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950.38011

Paulino, Carlos Daniel Mimoso; Braganca Pereira, Carlos Alberto de :(de Braganca Pereira, Carlos Alberto; Pereira, Carlos Alberto de Braganca )
Bayesian methods for categorical data under informative general censoring ( English )
Biometrika 82, No.2, 439-446 (1995).
Classification
*62F15 Bayesian inference

Publ. Year: 1995
Document Type: Journal

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801.62009

Iglesias, Pilar; Sandoval, Monica C.; de Braganca Pereira, Carlos Alberto :(Braganca Pereira, Carlos Alberto de )
Predictive likelihood in finite populations. ( English )
REBRAPE 7, No.1, 65-82 (1993).
Classification
*62D05 Statistical sampling theory
62B05 Sufficient statistics
Keywords
maximum likelihood predictor; nuisance parameter; pivotal quantity; prediction; minimal sufficient reduction; specific sufficiency; predictive intervals; superpopulation models; examples

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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809.62003

Braganca Pereira, Carlos Alberto de; Wechsler, Sergio :(De Braganca Pereira, Carlos Alberto )
On the concept of $P$-value. ( English )
REBRAPE 7, No.2, 159-177 (1993).
Classification
*62A99 Foundations of statistics
62G10 Nonparametric hypothesis testing
62F03 Parametric hypothesis testing
Keywords
Bayes factor; likelihood principle; null and alternative hypotheses; weighted likelihood ratio; $P$-value; prior distributions; significance tests

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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777.60011

Leite, Jose Galvao; Pereira, Carlos Alberto de Braganca; Rodrigues, Flavio Wagner :(Braganca Pereira, C.A.de; De Braganca Pereira, C.A.; Wagner Rodrigues, F. )
Waiting time to exhaust lottery numbers. ( English )
Commun. Stat., Theory Methods 22, No.1, 301-310 (1993).
Classification
*60C05 Combinatorial probability
Keywords
lotteries; expected waiting time to observe specific numbers in a sequence of lottery draws

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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725.62004

Basu, Debabrata; Braganca Pereira, Carlos Alberto de :
Blackwell sufficiency and Bernoulli experiments. ( English )
REBRAPE 4, No.2, 137-145 (1990).
Classification
*62B05 Sufficient statistics
62B15 Comparison of statistical experiments
Keywords
informative experiments; transition functions for sample spaces; Blackwell sufficiency; influence diagrams; geometrical solution; comparing Bernoulli experiments

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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719.62020

Leite, Jose Galvao; Braganca Pereira, Carlos Alberto de :
Bayes estimation of the size of a finite population: Capture/recapture sequential sample data. ( English )
Int. Stat. Rev. 58, No.3, 201-213 (1990).
Classification
*62D05 Statistical sampling theory
62F15 Bayesian inference
60F15 Strong limit theorems
Keywords
population size estimation; finite second moments; capture/recapture sequential sampling process; supermartingale; maximum likelihood estimator; sufficient statistic; finite, closed population; without replacement; Bayes estimator; sample properties; almost sure convergence; Bayes risk

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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707.62266

Braganca Pereira, Carlos Alberto de; Pericchi, Luis Raul :
Analysis of diagnosability. ( English )
J. R. Stat. Soc., Ser. C 39, No.2, 189-204 (1990).
Classification
*62P10 Appl. of statistics to biology
62F15 Bayesian inference
Keywords
Bayes factor; clinical indicant; Dirichlet distribution; divergence; weights of evidence; diagnosability

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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703.62104

Braganca Pereira, Carlos Alberto de; Barlow, Richard E. :
Medical diagnosis using influence diagrams. ( English )
Networks 20, No.5, 565-577 (1990).
Classification
*62P10 Appl. of statistics to biology
92C50 Medical appl. of mathematical biology
90B50 Multiple-criteria decision making
62F15 Bayesian inference
Keywords
Influence diagrams; clinical tests; Bayesian approach

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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632.62081

Leite, Jose Galvao; Oishi, Jorge; Braganca Pereira, Carlos Alberto de :(De Braganca Pereira, Carlos Alberto )
A note on the exact maximum likelihood estimation of the size of a finite and closed population. ( English )
Biometrika 75, No.1, 178-180 (1988).
Classification
*62L12 Sequential estimation
62D05 Statistical sampling theory
62L99 Sequential statistical methods
Keywords
sufficient statistic; general capture-recapture sequential sampling process; maximum likelihood estimate; population size; bounded likelihood functions; maxima

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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643.62003

Bolfarine, Heleno; Braganca Pereira, Carlos Alberto de; Rodrigues, Josemar :
Robust linear prediction in finite populations: A Bayesian perspective. ( English )
Sankhya, Ser. B 49, No.1, 23-35 (1987).
Classification
*62D05 Statistical sampling theory
62F15 Bayesian inference
Keywords
robust linear prediction; weak robustness set; robustness set; balanced sample; shrinkage factor; multiple regression model; finite population; normal priors; posterior distribution; noninformative priors; omission of additional auxiliary regression variables; ratio estimator

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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618.62104

Galvao Leite, Jose; Braganca Pereira, Carlos Alberto de :
An urn model for the multi-sample capture/recapture sequential tagging process. ( English )
Sequential Anal. 6, 179-186 (1987).
Classification
*62P10 Appl. of statistics to biology
62D05 Statistical sampling theory
Keywords
random allocation; allocation process; sufficient statistic; capture-mark- release-recapture sampling process; multisample CMRR generalized sequential sampling process; single urn model

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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549.62007

Braganca Pereira, Carlos Alberto de; Rodrigues, Josemar :
Robust linear prediction in finite populations. ( English )
Int. Stat. Rev. 51, 293-300 (1983).
Classification
*62D05 Statistical sampling theory
62J05 Linear regression
Keywords
balanced sample; overbalanced sample; xi-model; robustness of linear predictors; survey sampling; superpopulation approach; linear models; best linear predictor

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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