1.
Interpreting DNA Evidence: A Review - Foreman, L.A.; Champod, C.; Evett, I.W.; Lambert, J.A.; Pope, S.
The paper provides a review of current issues relating to the use of DNA profiling in
forensic science. A short historical section gives the main statistical milestones that
occurred during a rapid development of DNA technology and operational uses.
Greater detail is then provided for interpretation issues involving STR DNA profiles,
including:
¶ methods that take account of population substructure in DNA calculations;
¶ parallel work carried out by the US National Research Council;
¶ the move away from multiple independence testing in favour of experiments that demonstrate the robustness of casework procedures;
¶ the questionable practice of source attribution `with reasonable scientific certainty';
¶ the effect on the...
2.
The Statistical Interpretation of Forensic Glass Evidence - Curran, James M.
When examining a sample of glass fragments recovered from a suspect in a forensic
case, many questions arise: "Did this man break that window?", "Are these fragments
from the crime scene source?", "Do the fragments recovered from the suspect come
from more than one source?", "How common is it to find glass on someone unrelated
with crime?" etc. Such questions are usually answered with the help of statistical
methods. This paper reviews some of the statistical solutions and problems
encountered in the interpretation and evaluation of forensic glass evidence.
3.
Questioning a Courtroom Proof of the Uniqueness of Fingerprints - Kaye, David H.
Forensic scientists or analysts concerned with "individualization" often presume that
features such as fingerprint minutia are unique to each individual. In the United States,
defendants in criminal cases have been demanding proof of such assumptions. In at least two
cases, the government of the United States has successfully relied on an unpublished statistical
study prepared specifically for litigation to demonstrate the uniqueness of fingerprints. This
article suggests that the study is neither designed nor executed in a way that can show whether an
individual's fingerprint impressions are unique.
4.
Sentencing Illicit Drug Traffickers: How do the Courts Handle Random Sampling Issues? - Izenman, Alan J.
While many European justice systems distinguish between possession of and trafficking in illicit drugs,
sentencing in drug cases in those countries tends not to depend (at least formally) upon
the quantity of drugs seized from a defendant, but rather on the circumstances in which
the defendant was found with drugs. Courts in the United States, on the other hand,
penalize those convicted of drug crimes through an elaborate system of sentencing rules and
guidelines. These sentences depend only upon the amount of drugs (possibly adjusted for
circumstances) and the defendant's criminal history. Because of the enormous amount of work
needed to determine drug type and quantity in...
5.
Copyright Damages and Statistics - Basmann, Robert L.; Slottje, Daniel J.
This paper discusses the statistical issues that arise in conducting an economic damages
analysis in the context of a litigation matter involving copyrights. Calculating damages
in copyright cases turns out to be a natural application for econometric modelling
methods. Surprisingly, elementary statistical issues can be a source of significant debate
between the experts in such matters. In this paper, we present a case study and illustrate
how issues such as interpretation of $p$-values and what "rejection of the null hypothesis"
really "means" in such matters.
6.
Statistical Issues Arising in Disparate Impact Cases and the Use of the Expectancy Curve in Assessing the Validity of Pre-Employment Tests - Gastwirth, Joseph L.; Miao, Weiwen; Zheng, Gang
Disparate impact cases concern the potential adverse effect seemingly neutral employment
practices, such as passing a pre-employment test or possessing a fixed level of education,
have on minority applicants. Their purpose is to eliminate discrimination by subterfuge, i.e.,
imposing a requirement that eliminates many minority individuals who could do the job but who
do not meet the requirement. When a significantly higher fraction of applicants from minority
groups fail the requirement compared to majority applicants, the requirement needs to be shown
to be job-related. Statistical techniques used at the various stages of a disparate impact
claim are described. Properties of the expectancy curve, which describes the utility...
7.
Multiple Imputation: Theory and Method - Zhang, Paul
In this review paper, we discuss the theoretical background of multiple imputation, describe how
to build an imputation model and how to create proper imputations. We also present the rules for
making repeated imputation inferences. Three widely used multiple imputation methods, the
propensity score method, the predictive model method and the Markov chain Monte Carlo (MCMC)
method, are presented and discussed.
8.
Proper and Improper Multiple Imputation - Feodor Nielsen, Soren
Multiple imputation has become viewed as a general solution to
missing data problems in statistics. However, in order to lead to
consistent asymptotically normal estimators, correct variance
estimators and valid tests, the imputations must be proper.
So far it seems that only Bayesian multiple imputation, i.e.\
using a Bayesian predictive distribution to generate the
imputations, or approximately Bayesian multiple imputations has
been shown to lead to proper imputations in some settings. In this
paper, we shall see that Bayesian multiple imputation does not
generally lead to proper multiple imputations. Furthermore, it
will be argued that for general statistical use, Bayesian multiple
imputation is inefficient even when it is proper.
9.
Dimension Reduction with Linear Discriminant Functions Based on an Odds Ratio Parameterization - van der Linde, Angelika
The association of two random elements with positive joint
probability density function is given by an odds ratio function. The
covariance is an adequate description only in the case of two jointly
Gaussian variables. The impact of the association structure on the set-up
and solution of problems of linear discrimination is investigated, and the
results are related to standard techniques of multivariate analysis,
particularly to canonical correlation analysis, analysis of contingency tables,
discriminant analysis and multidimensional scaling.
10.
Introduction - Balding, David J.; Gastwirth, Joseph L.
The word "statistics" derives from the collection and use of data to assist in the
administration of a state (nation). The justice system is one of the fundamental pillars of
a state, and is central to the political life of most countries. Ideas from probability and
statistics have been used to try to model and improve methods of legal decision-making
since the earliest days of our discipline in the 16th and 17th centuries. More recently, the
debate over the Bayesian statistical paradigm, rooted in probability theory, as a model for
legal reasoning has not subsided since being ignited by Finkelstein & Farley (1970); see
Balding (1998) for...
11.
Environmental Statistics---A Personal View - Guttorp, Peter
The field of environmental statistics is one of rapid growth at the moment. Environmental
decision-making is prevalent in much of the world, and politicians and other
decision makers are requesting new tools for understanding the state of the environment.
In this paper, three case studies involving water pollution, air pollution, and climate
change assessment are presented, together with brief descriptions of some other areas of
environmental statistics. A discussion of future directions of the field concludes the
paper.
12.
\bf Hierarchical Models in Environmental Science - Wikle, Christopher K.
Environmental systems are complicated. They include very intricate
spatio-temporal processes, interacting on a wide variety of
scales. There is increasingly vast amounts of data for such processes
from geographical information systems, remote sensing platforms,
monitoring networks, and computer models. In addition, often there is
a great variety of scientific knowledge available for such systems,
from partial differential equations based on first principles to panel
surveys. It is argued that it is not generally adequate to consider
such processes from a joint perspective. Instead, the processes often
must be considered as a coherently linked system of conditional
models. This paper provides a brief overview of hierarchical
approaches applied to environmental processes. The...
13.
Statistical Assessment of Numerical Models - Fuentes, Montserrat; Guttorp, Peter; Challenor, Peter
Evaluation of physically based computer models for air quality
applications is crucial to assist in control strategy selection. The
high risk of getting the wrong control strategy has costly economic and
social consequences. The objective comparison of modeled concentrations
with observed field data is one approach to assessment of model
performance. For dry deposition fluxes and concentrations of
air pollutants there is a very limited supply of evaluation data sets.
We develop a formal method for
evaluation of the performance of numerical models, which can be
implemented even when the field measurements are very sparse. This
approach is applied to a current U.S. Environmental Protection Agency
air quality model. In other...
14.
Sequential Data Assimilation Techniques in Oceanography - Bertino,, Laurent; Evensen, Geir; Wackernagel, Hans
We review recent developments of sequential data assimilation techniques
used in oceanography to integrate spatio-temporal observations into
numerical models describing physical and ecological dynamics.
Theoretical aspects from the simple case of linear dynamics to the
general case of nonlinear dynamics are
described from a geostatistical point-of-view. Current methods derived
from the Kalman filter are presented from the least complex to the most
general and perspectives for nonlinear estimation by sequential importance resampling
filters are discussed. Furthermore an extension of the ensemble Kalman filter
to transformed Gaussian variables is presented and illustrated using a simplified ecological
model. The described methods are designed for predicting over geographical regions
using a high spatial resolution...
15.
Health Effects of Air Pollution:\\ A Statistical Review - Dominici, Francesca; Sheppard, Lianne; Clyde, Merlise
We critically review and compare epidemiological designs and statistical approaches
to estimate associations between air pollution and health. More specifically, we aim to address the
following questions:
\begin{enumerate}
\item[1.]{\bfWhich epidemiological designs and statistical methods are
available to estimate associations between air pollution and health?}
\item[2.]{\bfWhat are the recent methodological advances in the estimation
of the health effects of air pollution in time series studies?}
\item[3.]{\bfWhat are the the main methodological challenges and future research opportunities relevant to regulatory policy?}
\end{enumerate}
In question 1, we identify strengths and limitations of time series,
cohort, case-crossover and panel sampling designs. In question 2, we
focus on time series studies and we review statistical methods for:
1)...
16.
Reflections on Fourteen Cryptic Issues Concerning the Nature of Statistical Inference - Kardaun, O.J.W.F.; Salomé, D.; Schaafsma, W.; Steerneman, A.G.M.; Willems, J.C.; Cox, D.R.
The present paper provides the original formulation and a joint
response of a group of
statistically trained scientists
statisticians
to fourteen cryptic issues for discussion,
which were handed out to the public by Professor Dr. D.R. Cox after
his Bernoulli Lecture 1997 at Groningen University.
¶
footnote: Part of this work was funded by a collaboration between IPP and Euratom. The contents of this work is the sole responsibility of the authors. In particular, the views expressed therein are not to be construed as being official and do not necessarily reflect those of the European Commission or the Max-Planck-Gesellschaft.
17.
Statistical Regularity and Free Will:\\ L.A.J. Quetelet and P.A. Nekrasov - Seneta, Eugene
In the 19th century, causes of empirically observed stability of averages in settings
relating to human behaviour were a topic of intense discussion in western Europe.
This followed an extensive study of empirical stability by the founder of modern statistics
(and of the International Statistical Institute) L.A.J. Quetelet, published
in 1835, in what he called "Social Physics''. The eminent mathematician of strong
probabilistic and philosophical inclination and Russian Orthodox religious belief,
P.A. Nekrasov, took up and modified Quetelet's Social Physics in 1902, with (social)
independence seen as prime cause of statistical regularity. Our paper focuses on the role free
will plays in the statistical writings of Quetelet and...
18.
Bridging the Gap between Different Statistical Approaches: An Integrated Framework for Modelling - Kuhnert, Petra M.; Mengersen, Kerrie; Tesar, Peter
This paper proposes a template for modelling complex datasets that
integrates traditional statistical modelling approaches with more
recent advances in statistics and modelling through an exploratory
framework. Our approach builds on the well-known and long standing
traditional idea of `good practice in statistics' by establishing a
comprehensive framework for modelling that focuses on exploration,
prediction, interpretation and reliability assessment, a relatively
new idea that allows individual assessment of predictions.
¶
The integrated framework we present comprises two stages. The first
involves the use of exploratory methods to help visually understand
the data and identify a parsimonious set of explanatory variables.
The second encompasses a two step modelling process, where the
use of non-parametric...
19.
A Bayesian Formulation of Exploratory Data Analysis and Goodness-of-fit Testing - Gelman, Andrew
Exploratory data analysis (EDA) and Bayesian inference (or, more
generally, complex statistical modeling)---which are generally
considered as unrelated statistical paradigms---can be particularly
effective in combination. In this paper, we present a Bayesian
framework for EDA based on posterior predictive checks. We explain
how posterior predictive simulations can be used to create reference
distributions for EDA graphs, and how this approach resolves some
theoretical problems in Bayesian data analysis. We show how the
generalization of Bayesian inference to include replicated data $y^{\rm rep}$
and replicated parameters $\theta^{\rm rep}$ follows a long tradition of generalizations in
Bayesian theory.
¶
On the theoretical level, we present a predictive Bayesian formulation of
goodness-of-fit testing, distinguishing between $p$-values...
20.
Some Aspects Of Neutral To Right Priors - Dey, Jyotirmoy; Erickson, R.V.; Ramamoorthi, R.V.
Neutral to right priors are generalizations of Dirichlet process priors that
fit in well with right-censored data. These priors are naturally induced by
increasing processes with independent increments which, in turn, may be viewed
as priors for the cumulative hazard function. This connection together with the
L\'{e}vy representation of independent increment processes provides a
convenient means of studying properties of \nr\ priors.
¶
This article is a review of the theoretical aspects of \nr\ priors and provides
a number of new results on their structural properties. Notable among the new
results are characterizations of \nr\ priors in terms of the posterior and the
cumulative hazard function. We also show that...
1.
