variable, in which case the computational requirements would scale linearly with the number of data samples. Variational autoencoders use a further approximation process known as amortization to replace inference over the many individual variational parameters with a single global set of parameters — known as a recognition network — that are used to parameterize a DNN that outputs the local variational parameters for each data point.

Remarkably, when the model and inference are combined and interpreted together, the variational autoencoder has an elegant interpretation as an encoding-decoding algorithm: it consists of a probabilistic encoder — a DNN that maps every observation to a distribution in the latent space — and a probabilistic decoder — a complementary DNN that maps each point in the latent space to a distribution in the observation space. Thus, model specification and inference have become entangled within the variational autoencoder, demonstrating the increasingly blurry boundary between principled Bayesian modelling and algorithmic deep learning techniques.

Other recent examples include the use of DNNs to construct probabilistic models that define distributions over possible functions , , , build complex probability distributions by applying a sequence of invertible transformations , and define models for exchangeable sequence data The expressive power of DNNs and their utility within model construction and inference algorithms come with compromises that will require Bayesian research.

The trend towards entangling models and inference has popularized these techniques for large-scale data problems; however, fundamental Bayesian concepts remain to be fully incorporated within this paradigm.

Integrating-out, model-averaging decision theoretic approaches rely on accurate posterior characterization, which remains elusive owing to the challenge posed by high-dimensional neural network parameter spaces Although Bayesian approaches to neural network learning have been around for decades , , , , further investigation into prior specifications for modern Bayesian deep learning models that involve complex network structures is required to understand how priors translate to specific functional properties Recent debates within the field of artificial intelligence have questioned the requirement for Bayesian approaches and highlighted potential alternatives.

For instance, deep ensembles have been shown to be alternatives to Bayesian methods for dealing with model uncertainty.

However, more recent work has shown that deep ensembles can actually be reinterpreted as approximate Bayesian model averaging Similarly, dropout is a regularization approach popularized for use in the training of DNNs to improve robustness by randomly dropping out nodes during the training of the network Dropout has been empirically shown to improve generalizability and reduce overfitting. Bayesian interpretations of dropout have emerged, linking it to forms of Bayesian approximation of probabilistic deep Gaussian processes Although the full extent of Bayesian principles has not yet been generalized to all recent developments in artificial intelligence, it is nonetheless a success that Bayesian thinking is deeply embedded and crucial to numerous innovations that have arisen.

The next decade is sure to bring a new wave of exciting innovative developments for Bayesian intelligence. Bayes, M. An essay towards solving a problem in the doctrine of chances. By the late Rev. Bayes, F. Price, in a letter to John Canton, A. R Soc. B Biol. Laplace, P. Essai Philosophique sur les Probabilities Courcier, Bayesian statistics in educational research: a look at the current state of affairs.

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Online stats training. Heo, I. This book presents a great collection of information with respect to prior elicitation, and includes elicitation techniques, summarizes potential pitfalls and describes examples across a wide variety of disciplines. Howard, G. The proof of the pudding: an illustration of the relative strengths of null hypothesis, meta-analysis, and Bayesian analysis.

Methods 5 , — Veen, D. Proposal for a five-step method to elicit expert judgement. Johnson, S. Methods to elicit beliefs for Bayesian priors: a systematic review. Morris, D. A web-based tool for eliciting probability distributions from experts. Garthwaite, P. Prior distribution elicitation for generalized linear and piecewise-linear models.

Elfadaly, F. Eliciting Dirichlet and Gaussian copula prior distributions for multinomial models. Expert elicitation for latent growth curve models: the case of posttraumatic stress symptoms development in children with burn injuries. Runge, A. An interactive tool for the elicitation of subjective probabilities in probabilistic seismic-hazard analysis.

Zondervan-Zwijnenburg, M. Application and evaluation of an expert judgment elicitation procedure for correlations. Cooke, R. TU Delft expert judgment data base.

Hanea, A. Dias, L. Elicitation Springer, Ibrahim, J. The power prior: theory and applications. Incorporation of historical data in the analysis of randomized therapeutic trials.

Trials 32 , — Bayesian PTSD-trajectory analysis with informed priors based on a systematic literature search and expert elicitation. Multivariate Behav. Berger, J. The case for objective Bayesian analysis. Bayesian Anal. This discussion of objective Bayesian analysis includes criticisms of the approach and a personal perspective on the debate on the value of objective Bayesian versus subjective Bayesian analysis.

Brown, L. In-season prediction of batting averages: a field test of empirical Bayes and Bayes methodologies. Candel, M. Performance of empirical Bayes estimators of level-2 random parameters in multilevel analysis: a Monte Carlo study for longitudinal designs. Using response times for item selection in adaptive testing. Darnieder, W. Richardson, S. On Bayesian analysis of mixtures with an unknown number of components with discussion.

Series B 59 , — Wasserman, L. Asymptotic inference for mixture models by using data-dependent priors.

Series B 62 , — Muthen, B. Bayesian structural equation modeling: a more flexible representation of substantive theory. Methods 17 , — Facing off with Scylla and Charybdis: a comparison of scalar, partial, and the novel possibility of approximate measurement invariance. Smeets, L. Code for the ShinyApp to determine the plausible parameter space for the PhD-delay data version v1.

Chung, Y. Weakly informative prior for point estimation of covariance matrices in hierarchical models. Gelman, A. A weakly informative default prior distribution for logistic and other regression models. Bayesian Data Analysis Vol. Jeffreys, H. Theory of Probability Vol. Seaman III, J. Hidden dangers of specifying noninformative priors. Prior distributions for variance parameters in hierarchical models comment on article by Browne and Draper. Lambert, P. How vague is vague? Depaoli, S. Mixture class recovery in GMM under varying degrees of class separation: frequentist versus Bayesian estimation.

Methods 18 , — Methods 22 , This article describes, in a step-by-step manner, the various points that need to be checked when estimating a model using Bayesian statistics. It can be used as a guide for implementing Bayesian methods. Prior sensitivity analysis in default Bayesian structural equation modeling. Methods 23 , — McNeish, D. On using Bayesian methods to address small sample problems. Modeling 23 , — Schuurman, N. A comparison of inverse-Wishart prior specifications for covariance matrices in multilevel autoregressive models.

Liu, H. Comparison of inverse Wishart and separation-strategy priors for Bayesian estimation of covariance parameter matrix in growth curve analysis. Ranganath, R. Population predictive checks. Daimon, T. Predictive checking for Bayesian interim analyses in clinical trials.

Trials 29 , — Box, G. A , — Gabry, J. Visualization in Bayesian workflow. Silverman, B. Nott, D. Approximation of Bayesian predictive p -values with regression ABC. Evans, M. Checking for prior—data conflict. A limit result for the prior predictive applied to checking for prior—data conflict. Young, K. Measuring discordancy between prior and data.

Series B Methodol. Kass, R. Bayes factors. This article provides an extensive discussion of Bayes factors with several examples. Bousquet, N. Diagnostics of prior—data agreement in applied Bayesian analysis. Entropy 20 , Checking for prior—data conflict using prior to posterior divergences. Lek, K.

How the choice of distance measure influences the detection of prior—data conflict. Entropy 21 , Bayesian statistics: principles and benefits.

Frontis 3 , 31—45 Etz, A. Introduction to the concept of likelihood and its applications. Methods Practices Psychol. Pawitan, Y. Press, The prior can often only be understood in the context of the likelihood. Master of Computer Science. Master of Computer Science in Data Science. Bachelor of Applied Arts and Sciences. Master of Science in Electrical Engineering. Master of Business Administration.

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