7.統計科学コース
Statistical Science
Course Code40STS001**

40STS002**

40STS003**

40STS004**

CourseIntroduction to Time Series and Spatial
Modeling

Introduction to Multivariate Analysis

Introduction to Probability andStochastic Processes

Introduction to Mathematical Statistics

CreditContent of Subject

2

This course introduces the foundations of timeseries analysis, point process, and spatial/spatiotemporal modeling. Emphasis is placed on
statistical modeling and model selection by
information criteria.
※Students who have already taken "Introduction
to Statistical ModelingⅠ（10SMS001）","Introduction to Statistical ModelingⅡ（10SMS002）" can't take this course.

2This course deals with a wide range of techniques(regression analysis, discriminant analysis,
principal component analysis, factor analysis,
covariance structure analysis, etc.) for analyzing
multivariate data.
※Students who have already taken "Introduction to Statistical Data Science Ⅰ（10SMS003）" "Introduction to Statistical Data
Science Ⅱ（10SMS004）" can't take this subject.

2

The lectures in this subject explore fundamental
concepts relating to theories of probability andstochastic processes. More specifically, thesubject covers probability space, random variable,
convergence, generating and characteristic
functions, Poisson process, and Markov chain.
※Students who have already taken "Introduction
to Statistical Inference Ⅰ（10SMS005）" can'ttake this subject.

2

This lecture course provides an overview of thetheory of mathematical statistics. The main topic
of the course is the theory of statisticalinference. Specifically, the course deals withsummary statistics, sampling distributions, point
estimation, interval estimation, hypothesis testing
and regression models. Applications of the theoryof mathematical statistics to real problems arealso discussed.
※Students who have already taken "Introduction
to Statistical Inference Ⅱ（10SMS006）" can'ttake this subject.

7.統計科学コース
Statistical Science
Course Code40STS005**

40STS006**

40STS007**

40STS008**

40STS009**

40STS010**

CourseIntroduction to Computational
Mathematics

Introduction to Statistical Machine
Learning

Introduction to Computational
InferenceSpecial Topics in Statistical ModelingComplex Systems Analysis

Special Topics in Modeling 1

CreditContent of Subject

2

The lectures cover fundamentals ofcomputational mathematics such as matrix
differential calculus，theory and algorithms ofapplied/numerical linear algebra，linear
programming, integer programming，dynamic
programming，theory and algorithms of
optimization，and conic programming.
※Students who have already taken"Computational Methodology in Statistical
InferenceⅠ（10SMS007）" can't take thissubject.

2

The lectures discuss methods and theory ofstatistical machine learning including support
vector machines, deep learning, Gaussian
processes, ensemble learning, transfer learning,
reinforcement learning, and statistical learningtheory.
※Students who have already taken"Computational Methodology in Statistical Ⅱ（10SMS008）" can't take this subject.

2

This course deals with methodologies incomputational statistics with their applications instatistics and machine learning. Topics include
nonparametric bootstrap, Markov chain Monte
Carlo, particle filter, graphical modeling and belief
propagation, EM algorithm, and variational
Bayesian inference.
※Students who have already taken"Computational Methodology in Statistical Ⅱ（10SMS008）" can't take this subject.

2

The course will discuss the basics of theinference for un-normalized models and sparsemodeling and its applications. Also, methodologies
of formulating problems into "solvable" forms forvarious real-world problems are discussed.

2

The lecture will discuss deterministic andprobabilistic approaches to time series data
analysis and modeling. In addition, students taketurns reading books and papers about detecting
significant signals, spatial correlations, andcausality in time series data.

2

Shannon's information theory is lectured as abasic theory for analysis of information sources.
The amount of information, entropy, andcommunication sysytems are discussed. And
actual radio communication systems are lectured.

7.統計科学コース
Statistical Science
Course Code40STS011**

40STS012**

40STS013**

40STS014**

CourseSpecial Topics in Modeling 2

Special Topics in Time Series Analysis

Stochastic ModelingSpecial Course on Data Assimilation

CreditContent of Subject

2

This course deals with advanced computational
statistics with their applications. Examples are
specialized topics in Markov Chain Monte Carlo,
sequential Monte Carlo, bootstrap, and theirapplications in Bayesian statistics and model
selection.

2

After covering the basics of stationary timeseries models that were not fully covered in
Introduction to Time Series and Spatial Modeling,causality analysis based on multivariate
autoregressive (VAR) models, impulse responses,
etc. will be covered. After introducing unit root
tests, we will expand our understanding tocointegration models. With financial time series(rate of return data) in mind, the conditional
heteroscedasticity models will be outlined. In
addition, time-varying variance modeling will be
discussed in relation to local stationary AR
models and non-Gaussian filters. Computer
exercises using R or R Shiny applications will be
conducted once after every two or threelectures.

22This course provides an introduction tostochastic processes, with their applications toreal-world situations. This course covers
elementary stochastic processes such as
Gaussian, Poisson, Markov and renewal
processes.

This is a course of seminar and practice onsequential data assimilation methods orvariational data assimilation methods. On thebasis of the state-space model, students derive
the sequential methods or the variational
methods, and implement the procedure.

7.統計科学コース
Statistical Science
Course Code40STS015**

40STS016**

40STS017**

40STS018**

CourseBasic Theory of Point Processes

Applied Probability

Multimedia Information Processing

Spatial Statistics and Stochastic
Geometry

CreditContent of Subject

2

This course is on the foundamental mathematicaltheory of point processes. It introduces basic
concepts and theories related point processes,
including random measures, Janossy measures,
Janossy density, Campbell measure, momentmeasure, conditional intensity, Papangelou
intensity, and Palm intensity. Its objectives
include: (1) To learn the point process theory
from the viewpoint of modern probability theory.
(2) To understand the theoretical relationshipbetween each type of point processes.

2

In this lecture, we will outline the basics ofstochastic processes, including Poissonprocesses, random walks, and Brownian motion,
while showing examples of applications of
stochastic processes. In addition, we will explain
the mathematical economic analysis of resource
management risks by applying macro-renewable
resource supply forecasting and option theory,targeting renewable resources such as forests.

2

The digital age has fostered the broadcasting ofan ever increasing quantity of complex multimedia
documents， be it through the internet or moreversatile electronic channels. These evolutions
have called for new tools and technologies toclassify and analyze multimedia contents. We
study in this course algorithms which are usefulfor these tasks.

2

In this course, I will lecture spatial modeling for
spatial data such as geostatistics, lattice model,
directional statistics, and spatial point process, aswell as random partitioning and random packing.
Unlike the generalized linear model and its related
statistics, a likelihood of a spatial model is not a
simple product over independent data, which isone of essences for spatial modeling.

7.統計科学コース
Statistical Science
Course Code40STS019**

CourseGenomic Data Analysis

CreditContent of Subject

2

This course deals with data analysis of genetic
information by applying the methods of statisticalscience.
To infer the phylogenetic relationships oforganisms, we compare homologous genes
between organisms.
Explanations and exercises will be given on how
to construct a model for that purpose andmaximum likelihood estimation of phylogenetic
trees.

40STS020**

Topics in Sampling Theory

2

This course deals with the design of datacollection, focusing on sample survey methods,
and statistical inference under that design. Follow
three topics will be covered: (1) sample survey
methods used in social surveys, (2) design ofexperiments and observational studies in contrast
to survey research, and (3) typical data analysis
methods for survey data. The course will consist
mainly of lectures, with some simple exercises in
the latter part.

40STS021**

Survey Design2This course covers systematic explanations ofpractical methodologies of survey design fororganizations or regions.

2This course deals with the basic probabilistic
framework for statistical treatment of natural
language and related discrete data. It will cover
the basic statistical and computational methods
necessary to understand the characteristics ofhigh-dimensional discrete data.

1

This is a general course of statistical science.
Students are requested to attend the statisticalmathematics seminar held at the institute ofstatistical mathematics to learn various recent
developments in statistical science.

40STS022**

40STS023**

Machine Learning for Statistical
Natural Language Processing

Statistical Mathematics Seminar 1

7.統計科学コース
Statistical Science
Course Code40STS024**

40STS025**

40STS026**

CourseStatistical Mathematics Seminar 2

Statistical Mathematics Seminar 3

Statistical Mathematics Seminar 4

40STS027**

Statistical Mathematics Seminar 5

40STS028**

Special Topics in Statistical Inference
and Mathematics 1

40STS029**

40STS030**

Special Topics in Statistical Inference
and Mathematics 2

Statistical Computing

CreditContent of Subject

1

This is a general course of statistical science.
Students are requested to attend the statisticalmathematics seminar held at the institute ofstatistical mathematics to learn various recent
developments in statistical science.

1

This is a general course of statistical science.
Students are requested to attend the statisticalmathematics seminar held at the institute ofstatistical mathematics to learn various recent
developments in statistical science.

1

This is a general course of statistical science.
Students are requested to attend the statisticalmathematics seminar held at the institute ofstatistical mathematics to learn various recent
developments in statistical science.

1

This is a general course of statistical science.
Students are requested to attend the statisticalmathematics seminar held at the institute ofstatistical mathematics to learn various recent
developments in statistical science.

2

Probability theory is basic mathematics forstatistical science. This course deals withmathematical topics that link to statisticalapplications.

2

One of the topics below will be chosen: (1)Distribution theory, asymptotic theory, statisticalinference, (2) Gaussian random processes/fields,(3) Contingency table and graphical model, (4)Differential and integral geometric approach tostatistics, (5) Algebraic statistics, (6) Randommatrices, (7) Mathematics in statistics including
convex analysis, combinatorics, and measure
theory.

2

Lectures on statistical computing using a parallel
computer will be given in this course. In
particular，the following subjects will be
discussed: problems which requires hugematrices，the particle filter using a parallel
computer，and implementation of the ensemble
Kalman filter on a parallel computer.

7.統計科学コース
Statistical Science
Course Code40STS031**

40STS032**

40STS033**

40STS034**

40STS035**

CourseInformation Security

Bayesian Computation

Special Topics in Environmental
Statistics

Financial Statistics

Longitudinal Data Analysis

CreditContent of Subject

2

This course covers major privacy-preserving
techniques such as anonymization, differential
privacy, and statistical disclosure control, which
realize safe analysis of big data. We also cover
topics on machine learning security with emphasison empirical evaluation methods.

2

The course covers some theoretical andmethodological topics of Bayesian computation.
Markov chain Monte Carlo methods are also
covered.

2

The goal of this course is to provide students
with the ability to understand and implement thevarious statistical methods used in environmental
data analysis. Students will read the textbooks
and attend lectures on specific topics.

2

Concrete cases will be presented and researchlectures will be given on theoreticalmethodologies for quantification of credit risk, risk
assessment of financial markets, and investment
strategies. In particular, students will acquire
practical knowledge of statistical models that areconsistent with relevant laws and regulations
such as the Basel Accord and corporate
accounting, forecasting using stochastic
processes and time-series models, and risk
assessment through the use of actual data.

2

This course focus on the study of statisticalmodels, such as linear mixed-effects models andtheir extensions, used in the longitudinal data
analysis in which a response variable is measured
repeatedly over time for multiple subjects. The
course will also focus on the study of research
designs, such as randomization, and on the studyof statistical methods used in actual problems.

7.統計科学コース
Statistical Science
Course Code40STS036**

40STS037**

40STS038**

40STS039**

40STS040**

40STS041**

CourseSpecial Topics in Biostatistics

Application in Data Science

Bayesian Uncertainty Quantification forEngineering Applications

Statistical Inference

Statistical Machine Learning

Special Topics in Signal Processing

CreditContent of Subject

2

This course deals with recent relevant topics on
biostatistics, especially, (i) Biostatisticalmethodology on clinical and epidemiologic studies,(ii) Designs and analyses of clinical trials, (iii)
Evidence synthesis methods, and (iv) statisticalanalyses of large-scale genomic data.

2

This course deals with various data analysis
methods for practical applications, including
statistical machine learning, deep learning,
Bayesian inference, Python/R programming, etc.,
through several case studies including materials
data analysis.

2

Students will learn about the concept andimplementation of uncertainty quantification forBayesianinference of physical models. Examples
of model comes from structural engineering,
geotechnicalengineering, etc.

2This course introduces the estimation and testingof regression models with nonlinearities andrelated statistical theory as basic topics, andtreats sparse modeling, robust statistics, missing
data analysis, deivergence-based inference asadvanced topics.

2

Research work is directed on the methodology ofstatistical machine learning such as deep learningand kernel methods for analyzing large highdimensional data. The course aims to provide
students with knowledge of machine learningtheory and methods, and the ability to apply
machine learning methods to data analysis. The
course will be conducted in the form of seminars,
and students will be evaluated based on theirpresentations.

2

Basic theories of signal processing such as
Fourier and wavelet transforms, principal
component analysis and independent component
analysis are explained. Practical examples will begiven, using sound processing, image processing,biomedical measurement signals and astronomical
data analysis as examples.

7.統計科学コース
Statistical Science
Course Code40STS042**

CourseParametric Statistical Models

CreditContent of Subject

2

This course deals with either of the following two
topics based on interests of students: (i) thetheory of well-known probability distributions andrelated statistical models, or (ii) the theory ofgeneralized linear models and its applications toreal problems.

40STS043**

Systems Optimization

2

This course is intended to serve an introduction
to systems design and focuses on the theoreticalaspects of mathematical optimization based onconvex analysis, duality theory, numerical linear
algebra, and functional analysis.

40STS044**

Stochastic Models

2This course discusses algebraic and combinatorial
methods for stochastic computing arising instatistical inference.

2

We study the theory of semiparametric inference,
its application and (or) some related topics. The
standard knowledge of mathematical statistics
and the basic mathematical skill on calculus,
abstract linear algebra, metric space (or general
topology) and probability theory are required.

40STS045**

Topics of Statistical Inference7.統計科学コース
Statistical Science
Course Code40STS046**

40STS047**

CourseIrregular Statistical Theory

Convex Analysis and Conic
Optimization

CreditContent of Subject

2

After outlining asymptotic theory for regularstatistical models, asymptotic theory for locallyconic models will be introduced and the geometricmethods required in their evaluation will be
explained. Alternatively, after outlining the basic
methods for causal inference, semiparametricapproaches using propensity scores will be
introduced and information criteria for causal
inference models will be explained. The goal of
the lecture is to provide fundamentals anddevelopments of statistical asymptotics or causal
inference.

2

In this course we will discuss the fundamentals of
convex analysis such as
separation theorems, subdifferential theory andseveral duality results. At the end, we will discuss
some extensions and related topics. Alternatively,
we might also discuss modelling and theoreticalaspects of conic linear programs.

40STS048**

Topics in Computational Mathematics

2

This course deals with numerical algorithms inmathematical optimization and related areas.
Specifically, we choose some topics in numericalalgorithms for continuous optimization problems,
matrix and eigenvalue problems, and so on, anddiscuss their mathematical foundations.

40STS049**

High Dimensional Probability andStatistics

2

This course discusses topics in probability andstatistics in higher and infinite dimensions.

40STS050**

Mean Field Theory for Random System

2Students will learn the mean field theory for
random systems: (1) how to analyze magnetic
models (2) basic analytical methods

7.統計科学コース
Statistical Science
Course Code40STS051**

40STS052**

40STS053**

40STS054**

CourseIntroduction to Statistical Science

Survival Analysis

Topics in combinatorial optimization

Addvanced Spatial Statistics

40STS055**

Differential Privacy

40STS056**

Nonlinear Optimization for Large-scale
Machine Learning

CreditContent of Subject

2

After dealing with probability including randomvariables, probability distributions, expectationand variance, students will learn methods
indispensable for statistical analysis, such as
point estimation, interval estimation andstatistical hypothesis testing..

2

Survival analysis deals with patients' and/or
equipments' survival time data. When analyzing
survival data, one typically entounters
incompletely observed survival times that are
censored or truncated. This type of survival dataarises in a variety of fields, including medicine,reliability, ecology, insurance, economics, finance,and marketing. In this course, we study statisticalmodels and inference methods based on survival
data.

2

Lectures or seminars on basic topics of
combinatorial optimization and algorithm design
will be given. The topics will include linear
programming, matching, network flows, matroids,
and submodular functions, but other topics may
be covered depending on the interests of thestudents.

2

This lecture introduces statistical methods for
spatial data and their applications. Specifically,methods in geostatistics, spatial econometrics,
and relevant areas are introducesd together with
their implementation with R.

2

This course deals with differential privacy (DP),which is known as a de facto standard privacy
notion for privacy protection. We first study somebasic topics, such as the privacy properties ofDP, the Laplace and exponential mechanisms, thecomposition theorems, and the SVT (Sparse
Vector Technique). Then, we study moreadvanced topics, such as various
extensions/variants of DP, the local model, andthe shuffle model.

2

Lecture and research guidance on nonlinear
optimization algorithm and analysis, with a focus
on those suitable for real problems in large-scalemachine learning.

7.統計科学コース
Statistical Science
Course Code80STS001**

80STS002**

80STS003**

80STS004**

80STS005**

80STS006**

80STS007**

80STS008**

80STS009**

80STS010**

CourseStatistical Science Study 1

Statistical Science Study 2

Statistical Science Study 3

Statistical Science Study 4

Statistical Science Study 5

Statistical Science Study 6

Statistical Science Study 7

Statistical Science Study 8

Statistical Science Study 9

Statistical Science Study 10

CreditContent of Subject

2

This is a general research course of statisticalscience. Students are requested to present
progress of their research by giving seminars andtalks.

2This is a general research course of statisticalscience. Students are requested to present
progress of their research by giving seminars andtalks.

2This is a general research course of statisticalscience. Students are requested to present
progress of their research by giving seminars andtalks.

2This is a general research course of statisticalscience. Students are requested to present
progress of their research by giving seminars andtalks.

2This is a general research course of statisticalscience. Students are requested to present
progress of their research by giving seminars andtalks.

2This is a general research course of statisticalscience. Students are requested to present
progress of their research by giving seminars andtalks.

2This is a general research course of statisticalscience. Students are requested to present
progress of their research by giving seminars andtalks.

2This is a general research course of statisticalscience. Students are requested to present
progress of their research by giving seminars andtalks.

2This is a general research course of statisticalscience. Students are requested to present
progress of their research by giving seminars andtalks.

2This is a general research course of statisticalscience. Students are requested to present
progress of their research by giving seminars andtalks.