High-dimensional tests are applied to find relevant sets of variables and
relevant models. If variables are selected by analyzing the sums of products
matrices and a corresponding mean-value test is performed, there is the danger
that the nominal error of first kind is exceeded. In the paper, well-known
multivariate tests receive a new mathematical interpretation such that the
error of first kind of the combined testing and selecting procedure can more
easily be kept.

We consider the problem of modeling the dependence among many time series. We
build high dimensional time-varying copula models by combining pair-copula
constructions (PCC) with stochastic autoregressive copula (SCAR) models to
capture dependence that changes over time. We show how the estimation of this
highly complex model can be broken down into the estimation of a sequence of
bivariate SCAR models, which can be achieved by using the method of simulated
maximum likelihood.

While there is substantial need for dependence models in high dimensions,
most existing models strongly suffer from the curse of dimensionality and
barely balance parsimony and flexibility. In this paper, the new class of
hierarchical Kendall copulas is proposed which tackles these problems.
Constructed with flexible copulas specified for groups of variables in
different hierarchical levels, hierarchical Kendall copulas are able to model
complex dependence patterns without severe restrictions.

A new family of tree models is proposed, which we call "differential trees."
A differential tree model is constructed from multiple data sets and aims to
detect distributional differences between them. The new methodology differs
from the existing difference and change detection techniques in its
nonparametric nature, model construction from multiple data sets, and
applicability to high-dimensional data.

A general approach for Bayesian filtering of multi-object systems is studied,
with particular emphasis on the model where each object generates observations
independently of other objects. The approach is based on variational calculus
applied to generating functionals, using the general version of Faa di Bruno's
formula for Gateaux differentials. This result enables us to determine some
general formulae for the updated generating functional after the application of
a multi-object analogue of Bayes' rule.

Meta-analysis involves combining summary information for related but
independent studies. It uses different relationship to combine position measure
as well as dispersion measures. The objective of this study is to discuss a
relationship among the standard deviation of a data set and the standard
deviation and mean of two part of this set. The problem was proposed in a
systematic review with meta-analysis that combined two studies with missing
data.

Discussion of "Is Bayes Posterior just Quick and Dirty Confidence?" by D. A.
S. Fraser [arXiv:1112.5582].

This paper derives the asymptotic distribution of variance weighted
Kolmogorov-Smirnov statistics for conditional moment inequality models for the
case of a one dimensional covariate. The asymptotic distribution depends on the
data generating process only through the variance of a single random variable,
leading to critical values that can be calculated analytically. By arguments in
Armstrong (2011b), the resulting tests achieve the best minimax rate for local
alternatives out of available approaches in a broad class of settings.

The ultimate goal of regression analysis is to obtain information about the
conditional distribution of a response given a set of explanatory variables.
This goal is, however, seldom achieved because most established regression
models only estimate the conditional mean as a function of the explanatory
variables and assume that higher moments are not affected by the regressors.
The underlying reason for such a restriction is the assumption of additivity of
signal and noise. We propose to relax this common assumption in the framework
of transformation models.

Cluster analysis of biological samples using gene expression measurements is
a common task which aids the discovery of heterogeneous biological
sub-populations having distinct mRNA profiles. Several model-based clustering
algorithms have been proposed in which the distribution of gene expression
values within each sub-group is assumed to be Gaussian. In the presence of
noise and extreme observations, a mixture of Gaussian densities may over-fit
and overestimate the true number of clusters.

We discuss a parametric family of binary distributions for modelling and
sampling high-dimensional binary data with strong dependencies. We extend the
linear conditionals family proposed by Qaqish (2003) to a non-linear
conditionals family which we show to encompass every feasible combination of
mean vector and correlation matrix. We can both sample from this parametric
family and evaluate its mass function point-wise which allows for immediate use
in the context of stochastic optimization, importance sampling or Markov chain
algorithms.

A pair-copula construction is a decomposition of a multivariate copula into a
structured system, called regular vine, of bivariate copulae or pair-copulae.
The standard practice is to model these pair-copulae parametrically, which
comes at the cost of a large model risk, with errors propagating throughout the
vine structure. The empirical pair-copula proposed in the paper provides a
nonparametric alternative still achieving the parametric convergence rate.

Early detection of disease outbreaks is of paramount importance to
implementing intervention strategies to mitigate the severity and duration of
the outbreak. We build methodology that utilizes the characteristic profile of
disease outbreaks to reduce the time to detection and false positive rate. We
model daily counts through a Poisson distribution with additive background plus
outbreak components. The outbreak component has a parametric form with unknown
underlying parameters. A mixture likelihood ratio scan statistic is developed
to maximize parameters over a window in time.

We are concerned with the problem of detecting whether an associations of any
kind exists between random vectors of any dimension. Few tests of independence
exist to date that are consistent against all dependent alternatives. We
propose a powerful test that is applicable in all dimensions, is robust to
outliers, and is consistent against all alternatives. The test has a simple
form and is easy to implement. We demonstrate its good power properties in
simulations and on an example.

Inference for causal effects can benefit from the availability of an
instrumental variable (IV) which, by definition, is associated with the given
exposure, but not with the outcome of interest other than through a causal
exposure effect.

David Ross Brillinger was born on the 27th of October 1937, in Toronto,
Canada. In 1955, he entered the University of Toronto, graduating with a B.A.
with Honours in Pure Mathematics in 1959, while also serving as a Lieutenant in
the Royal Canadian Naval Reserve. He was one of the five winners of the Putnam
mathematical competition in 1958. He then went on to obtain his M.A. and Ph.D.
in Mathematics at Princeton University, in 1960 and 1961, the latter under the
guidance of John W. Tukey.

We propose a simple and intuitive algorithm for clustering analysis. This
algorithm stands from the viewpoint of elements to be clustered, and simulates
the process of how they perform self-clustering. At the end of the process,
elements belong to the same cluster converge to the same position, which
represents the cluster's location in a p-dimensional space. The algorithm also
manages to isolate noise, therefore is able to produce satisfactory clustering
results even when the level of noise is high enough to obscure or distort the
underlying patterns in the data.

Models for distributions of shapes contained within images can be widely used
in biomedical applications ranging from tumor tracking for targeted radiation
therapy to classifying cells in a blood sample. Our focus is on hierarchical
probability models for the shape and size of simply connected 2D closed curves,
avoiding the need to specify landmarks through modeling the entire curve while
borrowing information across curves for related objects.

In survey statistics, the usual technique for estimating a population total
consists in summing appropriately weighted variable values for the units in the
sample. Different weighting systems exit: sampling weights, GREG weights or
calibration weights for example. In this article, we propose to use the inverse
of conditional inclusion probabilities as weighting system. We study examples
where an auxiliary information enables to perform an a posteriori
stratification of the population. We show that, in these cases, exact
computations of the conditional weights are possible.

Goodness-of-fit tests based on the Euclidean distance often outperform
chi-square and other classical tests (including the standard exact tests) by at
least an order of magnitude when the model being tested for goodness-of-fit is
a discrete probability distribution that is not close to uniform. The present
article discusses numerous examples of this.

Nowadays, the high-precision estimation of nonlinear parameters such as
quantiles, Gini indices or other measures of inequality is particularly
crucial. In the present paper, we propose a general class of estimators for
such parameters that take into account complete univariate auxiliary
information. We construct unique survey weights through a nonparametric
model-assisted approach that can be used by means of the plugg-in principle to
estimate the nonlinear parameters.

Discussion of "Feature Matching in Time Series Modeling" by Y. Xia and H.
Tong [arXiv:1104.3073]

Discussion of "Feature Matching in Time Series Modeling" by Y. Xia and H.
Tong [arXiv:1104.3073]

In applied sciences, we often deal with deterministic simulation models that
are too slow for simulation-intensive tasks such as calibration or real-time
control. In this paper, an emulator for a generic dynamic model, given by a
system of ordinary non-linear differential equations, is developed. The
non-linear differential equations are linearized and Gaussian white noise is
added to account for the non-linearities. The resulting linear stochastic
system is conditioned on a set of solutions of the non-linear equations that
have been calculated prior to the emulation.

Bayes linear analysis and approximate Bayesian computation (ABC) are
techniques commonly used in the Bayesian analysis of complex models. In this
article we connect these ideas by demonstrating that regression-adjustment ABC
algorithms produce samples for which first and second order moment summaries
approximate adjusted expectation and variance for a Bayes linear analysis. This
gives regression-adjustment methods a useful interpretation and role in
exploratory analysis in high-dimensional problems.

This paper outlines a uni?ed framework for high dimensional variable
selection for classification problems. Traditional approaches to ?nding
interesting variables mostly utilize only partial information through moments
(like mean difference). On the contrary, in this paper we address the question
of variable selection in full generality from a distributional point of view.
If a variable is not important for classification, then it will have similar
distributional aspect under different classes.

In this paper we propose a sparse coefficient estimation procedure for
autoregressive (AR) models based on penalized conditional maximum likelihood.
The penalized conditional maximum likelihood estimator (PCMLE) thus developed
has the advantage of performing simultaneous coefficient estimation and model
selection. Mild conditions are given on the penalty function and the innovation
process, under which the PCMLE satisfies a strong consistency, local $N^{-1/2}$
consistency, and oracle property, respectively, where N is sample size.

We present a new computational approach to approximating a large, noisy data
table by a low-rank matrix with sparse singular vectors. The approximation is
obtained from thresholded subspace iterations that produce the singular vectors
simultaneously, rather than successively as in competing proposals. We
introduce novel ways to estimate thresholding parameters which obviate the need
for computationally expensive cross-validation.

In this paper we have demonstrated a complete framework for the analysis of
microarray time series data. The unique characteristics of microarry data lend
themselves well to a functional data analysis approach and we have shown how
this naturally extends to the inclusion of covariates such as age and sex.

In this paper we discuss the variable selection method from \ell0-norm
constrained regression, which is equivalent to the problem of finding the best
subset of a fixed size. Our study focuses on two aspects, consistency and
computation. We prove that the sparse estimator from such a method can retain
all of the important variables asymptotically for even exponentially growing
dimensionality under regularity conditions.

In this article two methods to distinguish between polynomial and exponential
tails are introduced. The methods are mainly based on the properties of the
residual coefficient of variation for the exponential and non-exponential
distributions. A graphical method, called CV-plot, shows departures from
exponentiality in the tails. It is, in fact, the empirical coefficient of
variation of the conditional excedance over a threshold. The plot is applied to
the daily log-returns of exchange rates of US dollar and Japan yen.

The most popular approach in extreme value statistics is the modelling of
threshold exceedances using the asymptotically motivated generalised Pareto
distribution. This approach involves the selection of a high threshold above
which the model fits the data well. Sometimes, few observations of a
measurement process might be recorded in applications and so selecting a high
quantile of the sample as the threshold leads to almost no exceedances.

In this paper linear canonical correlation analysis (LCCA) is generalized by
applying a structured transform to the joint probability distribution of the
considered pair of random vectors, i.e., a transformation of the joint
probability measure defined on their joint observation space. This framework,
called measure transformed canonical correlation analysis (MTCCA), applies LCCA
to the data after transformation of the joint probability measure.

In the this paper, the authors propose to estimate the density of a targeted
population with a weighted kernel density estimator (wKDE) based on a weighted
sample. Bandwidth selection for wKDE is discussed. Three mean integrated
squared error based bandwidth estimators are introduced and their performance
is illustrated via Monte Carlo simulation. The least-squares cross-validation
method and the adaptive weight kernel density estimator are also studied.

Regularization techniques are widely used for tackling
high-dimension-low-sample-size problems. Yet, finding the right amount of
regularization can be challenging, especially in the unsupervised setting such
as structure learning problems where traditional methods such as BIC or
cross-validation often do not work well. In this paper, we propose a new method
--- Bootstrap Inference for Network COnstruction (BINCO) --- to infer networks
by directly controlling the false discovery rates (FDRs) of the selected edges.
This method utilizes the idea of model aggregation.

We introduce a method for aggregating many least squares estimator so that
the resulting estimate has two properties: sparsity and structure. That is,
only a few candidate covariates are used in the resulting model, and the
selected covariates follow some structure over the candidate covariates that is
assumed to be known a priori. While sparsity is well studied in many settings,
including aggregation, structured sparse methods are still emerging.

We consider the Pickands process {equation*} P_{n}(s)=\log (1/s)^{-1}\log
\frac{X_{n-k+1,n}-X_{n-[k/s]+1,n}}{% X_{n-[k/s]+1,n}-X_{n-[k/s^{2}]+1,n}},
{equation*} {equation*} (\frac{k}{n}\leq s^2 \leq 1), {equation*} which is a
generalization of the classical Pickands estimate $P_{n}(1/2)$ of the extremal
index. We undertake here a purely stochastic process view for the asymptotic
theory of that process by using the
Cs\"{o}rg\H{o}-Cs\"{o}rg\H{o}-Horv\'{a}th-Mason (1986) \cite{cchm} weighted
approximation of the empirical and quantile processes to suitable Brownian
bridges.

We propose a Bayesian nonparametric approach to the problem of jointly
modeling multiple related time series. Our approach is based on the discovery
of a set of latent, shared dynamical behaviors. Using a beta process prior, the
size of the set and the sharing pattern are both inferred from data. We develop
efficient Markov chain Monte Carlo methods based on the Indian buffet process
representation of the predictive distribution of the beta process, without
relying on a truncated model.

We give an overview of several aspects arising in the statistical analysis of
extreme risks with actuarial applications in view. In particular it is
demonstrated that empirical process theory is a very powerful tool, both for
the asymptotic analysis of extreme value estimators and to devise tools for the
validation of the underlying model assumptions. While the focus of the paper is
on univariate tail risk analysis, the basic ideas of the analysis of the
extremal dependence between different risks are also outlined.

We present a model of voting behaviour based on a version of aggregated
overdispersed multinomial distributions; relative to a similar model by
\citet{BP86}, our model is based on more realistic assumptions and free from
certain shortcomings of the previous model.

The model evidence is a vital quantity in the comparison of statistical
models under the Bayesian paradigm. This paper presents a review of commonly
used methods. We outline some guidelines and offer some practical advice. The
reviewed methods are compared for two examples; non-nested Gaussian linear
regression and covariate subset selection in logistic regression.

For many decades, statisticians have made attempts to prepare the Bayesian
omelette without breaking the Bayesian eggs; that is, to obtain probabilistic
likelihood-based inferences without relying on informative prior distributions.
A recent example is Murray Aitkin's recent book, {\em Statistical Inference},
which presents an approach to statistical hypothesis testing based on
comparisons of posterior distributions of likelihoods under competing models.
Aitkin develops and illustrates his method using some simple examples of
inference from iid data and two-way tests of independence.

This paper introduces a general framework of covariance structures that can
be verified in many popular statistical models, such as factor and random
effect models. The new structure is a summation of low rank and sparse
matrices. We propose a LOw Rank and sparsE Covariance estimator (LOREC) to
exploit this general structure in the high-dimensional setting. Analysis of
this estimator shows that it recovers exactly the rank and support of the two
components respectively. Convergence rates under various norms are also
presented.

We consider the problem of estimating multiple related but distinct graphical
models on the basis of a high-dimensional data set with observations that
belong to distinct classes. A motivating example occurs in the analysis of gene
expression data for tissue samples with and without cancer. In this case, we
might wish to estimate a gene expression network for the normal tissue and a
gene expression network for the tumor tissue.

Extremely contagious, acute, immunizing childhood infections like measles can
exhibit spatiotemporal dynamics that depend on the nature of spatial contagion
and spatiotemporal variations in population structure and demography. We study
a metapopulation model for regional measles dynamics that uses a gravity
coupling model and a time series susceptible- infected-recovered (TSIR) model
for local dynamics.

The generalizations of instantaneous frequency and instantaneous bandwidth to
a bivariate signal are derived. These are uniquely defined whether the signal
is represented as a pair of real-valued signals, or as one analytic and one
anti-analytic signal. A nonstationary but oscillatory bivariate signal has a
natural representation as an ellipse whose properties evolve in time, and this
representation provides a simple geometric interpretation for the bivariate
instantaneous moments.

When a posterior distribution has multiple modes, unconditional expectations,
such as the posterior mean, may not offer informative summaries of the
distribution. Motivated by this problem, we propose to decompose the sample
space of a multimodal distribution into domains of attraction of local modes.
Domain-based representations are defined to summarize the probability masses of
and conditional expectations on domains of attraction, which are much more
informative than the mean and other unconditional expectations.

The purpose of this paper is to propose methodologies for statistical
inference of low-dimensional parameters with high-dimensional data. We focus on
constructing confidence intervals for individual coefficients and linear
combinations of several of them in a linear regression model, although our
ideas are applicable in a much broad context. The theoretical results presented
here provide sufficient conditions for the asymptotic normality of the proposed
estimators along with a consistent estimator for their finite-dimensional
covariance matrices.

The proposed smooth blockwise iterative thresholding estimator (SBITE) is a
model selection technique defined as a fixed point reached by iterating a
likelihood gradient-based thresholding function. The smooth James-Stein
thresholding function has two regularization parameters $\lambda$ and $\nu$,
and a smoothness parameter $s$. It enjoys smoothness like ridge regression and
selects variables like lasso.

We study properties of Fisher distribution (von Mises-Fisher distribution,
matrix Langevin distribution) on the rotation group SO(3). In particular we
apply the holonomic gradient descent, introduced by Nakayama et al. (2011), and
a method of series expansion for evaluating the normalizing constant of the
distribution and for computing the maximum likelihood estimate. The rotation
group can be identified with the Stiefel manifold of two orthonormal vectors.
Therefore from the viewpoint of statistical modeling, it is of interest to
compare Fisher distributions on these manifolds.

This paper is devoted to the theory and application of a novel class of
models for binary data, which we call log-mean linear (LML) models. The
characterizing feature of these models is that they are specified by linear
constraints on the LML parameter, defined as a log-linear expansion of the mean
parameter of the multivariate Bernoulli distribution. We show that marginal
independence relationships between variables can be specified by setting
certain LML interactions to zero and, more specifically, that graphical models
of marginal independence are LML models.

Choice models, which capture popular preferences over objects of interest,
play a key role in making decisions whose eventual outcome is impacted by human
choice behavior. In most scenarios, the choice model, which can effectively be
viewed as a distribution over permutations, must be learned from observed data.
The observed data, in turn, may frequently be viewed as (partial, noisy)
information about marginals of this distribution over permutations.

This paper proposes a strategy for regularized estimation in multi-way
contingency tables, which are common in meta-analyses and multi-center clinical
trials. Our approach is based on data augmentation, and appeals heavily to a
novel class of Polya-Gamma distributions. Our main contributions are to build
up the relevant distributional theory and to demonstrate three useful features
of this data-augmentation scheme.

In sparse regression modeling with regularization such as the lasso, elastic
net and bridge regression, it is important to select appropriate values of
tuning parameters including regularization parameters. The choice of tuning
parameters can be viewed as a model selection and evaluation problem. The
degrees of freedom, which leads to Mallows' $C_p$ criterion, plays a key role
in the theory of model selection. In the present paper, we propose an efficient
algorithm which computes the degrees of freedom sequentially by extending the
generalized path seeking (GPS) algorithm.

We propose new affine invariant tests for multivariate normality, based on
independence characterizations of the sample moments of the normal
distribution. The test statistics are obtained using canonical correlations
between sets of sample moments, generalizing the Lin-Mudholkar test for
normality. The tests are compared to some popular tests based on Mardia's
skewness and kurtosis measures in an extensive simulation power study and are
found to offer higher power against many of the alternatives.

This paper introduces a new approach to analysing spatial point data
clustered along or around a system of curves or `fibres'. Such data arise in
catalogues of galaxy locations, recorded locations of earthquakes, aerial
images of minefields, and pore patterns on fingerprints. Finding the underlying
curvilinear structure of these point-pattern data sets may not only facilitate
a better understanding of how they arise but also aid reconstruction of missing
data. We base the space of fibres on the set of integral lines of an
orientation field.

A conditional independence graph is a concise representation of pairwise
conditional independence among many variables. We propose Graphical Random
Forests (GRaFo) for estimating pairwise conditional independence relationships
among mixed-type, i.e. continuous and discrete, variables. The number of edges
is a tuning parameter in any graphical model estimator and there is no obvious
number that constitutes a good choice. Stability Selection helps choosing this
parameter with respect to a bound on the expected number of false positives
(error control).

A dynamic treatment regime effectively incorporates both accrued information
and long-term effects of treatment from specially designed clinical trials. As
these become more and more popular in conjunction with longitudinal data from
clinical studies, the development of statistical inference for optimal dynamic
treatment regimes is a high priority.

A function based nonlinear least squares estimation (FNLSE) method is
proposed and investigated in parameter estimation of Jelinski-Moranda software
reliability model. FNLSE extends the potential fitting functions of traditional
least squares estimation (LSE), and takes the logarithm transformed nonlinear
least squares estimation (LogLSE) as a special case.

We perform a Bayesian analysis on abundance data for ten species of North
American duck, using the results to investigate the evidence in favour of
biologically motivated hypotheses about the causes and mechanisms of density
dependence in these species. We explore the capabilities of our methods to
detect density dependent effects, both by simulation and through analyzes of
real data. The effect of the prior choice on predictive accuracy is also
examined.

If a discrete probability distribution in a model being tested for
goodness-of-fit is not close to uniform, then forming the Pearson chi-square
statistic can involve division by nearly zero. This often leads to serious
trouble in practice -- even in the absence of round-off errors -- as the
present article illustrates via numerous examples.

Discussion of "Estimating Random Effects via Adjustment for Density
Maximization" by C. Morris and R. Tang [arXiv:1108.3234]

Rejoinder of "Impact of Frequentist and Bayesian Methods on Survey Sampling
Practice: A Selective Appraisal" by J. N. K. Rao [arXiv:1108.2356]

Discussion of "Bayesian Models and Methods in Public Policy and Government
Settings" by S. E. Fienberg [arXiv:1108.2177]

This comment emphasizes the importance of model checking and model fitting
when making inferences about finite population quantities. It also suggests the
value of using unit level models when making inferences for small
subpopulations, that is, "small area" analyses [arXiv:1108.2356].

Discussion of "Bayesian Models and Methods in Public Policy and Government
Settings" by S. E. Fienberg [arXiv:1108.2177]

Fienberg convincingly demonstrates that Bayesian models and methods represent
a powerful approach to squeezing illumination from data in public policy
settings. However, no school of inference is without its weaknesses, and, in
the face of the ambiguities, uncertainties, and poorly posed questions of the
real world, perhaps we should not expect to find a formally correct inferential
strategy which can be universally applied, whatever the nature of the question:
we should not expect to be able to identify a "norm" approach.

We propose an automatic Bayesian approach to the selection of covariates and
their penalised splines transformations in generalised additive models.
Specification of a default, hyper-g prior for the model parameters and a
multiplicity-correction prior for the models themselves is crucial for this
task. We introduce the methodology in the normal model and extend it to
non-normal exponential families. Two applications from the literature
illustrate the proposed approach. An efficient implementation is available in
an R-package.

Discussion of "Objective Priors: An Introduction for Frequentists" by M.
Ghosh [arXiv:1108.2120]

Rejoinder of "Calibrated Bayes, for Statistics in General, and Missing Data
in Particular" by R. Little [arXiv:1108.1917]

Discussion of "Calibrated Bayes, for Statistics in General, and Missing Data
in Particular" by R. Little [arXiv:1108.1917]

We introduce state-space models where the functionals of the observational
and the evolu- tionary equations are unknown, and treated as random functions
evolving with time. Thus, our model is nonparametric and generalizes parametric
state-space models, such as the extended Kalman filter. This random function
approach also frees us from the restrictive assumption that the functional
forms, although time-dependent, are of fixed forms.

Identifying the risk factors for mental illnesses is of significant public
health importance. Diagnosis, stigma associated with mental illnesses,
comorbidity, and complex etiologies, among others, make it very challenging to
study mental disorders. Genetic studies of mental illnesses date back at least
a century ago, beginning with descriptive studies based on Mendelian laws of
inheritance.

We study asymptotic behavior of Monte Carlo method. Local consistency is one
of an ideal property of Monte Carlo method. However, it may fail to hold local
consistency for several reason. In fact, in practice, it is more important to
study such a non-ideal behavior. We call local degeneracy for one of a
non-ideal behavior of Monte Carlo methods. We show some equivalent conditions
for local degeneracy.

Starting with the neo-Bayesian revival of the 1950s, many statisticians
argued that it was inappropriate to use Bayesian methods, and in particular
subjective Bayesian methods in governmental and public policy settings because
of their reliance upon prior distributions. But the Bayesian framework often
provides the primary way to respond to questions raised in these settings and
the numbers and diversity of Bayesian applications have grown dramatically in
recent years.

Bayesian methods are increasingly applied in these days in the theory and
practice of statistics. Any Bayesian inference depends on a likelihood and a
prior. Ideally one would like to elicit a prior from related sources of
information or past data. However, in its absence, Bayesian methods need to
rely on some "objective" or "default" priors, and the resulting posterior
inference can still be quite valuable. Not surprisingly, over the years, the
catalog of objective priors also has become prohibitively large, and one has to
set some specific criteria for the selection of such priors.

In this paper, we present a generalized estimating equations based estimation
approach and a variable selection procedure for single-index models when the
observed data are clustered. Unlike the case of independent observations,
bias-correction is necessary when general working correlation matrices are used
in the estimating equations.

Mixed linear models are commonly used in repeated measures studies. They
account for the dependence amongst observations obtained from the same
experimental unit. Oftentimes, the number of observations is small, and it is
thus important to use inference strategies that incorporate small sample
corrections. In this paper, we develop modified versions of the likelihood
ratio test for fixed effects inference in mixed linear models. In particular,
we derive a Bartlett correction to such a test and also to a test obtained from
a modified profile likelihood function.

Covariate adjustment is an important tool in the analysis of randomized
clinical trials and observational studies. It can be used to increase
efficiency and thus power, and to reduce possible bias. While most statistical
tests in randomized clinical trials are nonparametric in nature, approaches for
covariate adjustment typically rely on specific regression models, such as the
linear model for a continuous outcome, the logistic regression model for a
dichotomous outcome and the Cox model for survival time. Several recent efforts
have focused on model-free covariate adjustment.

Wavelet coefficients are estimated recursively at progressively coarser
scales recursively. As a result, the estimation is prone to multiplicative
propagation of truncation errors due to quantization and round-off at each
stage. Yet, the influence of this propagation on wavelet filter output has not
been explored systematically.

This paper suggests five measures of association between two random vectors X
= (X_1, ..., X_p) and Y = (Y_1, ..., Y_q). They are copula based and therefore
invariant with respect to the marginal distributions of the components X_i and
Y_j. The measures capture positive as well as negative association of X and Y.
In case p = q = 1 they reduce to Spearman's rho. Various properties of these
new measures are investigated. Nonparametric estimators, based on ranks, for
the measures are derived and their small sample behaviour is investigated by
simulation.

We investigate the performance of the scan (maximum likelihood ratio
statistic) and of the average likelihood ratio statistic in the problem of
detecting a deterministic signal with unknown spatial extent in the
prototypical univariate sampled data model with white Gaussian noise. Our
results show that the scan statistic, a popular tool for detection problems, is
optimal only for the detection of signals with the smallest spatial extent. For
signals with larger spatial extent the scan is suboptimal, and the power loss
can be considerable.

We present a Bayesian surrogate model for the analysis of periodic or
quasi-periodic time series data. We describe a computationally efficient
implementation that enables Bayesian model comparison. We apply this model to
simulated and real exoplanet observations. We discuss the results and
demonstrate some of the challenges for applying our surrogate model to
realistic exoplanet data sets. In particular, we find that analyses of real
world data should pay careful attention to the effects of uneven spacing of
observations and the choice of prior for the "jitter" parameter.

The assumption of log-concavity is an attractive and flexible nonparametric
shape constraint in distribution modelling. In this work, we study the maximum
likelihood estimator (MLE) of a log-concave probability mass function. We show
that the MLE is strongly consistent and derive pointwise asymptotic theory,
which is used to calculate confidence bands for the true probability mass
function. The proposed estimator and associated confidence bands may be easily
computed using the R package logcondiscr.

Global Markov properties in mixed graphs are usually formulated in terms of
the path-oriented m-separation or by use of augmented graphs (similar to moral
graphs in the case of directed acyclic graphs). We provide an alternative
characterization that can be easily implemented.

We explore the Cauchy and a new heavy tailed (Fuquene, Perez and Pericchi
(2011)) priors to estimate proportions on small areas. Hierarchical models and
the Binomial likelihood in the exponential family form are used. We believe
that the heavy tailed priors in survey sampling settings could be more
effective than the choice of noninformative priors to eliminate antipathy
towards methods that involve subjective elements or assumptions. To illustrate
the robust Bayesian approach, we apply this methodology in a popular example:
"the clement problem".

Extreme-value copulas arise in the asymptotic theory for componentwise maxima
of independent random samples. An extreme-value copula is determined by its
Pickands dependence function, which is a function on the unit simplex subject
to certain shape constraints that arise from an integral transform of an
underlying measure called spectral measure. Multivariate extensions are
provided of certain rank-based nonparametric estimators of the Pickands
dependence function.

In this paper we propose a new wider class of hypergeometric heavy tailed
priors that are given as the convolution of a Student-t density for the
location parameter and a Scaled Beta2 prior for the variance. These priors have
heavier tails than Student-t prior, and the variances have a sensible behavior
both at the origin and at the tail, making it suitable for objective analysis.
Since the representation of our proposal is a scale mixture, it is suitable to
detect sudden changes in the model.

Statistical emulators of computer simulators have proven to be useful in a
variety of applications.

We study the properties of false discovery rate (FDR) thresholding, viewed as
a classification procedure. The "0"-class (null) is assumed to have a known,
symmetric log-concave density while the "1"-class (alternative) is obtained
from the "0"-class either by translation (location model) or by scaling (scale
model). Furthermore, the "1"-class is assumed to have a small number of
elements w.r.t. the "0"-class (sparsity). Non-asymptotic oracle inequalities
are derived for the excess risk of FDR thresholding.

In this paper we study grouped variable selection problems by proposing a
specified prior, called the nested spike and slab prior, to model collective
behavior of regression coefficients. At the group level, the nested spike and
slab prior puts positive mass on the event that the l2-norm of the grouped
coefficients is equal to zero. At the individual level, each coefficient is
assumed to follow a spike and slab prior.

We consider the problem of calibration and the GREG method as suggested and
studied in Deville and Sarndal (1992). We show that a GREG type estimator is
typically not minimal variance unbiased estimator even asymptotically. We
suggest a similar estimator which is unbiased but is asymptotically with a
minimal variance.

We consider the nonparametric regression estimation problem of recovering an
unknown response function $f$ on the basis of incomplete data when the design
points follow a known density $g$ with a finite number of well separated zeros.
In particular, we consider two different cases: when $g$ has zeros of a
polynomial order and when $g$ has zeros of an exponential order. These two
cases correspond to moderate and severe data losses, respectively.

Subject of this paper is ASN-Minimax (AM) double sampling plans by variables
for a normally distributed quality characteristic with unknown standard
deviation and two-sided specification limits.

Rejoinder of "Statistical Inference: The Big Picture" by R. E. Kass
[arXiv:1106.2895]

Discussion of "Statistical Inference: The Big Picture" by R. E. Kass
[arXiv:1106.2895]

Predictive recursion is an accurate and computationally efficient algorithm
for nonparametric estimation of mixing densities in mixture models. In
semiparametric mixture models, however, the algorithm fails to account for any
uncertainty in the additional unknown structural parameter. As an alternative
to existing profile likelihood methods, we treat predictive recursion as a
filter approximation to fitting a fully Bayes model, whereby an approximate
marginal likelihood of the structural parameter emerges and can be used for
inference.

This paper focuses on Bayesian shrinkage for covariance matrix estimation. We
examine posterior properties and frequentist risks of Bayesian estimators based
on new hierarchical inverse-Wishart priors. More precisely, we give the
existence conditions of the posterior distributions. Advantages in terms of
numerical simulations of posteriors are shown. A simulation study illustrates
the performance of the estimation procedures under three loss functions for
relevant sample sizes and various covariance structures.

Discussion of "Statistical Inference: The Big Picture" by R. E. Kass
[arXiv:1106.2895]

After a brief review of recent advances in sequential analysis involving
sequential generalized likelihood ratio tests, we discuss their use in
psychometric testing and extend the asymptotic optimality theory of these
sequential tests to the case of sequentially generated experiments, of
particular interest in computerized adaptive testing. We then show how these
methods can be used to design adaptive mastery tests, which are asymptotically
optimal and are also shown to provide substantial improvements over currently
used sequential and fixed length tests.

A factor effect study was conducted on a set of observations at the
contingency of a series of plant species and bacteria species regarding the
antibacterial activity of essential oil extracts. The study reveals a very good
agreement between the observations and the hypothesis of independent and
multiplicative effect of plant and bacteria species factors on the
antibacterial activity. Shaping of the observable to a Negative Binomial
distribution allowed the separation of two convoluted Gamma distributions in
the observable further assigned to the distribution of factors.

Image analysis frequently deals with shape estimation and image
reconstruction. The ob jects of interest in these problems may be thought of as
random sets, and one is interested in finding a representative, or expected,
set. We consider a definition of set expectation using oriented distance
functions and study the properties of the associated empirical set. Conditions
are given such that the empirical average is consistent, and a method to
calculate a confidence region for the expected set is introduced. The proposed
method is applied to both real and simulated data examples.

The danger of confusing long-range dependence with non-stationarity has been
pointed out by many authors. Finding an answer to this difficult question is of
importance to model time-series showing trend-like behavior, such as river
run-off in hydrology, historical temperatures in the study of climates changes,
or packet counts in network traffic engineering. The main goal of this paper is
to develop a test procedure to detect the presence of non-stationarity for a
class of processes whose $K$-th order difference is stationary.

The beta-Bernoulli process provides a Bayesian nonparametric prior for models
involving collections of binary-valued features. A draw from the beta process
provides an infinite collection of probabilities in the unit interval, and a
draw from the Bernoulli process turns these into binary-valued features. Recent
work has shown how to derive stick-breaking representations for the beta
process, by analogy to Sethuraman's derivation of a stick-breaking
representation for the Dirichlet process.

The R package spikeSlabGAM implements Bayesian variable selection, model
choice, and regularized estimation in (geo-)additive mixed models for Gaussian,
binomial, and Poisson responses. Its purpose is to (1) choose an appropriate
subset of potential covariates and their interactions, (2) to determine whether
linear or more flexible functional forms are required to model the effects of
the respective covariates, and (3) to estimate their shapes.

In this paper we propose a family of robust estimates for isotonic
regression: isotonic M-estimators. We show that their asymptotic distribution
is, up to an scalar factor, the same as that of Brunk's classical isotonic
estimator. We also derive the influence function and the breakdown point of
these estimates. Finally we perform a Monte Carlo study that shows that the
proposed family includes estimators that are simultaneously highly efficient
under gaussian errors and highly robust when the error distribution has heavy
tails.

The variance covariance matrix plays a central role in the inferential
theories of high dimensional factor models in finance and economics. Popular
regularization methods of directly exploiting sparsity are not directly
applicable to many financial problems. Classical methods of estimating the
covariance matrices are based on the strict factor models, assuming independent
idiosyncratic components. This assumption, however, is restrictive in practical
applications.

This paper presents a practical and simple fully nonparametric multivariate
smoothing procedure that adapts to the underlying smoothness of the true
regression function. Our estimator is easily computed by successive application
of existing base smoothers (without the need of selecting an optimal smoothing
parameter), such as thin-plate spline or kernel smoothers.

The propensity score analysis is one of the most widely used methods for
studying the causal treatment effect in observational studies. This paper
studies treatment effect estimation with the method of matching weights. This
method resembles propensity score matching but offers a number of new features
including efficient estimation, rigorous variance calculation, simple
asymptotics, statistical tests of balance, clearly identified target population
with optimal sampling property, and no need for choosing matching algorithm and
caliper size.

Starting from the characterization of extreme-value copulas based on
max-stability, large-sample tests of extreme-value dependence for multivariate
copulas are studied. The two key ingredients of the proposed tests are the
empirical copula of the data and a multiplier technique for obtaining
approximate p-values for the derived statistics. The asymptotic validity of the
multiplier approach is established, and the finite-sample performance of a
large number of candidate test statistics is studied through extensive Monte
Carlo experiments for data sets of dimension two to five.

We propose in this paper a random intercept Poisson model in which the random
effect distribution is assumed to follow a generalized log-gamma (GLG)
distribution. We derive the first two moments for the marginal distribution as
well as the intraclass correlation. Even though numerical integration methods
are in general required for deriving the marginal models, we obtain the
multivariate negative binomial model for a particular parameter setting of the
hierarchical model.

Latent variable models for ordinal data represent a useful tool in different
fields of research in which the constructs of interest are not directly
observable. In such models, problems related to the integration of the
likelihood function can arise since analytical solutions do not exist.
Numerical approximations, like the widely used Gauss Hermite (GH) quadrature,
are generally applied to solve these problems. However, GH becomes unfeasible
as the number of latent variables increases. Thus, alternative solutions have
to be found.

In a nonparametric linear regression model we study a variant of LASSO,
called square-root LASSO, which does not require the knowledge of the scaling
parameter $\sigma$ of the noise or bounds for it. This work derives new finite
sample upper bounds for prediction norm rate of convergence, $\ell_1$-rate of
converge, $\ell_\infty$-rate of convergence, and sparsity of the square-root
LASSO estimator. A lower bound for the prediction norm rate of convergence is
also established.

We consider the problem of learning causal information between random
variables in DAGs when allowing arbitrarily many latent and selection
variables. The FCI algorithm (Spirtes et al., 1999) has been explicitly
designed to infer conditional independence and causal information in such
settings. However, FCI is computationally infeasible for large graphs. We
therefore propose a new algorithm, the RFCI algorithm, which is much faster
than FCI. In some situations the output of RFCI is slightly less informative,
in particular with respect to conditional independence information.

We generalize the half-Cauchy prior for a global scale parameter to the wider
class of hypergeometric inverted-beta priors. We derive expressions for
posterior moments and marginal densities when these priors are used for a
top-level normal variance in a Bayesian hierarchical model. Finally, we prove a
result that characterizes the frequentist risk of the Bayes estimators under
all priors in the class.

In conventional target tracking systems, human operators use the estimated
target tracks to make higher level inference of the target behaviour/intent.
This paper develops syntactic filtering algorithms that assist human operators
by extracting spatial patterns from target tracks to identify
suspicious/anomalous spatial trajectories. The targets' spatial trajectories
are modeled by a stochastic context free grammar (SCFG) and a switched mode
state space model.

This paper develops nonparametric methods for the survival analysis of
epidemic data based on contact intervals. The contact interval from person i to
person j is the time between the onset of infectiousness in i and infectious
contact from i to j, where we define infectious contact as a contact sufficient
to infect a susceptible individual. We show that the Nelson-Aalen estimator
produces an unbiased estimate of the contact interval cumulative hazard
function when who-infects-whom is observed.

We investigate posterior consistency in linear models with a diverging number
of parameters. We first propose a parameter-free multivariate generalized
double Pareto distribution as a default prior choice that preserves some of the
desired characteristics of a joint double exponential distribution with
multivariate Cauchy-like tails. We give sufficient conditions for consistency
when $p/n\rightarrow 0$ and then investigate the behavior of the posterior
under normal, double exponential and multivariate generalized double Pareto
priors.

Reliability-based design optimization (RBDO) has gained much attention in the
past fifteen years as a way of introducing robustness in the process of
designing structures and systems in an optimal manner. Indeed classical
optimization (e.g. minimize some cost under mechanical constraints) usually
leads to solutions that lie at the boundary of the admissible domain, and that
are consequently rather sensitive to uncertainty in the design parameters. In
contrast, RBDO aims at designing the system in a robust way by minimizing some
cost function under reliability constraints.

In 1866 Gregor Mendel published a seminal paper containing the foundations of
modern genetics. In 1936 Ronald Fisher published a statistical analysis of
Mendel's data concluding that "the data of most, if not all, of the experiments
have been falsified so as to agree closely with Mendel's expectations." The
accusation gave rise to a controversy which has reached the present time. There
are reasonable grounds to assume that a certain unconscious bias was
systematically introduced in Mendel's experimentation.

Despite their importance in supporting experimental conclusions, standard
statistical tests are often inadequate for research areas, like the life
sciences, where the typical sample size is small and the test assumptions
difficult to verify. In such conditions, standard tests tend to be overly
conservative, and fail thus to detect significant effects in the data. Here we
define a novel statistical test for the two-sample problem.