13,063 research outputs found
Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models
Penalization of the likelihood by Jeffreys' invariant prior, or by a positive
power thereof, is shown to produce finite-valued maximum penalized likelihood
estimates in a broad class of binomial generalized linear models. The class of
models includes logistic regression, where the Jeffreys-prior penalty is known
additionally to reduce the asymptotic bias of the maximum likelihood estimator;
and also models with other commonly used link functions such as probit and
log-log. Shrinkage towards equiprobability across observations, relative to the
maximum likelihood estimator, is established theoretically and is studied
through illustrative examples. Some implications of finiteness and shrinkage
for inference are discussed, particularly when inference is based on Wald-type
procedures. A widely applicable procedure is developed for computation of
maximum penalized likelihood estimates, by using repeated maximum likelihood
fits with iteratively adjusted binomial responses and totals. These theoretical
results and methods underpin the increasingly widespread use of reduced-bias
and similarly penalized binomial regression models in many applied fields
Design Issues for Generalized Linear Models: A Review
Generalized linear models (GLMs) have been used quite effectively in the
modeling of a mean response under nonstandard conditions, where discrete as
well as continuous data distributions can be accommodated. The choice of design
for a GLM is a very important task in the development and building of an
adequate model. However, one major problem that handicaps the construction of a
GLM design is its dependence on the unknown parameters of the fitted model.
Several approaches have been proposed in the past 25 years to solve this
problem. These approaches, however, have provided only partial solutions that
apply in only some special cases, and the problem, in general, remains largely
unresolved. The purpose of this article is to focus attention on the
aforementioned dependence problem. We provide a survey of various existing
techniques dealing with the dependence problem. This survey includes
discussions concerning locally optimal designs, sequential designs, Bayesian
designs and the quantile dispersion graph approach for comparing designs for
GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Another Generalized Transmuted Family of Distributions: Properties and Applications
We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Another generalized transmuted family of distributions. We present some special models. We investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating functions, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Renyi entropies and order statistics, which hold for any baseline model, certain characterisations are presented. Further, we introduce a bivariate extensions of the new family. We discuss the dierent method of estimation of the model parameters and illustrate the potentiality of the family by means of two applications to real data. A brief simulation for evaluating Maximum likelihood estimator is done
Julian Ernst Besag, 26 March 1945 -- 6 August 2010, a biographical memoir
Julian Besag was an outstanding statistical scientist, distinguished for his
pioneering work on the statistical theory and analysis of spatial processes,
especially conditional lattice systems. His work has been seminal in
statistical developments over the last several decades ranging from image
analysis to Markov chain Monte Carlo methods. He clarified the role of
auto-logistic and auto-normal models as instances of Markov random fields and
paved the way for their use in diverse applications. Later work included
investigations into the efficacy of nearest neighbour models to accommodate
spatial dependence in the analysis of data from agricultural field trials,
image restoration from noisy data, and texture generation using lattice models.Comment: 26 pages, 14 figures; minor revisions, omission of full bibliograph
A generalized Gaussian process model for computer experiments with binary time series
Non-Gaussian observations such as binary responses are common in some
computer experiments. Motivated by the analysis of a class of cell adhesion
experiments, we introduce a generalized Gaussian process model for binary
responses, which shares some common features with standard GP models. In
addition, the proposed model incorporates a flexible mean function that can
capture different types of time series structures. Asymptotic properties of the
estimators are derived, and an optimal predictor as well as its predictive
distribution are constructed. Their performance is examined via two simulation
studies. The methodology is applied to study computer simulations for cell
adhesion experiments. The fitted model reveals important biological information
in repeated cell bindings, which is not directly observable in lab experiments.Comment: 49 pages, 4 figure
A survey of statistical network models
Networks are ubiquitous in science and have become a focal point for
discussion in everyday life. Formal statistical models for the analysis of
network data have emerged as a major topic of interest in diverse areas of
study, and most of these involve a form of graphical representation.
Probability models on graphs date back to 1959. Along with empirical studies in
social psychology and sociology from the 1960s, these early works generated an
active network community and a substantial literature in the 1970s. This effort
moved into the statistical literature in the late 1970s and 1980s, and the past
decade has seen a burgeoning network literature in statistical physics and
computer science. The growth of the World Wide Web and the emergence of online
networking communities such as Facebook, MySpace, and LinkedIn, and a host of
more specialized professional network communities has intensified interest in
the study of networks and network data. Our goal in this review is to provide
the reader with an entry point to this burgeoning literature. We begin with an
overview of the historical development of statistical network modeling and then
we introduce a number of examples that have been studied in the network
literature. Our subsequent discussion focuses on a number of prominent static
and dynamic network models and their interconnections. We emphasize formal
model descriptions, and pay special attention to the interpretation of
parameters and their estimation. We end with a description of some open
problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference
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