10,059 research outputs found
Efficient randomized-adaptive designs
Response-adaptive randomization has recently attracted a lot of attention in
the literature. In this paper, we propose a new and simple family of
response-adaptive randomization procedures that attain the Cramer--Rao lower
bounds on the allocation variances for any allocation proportions, including
optimal allocation proportions. The allocation probability functions of
proposed procedures are discontinuous. The existing large sample theory for
adaptive designs relies on Taylor expansions of the allocation probability
functions, which do not apply to nondifferentiable cases. In the present paper,
we study stopping times of stochastic processes to establish the asymptotic
efficiency results. Furthermore, we demonstrate our proposal through examples,
simulations and a discussion on the relationship with earlier works, including
Efron's biased coin design.Comment: Published in at http://dx.doi.org/10.1214/08-AOS655 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Matching on-the-fly in Sequential Experiments for Higher Power and Efficiency
We propose a dynamic allocation procedure that increases power and efficiency
when measuring an average treatment effect in sequential randomized trials.
Subjects arrive iteratively and are either randomized or paired via a matching
criterion to a previously randomized subject and administered the alternate
treatment. We develop estimators for the average treatment effect that combine
information from both the matched pairs and unmatched subjects as well as an
exact test. Simulations illustrate the method's higher efficiency and power
over competing allocation procedures in both controlled scenarios and
historical experimental data.Comment: 20 pages, 1 algorithm, 2 figures, 8 table
Handling Covariates in the Design of Clinical Trials
There has been a split in the statistics community about the need for taking
covariates into account in the design phase of a clinical trial. There are many
advocates of using stratification and covariate-adaptive randomization to
promote balance on certain known covariates. However, balance does not always
promote efficiency or ensure more patients are assigned to the better
treatment. We describe these procedures, including model-based procedures, for
incorporating covariates into the design of clinical trials, and give examples
where balance, efficiency and ethical considerations may be in conflict. We
advocate a new class of procedures, covariate-adjusted response-adaptive (CARA)
randomization procedures that attempt to optimize both efficiency and ethical
considerations, while maintaining randomization. We review all these
procedures, present a few new simulation studies, and conclude with our
philosophy.Comment: Published in at http://dx.doi.org/10.1214/08-STS269 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Multi-objective optimal designs in comparative clinical trials with covariates: The reinforced doubly adaptive biased coin design
The present paper deals with the problem of allocating patients to two
competing treatments in the presence of covariates or prognostic factors in
order to achieve a good trade-off among ethical concerns, inferential precision
and randomness in the treatment allocations. In particular we suggest a
multipurpose design methodology that combines efficiency and ethical gain when
the linear homoscedastic model with both treatment/covariate interactions and
interactions among covariates is adopted. The ensuing compound optimal
allocations of the treatments depend on the covariates and their distribution
on the population of interest, as well as on the unknown parameters of the
model. Therefore, we introduce the reinforced doubly adaptive biased coin
design, namely a general class of covariate-adjusted response-adaptive
procedures that includes both continuous and discontinuous randomization
functions, aimed to target any desired allocation proportion. The properties of
this proposal are described both theoretically and through simulations.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1007 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Coined quantum walks on percolation graphs
Quantum walks, both discrete (coined) and continuous time, form the basis of
several quantum algorithms and have been used to model processes such as
transport in spin chains and quantum chemistry. The enhanced spreading and
mixing properties of quantum walks compared with their classical counterparts
have been well-studied on regular structures and also shown to be sensitive to
defects and imperfections in the lattice. As a simple example of a disordered
system, we consider percolation lattices, in which edges or sites are randomly
missing, interrupting the progress of the quantum walk. We use numerical
simulation to study the properties of coined quantum walks on these percolation
lattices in one and two dimensions. In one dimension (the line) we introduce a
simple notion of quantum tunneling and determine how this affects the
properties of the quantum walk as it spreads. On two-dimensional percolation
lattices, we show how the spreading rate varies from linear in the number of
steps down to zero, as the percolation probability decreases to the critical
point. This provides an example of fractional scaling in quantum walk dynamics.Comment: 25 pages, 14 figures; v2 expanded and improved presentation after
referee comments, added extra figur
A simple evolutionary game with feedback between perception and reality
We study an evolutionary game of chance in which the probabilities for
different outcomes (e.g., heads or tails) depend on the amount wagered on those
outcomes. The game is perhaps the simplest possible probabilistic game in which
perception affects reality. By varying the `reality map', which relates the
amount wagered to the probability of the outcome, it is possible to move
continuously from a purely objective game in which probabilities have no
dependence on wagers, to a purely subjective game in which probabilities equal
the amount wagered. The reality map can reflect self-reinforcing strategies or
self-defeating strategies. In self-reinforcing games, rational players can
achieve increasing returns and manipulate the outcome probabilities to their
advantage; consequently, an early lead in the game, whether acquired by chance
or by strategy, typically gives a persistent advantage. We investigate the game
both in and out of equilibrium and with and without rational players. We
introduce a method of measuring the inefficiency of the game and show that in
the large time limit the inefficiency decreases slowly in its approach to
equilibrium as a power law with an exponent between zero and one, depending on
the subjectivity of the game.Comment: 11 pages, 6 figure
Structural Drift: The Population Dynamics of Sequential Learning
We introduce a theory of sequential causal inference in which learners in a
chain estimate a structural model from their upstream teacher and then pass
samples from the model to their downstream student. It extends the population
dynamics of genetic drift, recasting Kimura's selectively neutral theory as a
special case of a generalized drift process using structured populations with
memory. We examine the diffusion and fixation properties of several drift
processes and propose applications to learning, inference, and evolution. We
also demonstrate how the organization of drift process space controls fidelity,
facilitates innovations, and leads to information loss in sequential learning
with and without memory.Comment: 15 pages, 9 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/sdrift.ht
Directionally-unbiased unitary optical devices in discrete-time quantum walks
The optical beam splitter is a widely-used device in photonics-based quantum information processing. Specifically, linear optical networks demand large numbers of beam splitters for unitary matrix realization. This requirement comes from the beam splitter property that a photon cannot go back out of the input ports, which we call “directionally-biased”. Because of this property, higher dimensional information processing tasks suffer from rapid device resource growth when beam splitters are used in a feed-forward manner. Directionally-unbiased linear-optical devices have been introduced recently to eliminate the directional bias, greatly reducing the numbers of required beam splitters when implementing complicated tasks. Analysis of some originally directional optical devices and basic principles of their conversion into directionally-unbiased systems form the base of this paper. Photonic quantum walk implementations are investigated as a main application of the use of directionally-unbiased systems. Several quantum walk procedures executed on graph networks constructed using directionally-unbiased nodes are discussed. A significant savings in hardware and other required resources when compared with traditional directionally-biased beam-splitter-based optical networks is demonstrated.Accepted manuscriptPublished versio
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