591 research outputs found
Shrinkage Estimation in Multilevel Normal Models
This review traces the evolution of theory that started when Charles Stein in
1955 [In Proc. 3rd Berkeley Sympos. Math. Statist. Probab. I (1956) 197--206,
Univ. California Press] showed that using each separate sample mean from
Normal populations to estimate its own population mean can be
improved upon uniformly for every possible . The
dominating estimators, referred to here as being "Model-I minimax," can be
found by shrinking the sample means toward any constant vector. Admissible
minimax shrinkage estimators were derived by Stein and others as posterior
means based on a random effects model, "Model-II" here, wherein the
values have their own distributions. Section 2 centers on Figure 2, which
organizes a wide class of priors on the unknown Level-II hyperparameters that
have been proved to yield admissible Model-I minimax shrinkage estimators in
the "equal variance case." Putting a flat prior on the Level-II variance is
unique in this class for its scale-invariance and for its conjugacy, and it
induces Stein's harmonic prior (SHP) on .Comment: Published in at http://dx.doi.org/10.1214/11-STS363 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equations
Parameter inference for ordinary differential equations (ODEs) is of
fundamental importance in many scientific applications. While ODE solutions are
typically approximated by deterministic algorithms, new research on
probabilistic solvers indicates that they produce more reliable parameter
estimates by better accounting for numerical errors. However, many ODE systems
are highly sensitive to their parameter values. This produces deep local minima
in the likelihood function -- a problem which existing probabilistic solvers
have yet to resolve. Here, we show that a Bayesian filtering paradigm for
probabilistic ODE solution can dramatically reduce sensitivity to parameters by
learning from the noisy ODE observations in a data-adaptive manner. Our method
is applicable to ODEs with partially unobserved components and with arbitrary
non-Gaussian noise. Several examples demonstrate that it is more accurate than
existing probabilistic ODE solvers, and even in some cases than the exact ODE
likelihood.Comment: 9 pages, 5 figure
The survival of the Tick-Borne Encephalitis (TBE) virus in nymphs of Haemaphysalis inermis tick and its transmission to pygmy mouse (Micromys minutus)
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