David O. Siegmund - US grants

This research project involves a team of scholars involved in the following topics: (1) applications of group representations, (2) Bayesian statistics, (3) rates of convergence of Markov chains to their stationary distributions, (4) regression percentiles using an asymmetric least squares loss function, (5) using compliance as a covariate in a randomized clinical trial, (6) influence functions for confidence limits, (7) better automatic confidence intervals for parametric problems, (8) permutation tests for 'messy situations', (9) minimax estimation, (10) loss and risk estimation, (11) volumes of tubular neighborhoods and statistical applications, (12) maximum entropy methods, (13) confidence regions in semilinear regression, (14) change-point problems, (15) sequential tests and estimates, (16) the approximate evaluation of expectations, (17) bootstrap confidence intervals in complex models, (18) bootstrap choice of tuning parameters and adaptation, and (19) approximate inference for parametric models via least favorable families. The general aim of this project is the development of new statistical theory and methodology of interest to applied mathematics. The research involves a combination of traditional mathematical statistics and modern computational methods. Particular goals are understanding more complicated models than are traditionally used and automating insofar as possible statistical procedures for routine use.

[unreadable] DESCRIPTION (provided by applicant): Mapping genes associated with specific traits in human, plant and animal populations can be an important step in identifying the genes responsible for inherited diseases or in producing a better food supply. The aim of the proposed research is to develop and evaluate statistical methods to aid in the design and analysis of gene mapping studies in both human and experimental genetics, particularly when the whole genome or a portion is scanned to search for the relevant genes. The proposed statistical methodology is appropriate to the analysis of data obtained from any highly polymorphic, reasonably dense genetic map and can be applied to discrete, ordinal, or quantitative traits. Specific long term goals are the following: (1) Develop and evaluate general methodology for searching the genome to identify regions likely to contain genes affecting the trait or traits of interest. (2) Develop general, flexible models of multigenic traits, which allow gene x gene and gene x environment interactions; develop and compare statistical methods to study those models and for model selection. (3) Implement these methods in computer routines, concentrating on quantitative traits that are studied in moderately large, population based, multigenerational pedigrees. Results will be obtained by mathematical analysis and computer simulation, while analysis of experimental data will serve to validate and refine the models. The distinguishing features of the proposal are (i) systematic consideration of the effect of scanning markers distributed throughout the genome and (ii) exploitation of the relation between the statistics of gene map- ping problems and of "change-point" problems, which have been thoroughly studied in the recent statistical research. [unreadable] [unreadable] [unreadable]

A major direction of the proposed research is in sequential change-point detection schemes. Powerful techniques to tackle this problem are currently available from recent advances in sequential testing theory and boundary crossing problems in random fields. It is expected that relatively simple algorithms which are not too demanding in computational and memory requirements for on-line implementation and yet are nearly optimal from a statistical viewpoint will be developed for a wide variety of practical applications. Not only will the methodology to be developed address the widely recognized discrepancies between the assumptions underlying conventional control charts and today's industrial processes, but it will also integrate both the detection aspect and the quality measurement aspect of industrial quality control. Another closely related direction of research is in fixed sample change-point problems and its applications to econometrics, signal reconstruction and genetic linkage analysis. Related fundamental problems in boundary crossing probabilities of random processes and random fields will be investigated, and are expected to lead to definitive solutions of some long-standing problems concerning the distribution of generalized likelihood ratio statistics in change-point models. A third related area of research is estimation and control of time series models and stochastic dynamical systems whose parameters may change with time. Although in practice abrupt parameter changes typically occur very infrequently, the unknown times of their occurrence have led to prohibitive complexity of the Bayes estimators and controllers in the literature. By using parallel recursive algorithms and combining some new ideas in sequential change-point detection with empirical Bayes methodology, it is anticipated that asymptotically efficient estimation and control schemes which have manageable complexity and which can be implemented on-line will be developed. An important objeat ive of the proposed research is the development of a powerful statistical methodology for quality control of modern industrial processes and for automated fault detection in complex manufacturing systems. Another important goal is to develop statistical methods appropriate for analysis of genetic linkage data related to disease susceptibility and other traits in humans, animals and plants and for extraction of relevant information from these data that may lead to better diagnostic tests and treatments of the disease.

DESCRIPTION (Adapted from the Investigator's Abstract): Mapping human disease susceptibility genes can be the first in a series of steps leading to better diagnostic tests and ultimately strategies for combating or controlling the disease. The use of pairs or other small groups of relatives who share a trait as the basic unit for mapping genes has great advantages when the trait of interest is genetically complex or has low or age-dependent penetrance. The aim of the proposed research is to provide statistical methods to aid in the design and analysis of such gene mapping studies in human genetics and in experimental genetics, particularly when the whole genome or a portion thereof is scanned to search for the relevant genes. The problems emphasized in the proposal are motivated by the laboratory technique of Genomic Mismatch Scanning which is under development in the laboratory of Dr. Patrick O. Brown; but the proposed statistical ideas are relevant to the analysis of data obtained from any highly polymorphic, reasonably dense genetic map and can be applied to discrete or quantitative traits. Specific long term goals are the following: (1) Develop general methodology for searching the genome to identify regions of enriched identity by descent, hence likely to contain genes affecting the trait or traits of interest. (2) Develop general, flexible models of multigenic traits; develop statistical techniques appropriate for those models. Statistical models will be developed by mathematical analysis and computer simulation. The analysis of experimental data will serve to validate and refine the models. The distinguishing features of the proposal are: (1) systematic consideration of the effect of scanning markers distributed throughout the genome and (2) exploitation of the relation between the statistics of gene mapping problems and of "change-point problems," which have been thoroughly studied in recent statistical research.

Lai and Siegmund 9704324 The investigators develop a sequential method of change-point detection involving algorithms that are not too demanding in computational and memory requirements for on-line implementation and yet are nearly optimal from a statistical viewpoint. Powerful techniques to tackle this problem are derived from recent advances in sequential testing theory and boundary crossing problems in random fields. A closely related direction of research is fixed sample change-point problems and their applications to signal detection and gene mapping. Related fundamental problems in boundary crossing probabilities of random processes and random fields are also investigated and lead to definitive solutions of some long-standing questions concerning the distribution of generalized likelihood ratio statistics in change-point models. A third related area of research is estimation and control of time series models and stochastic dynamical systems whose parameters may change with time. Although in practice abrupt parameter changes typically occur very infrequently, the unknown times of their occurrence have led to prohibitive complexity of the Bayes estimators and controllers in the literature. By using parallel recursive algorithms and combining some new ideas in sequential change-point detection with empirical Bayes methodology, these difficulties are resolved to obtain asymptotically efficient estimation and control schemes of manageable complexity. One important objective of this research is the development of a powerful statistical methodology for quality control of modern industrial processes and for automated fault detection in complex manufacturing systems. Another objective development of statistical methods appropriate for analysis of genetic linkage data related to disease susceptibility and other traits in humans, animals and plants and for extraction of relevant information from these data that may ultimately lead to better diagnostic tests and tr eatments of the disease. Applications involve the strategic areas of manufacturing and biotechnology.

Abstract: Statistical Problems in Quality control, Stochastic Systems and Genetic Analysis

This project will address a number of related statistical problems having applications in (i) industrial quality control and complex engineering systems, (ii) in molecular biology and genetics, and (iii) in financial economics. (i) One objective of the proposed research is to develop a unified methodology of sequential change-point detection in industrial quality control and of automated fault detection in complex engineering systems. Relatively simple algorithms that are not too demanding in computational and memory requirements for on-line implementation and yet are nearly optimal from a statistical viewpoint will be developed for a variety of practical applications. This methodology will not only address the recognized discrepancies between the assumptions underlying conventional control charts and today's industrial processes, but it will also provide methodological advances for on-line detection and diagnosis of faults and potential failures of automated engineering systems. In this connection, estimation and forecasting problems in time series models and stochastic dynamical systems having parameters that may change with time will also be investigated. Although in practice abrupt parameter changes usually occur infrequently, the unknown times of their occurrence have led to detection algorithms of prohibitive complexity. By using parallel recursive algorithms and combining new ideas in change-point detection with empirical Bayes methodology, it is anticipated that asymptotically efficient estimation and prediction schemes of manageable complexity will be developed. (ii) Another direction of research involves fixed sample change-point problems and their applications to biomolecular sequence analysis and other problems of signal detection. A comprehensive statistical methodology will be developed for genome scanning to map anonymous genes using data based on crosses of pure strains in experimental genetics or based on regions of identity by descent of related individuals in human genetics. Related mathematical problems in boundary crossing probabilities of random fields will be investigated. (iii) A third direction of research is financial time series and stochastic control problems of financial economics. New statistical models, computational algorithms, and methods for data analysis and forecasting will be developed to address a variety of sequential decision, portfolio selection, and pricing problems in investments and financial markets.

The interdisciplinary research in financial economics and molecular biology not only leads to the development of new stochastic models and statistical methods, but it also provides valuable research opportunities for graduate and undergraduate students in these rapidly developing fields.

Proposal: DMS-0305749
PI: Tze L. Lai
Title: Detection, Estimation and Optimization Problems in Stochastic Systems, and Applications to Genetics, Engineering and Economics

ABSTRACT:

The investigators will study a large number of change-point like problems that arise in industrial quality control, automated fault detection of complex engineering systems and gene mapping. A common feature of these problems involves the probability that a random field exceeds a high threshold. A unified analytic approach will be developed to evaluate the relevant boundary crossing probabilities. Importance sampling techniques and sequential Monte Carlo methods will also be developed to supplement the analytic approximations. For on-line applications, relatively simple parallel, recursive algorithms, which are not too demanding in computational and memory requirements and yet are nearly optimal from a statistical viewpoint, will be developed. Another direction of research is financial time series and stochastic control problems in financial economics. New statistical models, computational algorithms, and data analysis and forecasting methods will be developed to address a variety of sequential decision, portfolio selection, and pricing problems in investments and financial markets.

The project will address problems of (i) industrial quality control, especially control of complex engineering systems, (ii) gene mapping, i.e., the identification of genomic regions containing a gene (or genes) affecting a trait of interest in humans, model experimental organisms, or agriculturally important crops, and (iii) financial economics, especially time series analysis of financial data. The problems will be studied by using recent developments in probability and statistical theory, and by extensive experiments involving computer simulations. Computational algorithms will be developed to facilitate applications. The investigators will also develop new undergraduate and graduate courses in statistical genetics and in financial mathematics and write textbooks for these courses.

Stanford University proposes a novel approach to increasing the visibility of graduate studies in statistics, and for drawing U.S. nationals who are talented and interested in quantitative sciences into its graduate programs in statistics. This effort builds upon the existing strength of Stanford's Statistics department and its developed links with three cognate "target" fields -- Computational Biology, Mathematical Finance, and Information Science -- resulting in the attraction of U.S. nationals into the mathematical sciences.

In each of the three target fields, the department will expand an existing successful research activity, which is a basis for classical Ph.D. training, in such a way as to attract the attention and participation of undergraduates, Masters' students, and beginning Ph.D. students in cognate fields. Such students are quantitatively able and will be "captured" into the orbit of the mathematical sciences by offering them a lively experience of intellectual discovery, and demonstrating how essential statistical methodology is to exciting scientific discoveries.

Vertical integration of research and education is to be achieved in part by hosting postdoctoral fellows and undergraduates specializing in each of these cognate fields, and by organizing thematic activities that promote the interaction between undergraduate students, graduate students, postdoctoral fellows, and faculty.

An outreach and mentoring effort will bring each year additional female participants and members of under-represented minority groups for summer research and education activities in the main themes of the project.

Stanford Statistics has a superb reputation, with a top national rating, and an outstanding mix of faculty with extremely high visibility. The fields chosen as targets are central areas of national importance, the Stanford faculty have international reputations as leaders in these fields, and the VIGRE effort will supervise postdocs and students in cutting-edge research in these areas. The effort aims exactly to move students in cognate fields with strong practical skills and quantitative talent to engage more directly in intellectual discovery at the frontiers of human knowledge, under the direction of acknowledged international leaders.

By expanding the Stanford Statistics department's reach into the cognate areas we expand the opportunities of all our students, both VIGRE participants and everyone else in the orbit of the department. By posing formal initiatives in Financial Mathematics, Computational Biology and Information Science, Stanford will bring new energy and focus into its statistics curriculum. As Stanford has a national leadership position in the field of Statistics, many other U.S. universities are expected to closely watch this effort and replicate its most successful initiatives.

Searching a parameter set for the location of one or more signals in a noisy background arises in gene mapping, brain mapping, bioinformatics and astronomy. An important part of the solution of these problems involves the probability that a random field exceeds a high threshold. The proposed research develops a unified analytic approach to evaluate these boundary crossing probabilities, and importance sampling and sequential Monte Carlo methods to supplement the analytic approximations. A closely related area of research is estimation and forecasting problems in time series models and stochastic dynamical systems whose parameters may change with time. Although in practice abrupt parameter changes typically occur very infrequently, the unknown times of their occurrence have led to prohibitive complexity of the Bayes estimators and predictors in the literature. By using parallel recursive algorithms and combining some new ideas in change-point detection with empirical Bayes methodology, the proposed research develops asymptotically efficient estimation and prediction schemes with manageable complexity.
Bayesian models of parameter changes in Markovian systems are special cases of hidden Markov models. A goal of the proposed research is to develop a comprehensive theory of efficient parameter estimation, filtering and smoothing in hidden Markov models on general state spaces. Another related direction of research is econometric time series and stochastic optimization problems in financial economics.

Important objectives of the proposed research are to develop statistical methods for gene mapping, signal processing, adaptive control of engineering systems, and decision and pricing problems in financial markets. The broader implications of the research include (i) direct applications in engineering, finance, and genetics where mapping can be the first step towards better diagnostics or treatment of a disease or towards improving plant or animal stock, and (ii) training the next generation of scientists by involving graduate students in all phases of the research.

Successful statistical analysis of the massive amounts of data available today can lead to successful, early threat detection. This proposal consists of two parts. The first part focuses on the detection of mutations in pathogen samples. Many emerging health threats are due to new mutations in evolving pathogen populations, which can now be profiled using massively parallel sequencing experiments. The investigators work with Dr. Hanlee Ji's laboratory in the Stanford Genome Technology Center, whose deep sequencing platform allows the detection of low prevalence mutations in pathogen samples. This problem was previously treated mainly from an algorithmic perspective, lacking statistical models for error estimates. The investigators propose methods for analysis of single nucleotide changes and general structural variants, and consider the analysis of single samples, the simultaneous analysis of multiple samples, and the comparison of matched samples. The second part of the proposal considers threat detection in a more general framework: detection of changes from background condition in one or more parallel streams of data. Examples are cyber-attacks on computer networks, introduction of belligerent agents (e.g. landmines, aircraft) into previously quiescent environments, appearance of noxious chemicals, genetic modifications of viruses or bacteria, etc. The main contribution is a general conceptual framework for integrating data from a large number of distributed sources, when the signal of interest may be present in only a small fraction of the sources. This proposal motivates theoretical developments in the areas of change-point detection, mixture estimation, empirical Bayes estimation, and false discovery rate control.

Successful statistical analysis of the massive amounts of data collected in modern scientific and technological activities can lead to successful, early threat detection. This proposal consists of two parts. The first part focuses on the detection of mutations in pathogen samples. Many emerging health threats are due to new mutations in evolving pathogen populations, which can now be profiled using next generation sequencing experiments. The accurate detection of new mutations is important, because they may confer survival advantage to the virus that carries it. Currently, this problem has been treated mainly from an algorithmic perspective, lacking statistical models for error estimates. The methods developed in this proposal will bridge this gap. The second part of the proposal considers threat detection in a more general framework: detection of changes from background condition in one or more parallel streams of data. Examples include cyber-attacks on computer networks, introduction of belligerent agents (e.g. landmines, aircraft) into previously quiescent environments, appearance of noxious chemicals, genetic modifications of viruses or bacteria, etc. The main contribution is a general conceptual framework for integrating data from a potentially large number of distributed sources, when the signal of interest may be present in only a small fraction of the sources.

An important objective of the proposed research is to
develop methods for gene mapping, i.e., the identification
of genomic regions containing a gene (or genes) affecting
a trait of interest in either humans or in experimental organisms.
Searching a parameter set for the location of one or more
signals in a noisy background arise in gene mapping where the
signals indicate the presence of a gene. Similar problems arise
in brain mapping, astronomy, and bioinformatics. An important
part of their solution involves the probability that a random field
exceeds a high threshold. A unified analytic approach and
sequential Monte Carlo methods will be developed to evaluate
these boundary crossing probabilities. Other methodological
innovations of the proposed research are new dynamic empirical
Bayes models and methods, sequential surveillance procedures,
and adaptive control schemes for input-output systems that may
undergo occasional abrupt structural changes.

The dynamic empirical Bayes approach under development has
applications to insurance rate-making, dynamic panel data in
economics, longitudinal data in biomedical studies, and risk
management. Sequential surveillance and adaptive risk control
are of timely relevance in the aftermath of the recent financial
crisis and oil spill disaster. Sequential Monte Carlo methods have
important applications to nonlinear filtering and to rare event
simulation in communication networks and risk management. Gene
mapping provides an important tool in the study of human diseases,
and in agriculture and animal husbandry. The broader implications
of the proposed research include (i) direct implications in genetics,
engineering, finance, insurance, risk management and surveillance,
and (ii) training of the next generation of scientists in academia,
industry, and government by developing new advanced courses and
involving graduate students in all phases of the research.