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Superpopulation models are transformed
in predictive models in order to permit the use of standard classical statistics
techniques. Confidence intervals based on predictive models replace the predictive
intervals based on superpopulation models. The ideas are illustrated by various
examples and the normal case turns out to produce intervals that are also obtained
by the standard classical survey sampling techniques.
Publ. Year: 1993
Document Type: Journal
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Simple examples illustrate how misleading
a $p$-value constructed with no regard to the alternative hypothesis can be.
A $p$-value which regards the alternative hypothesis, called here $P$-value,
is precisely defined. It is shown that the use of the $P$-value avoids the kind
of inconsistencies illustrated by the examples. Although $P$-values could be
considered useless by Bayesians, the use of prior distributions (to obtain weighted
likelihoods) is a way by which classical statisticians could regard alternative
composite hypotheses when performing significance tests.
Publ. Year: 1993
Document Type: Journal
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Questions related to lotteries are
usually of interest to the public since people think there is a magic formula
which will help them to win lottery draws. This note shows how to compute the
expected waiting time to observe specific numbers in a sequence of lottery draws
and show that surprising facts are expected to occur.
Publ. Year: 1993
Document Type: Journal
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The intuition behind the Blackwell
sufficiency concept is discussed using influence diagrams. A simple geometrical
solution for the problem of comparing Bernoulli experiments is presented.
Publ. Year: 1990
Document Type: Journal
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Consider a finite, closed population
of size N. Select a first random sample of size $m\sb 1$ without replacement.
Mark its units and return them to the population. Let $U\sb 1=m\sb 1$. The j
th random sample of size $m\sb j$ is drawn without replacement and the units
already marked are returned to the population. The remaining $U\sb j$ unmarked
sample units are then marked and returned to the population. After k samples
are drawn, the data (random) vector is ${\bbfD}\sb k=(U\sb 1,U\sb 2,...,U\sb
k)$, and the statistic $T\sb k=U\sb 1+U\sb 2+...+U\sb k$ is the number of distinct
units in the whole sampling process. \par Using a prior $\pi$ for N, a Bayes
estimator of N is derived. Large sample properties of the Bayes estimator are
also obtained using standard martingale results. The almost sure convergence
of the Bayes estimator to N and of the Bayes risk to zero are established.
T.J.Rao (Santa Barbara)
Publ. Year: 1990
Document Type: Journal
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The diagnostic probabilities of having
a disease based on possible responses (indicants) to a clinical question (tests,
signs or symptoms) are generally given without reference to their precision.
Here, a Bayesian approach is used to provide a full analysis of the diagnostic
probabilities, the weights of evidence provided by each indicant and the average
weight of evidence (diagnosability) provided by the question. The method is
extended to a sequence of questions in which a particular response may influence
whether a subsequent question is asked. The role of imprecise diagnostic probabilities
in decision making is discussed.
Publ. Year: 1990
Document Type: Journal
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Influence diagrams are used to illustrate
how the probability of having a disease can be updated given the results from
two or more clinical tests. The problem of calibrating a register using results
from a survey, as discussed by {\it J. Heldal} and {\it E. Spjoetvoll} [Int.
Stat. Rev. 56, 153-164 (1988)] is solved using a Bayesian approach.
Publ. Year: 1990
Document Type: Journal
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Using data obtained by the general
capture-recapture sequential sampling process, an analytical expression for
the maximum likelihood estimate of the population size is introduced. It is
shown that the bounded likelihood functions have at most two maxima. For the
simple one-to-one case the estimate is unique.
Publ. Year: 1988
Document Type: Journal
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The multiple regression model is
used to describe relationships among quantities associated to finite population
units. Postulating normal priors for the regressor parameters and for the error
vector, after observing a sample, a posterior distribution for the unsampled
part of the population is obtained. The case of noninformative priors is covered
as a limit of the normal priors. We describe the general conditions under which
omission of additional auxiliary regression variables does not affect the posterior
prediction. \par Some standard situations are discussed under this Bayesian
approach. A general class of predictors suggested by such robustness conditions
is considered and some well known predictors (the ratio estimator for example)
are shown to be elements of this class, proving that there are situations where
they are robust predictors.
Publ. Year: 1987
Document Type: Journal
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The probability distribution associated
with the multisample CMRR generalized sequential sampling process is obtained
by using an analogy with a single urn model. Some statistical features are also
discussed.
Publ. Year: 1987
Document Type: Journal
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The paper deals with robustness of
linear predictors in survey sampling under the superpopulation approach. With
the help of general results of the theory of linear models, robustness in linear
prediction is characterized. \par The inference is based on an assumed model
(the $\xi$-model), which not necessarily coincides with the true model (the
$\xi\sp*$-model). Necessary and sufficient conditions are given under which
the $\xi$-best linear predictor also is $\xi\sp*$-best. Some known examples
are used to illustrate the results.
B.Ranneby
Publ. Year: 1983
Document Type: Journal
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