Bayesian sequential methods for choosing the best multinomial cell: some simulation results

Jones, Peter W.; Madhi, Saad Abed

doi:10.1007/bf02924517

Cited by 2 publications

(3 citation statements)

References 4 publications

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“…According to the Bayes theorem, after m observations resulting in x i in the i-th classes, the posterior density of p is given by a Dirichlet with parameters a 0 + m, a i + x i , where m is the total number of observations or the sample size, and x i is the number of observations in each of the i-th classes (Jones and Madhi, 1988).…”

Section: Stopping Criteria For the Bayesian Sequential Estimation Of ...mentioning

confidence: 99%

“…The dynamic programming equations providing the partition for the stop and continuation points are given by (Jones, 1976;Jones and Madhi, 1988):…”

Section: And This Has the General Quadratic Form (P -D) T K(p -D)mentioning

confidence: 99%

“…For this purpose, a point (x, m) = (x 1 , x 2 , …, x k , m) is considered. If c is the sampling cost of an observation, B(x, m) the risk of making an additional observation at a cost c (expected risk), and D(x, m) is the minimum risk or ideal risk, then the dynamic programming equations providing the partition for the stop and continuation points are (Jones, 1976;Jones and Madhi, 1988):…”

Section: Development Of the Stopping Criterionmentioning

confidence: 99%

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Bayesian sequential estimation of the proportion of damage in maize seeds

Lima,

Brighenti,

Pires

2024

Sci. agric. (Piracicaba, Braz.)

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Sampling is an essential step in estimating a parameter: thus, cost and time associated to this step should be minimized. Sequential sampling is characterized by using samples of variable sizes given as a function of observations, and sequential sampling provides a smaller sample size than a fixed-size sample in most cases. In addition, the Bayesian decision theory can be incorporated into sequential sampling to perform parameter estimation because it allows the inclusion of a priori information about the parameter of interest, which optimizes the procedure. However, the great challenge to performing the Bayesian sequential estimation in establishing the stopping criteria. Most studies in this area investigate binomial distributions, while few analyze multinomial distributions. This study aimed to define the stopping criteria for the Bayesian sequential estimation of the parameters of multinomial distributions with conjugate Dirichlet priors. The proposed methodology was applied to a set of X-ray test data for quality control of maize seed lots. This test uses conventional sampling techniques in which a sample has a fixed size with 200 seeds. The influence of two priors on the stopping criteria was evaluated, one uniform and one conjugate, with hyperparameters based on reference information from the literature. The results indicated a reduction in the sample size in most lots evaluated.

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Section: Stopping Criteria For the Bayesian Sequential Estimation Of ...mentioning

confidence: 99%

“…The dynamic programming equations providing the partition for the stop and continuation points are given by (Jones, 1976;Jones and Madhi, 1988):…”

Section: And This Has the General Quadratic Form (P -D) T K(p -D)mentioning

confidence: 99%

Section: Development Of the Stopping Criterionmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian sequential estimation of the proportion of damage in maize seeds

Lima,

Brighenti,

Pires

2024

Sci. agric. (Piracicaba, Braz.)

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Multilocus ordering strategies based on sperm typing

Goradia

Lange

1990

Annals of Human Genetics

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Sperm typing is a promising new approach for fine-structure human gene mapping. We examine three-locus sperm typing and its implications for the estimation of recombination fractions and for locus ordering. In particular, we compare some sequential stopping rules for three-locus assignment and develop methods for approximating their mean stopping times and error probabilities. A stopping rule recently described by Thompson and Boehnke et al. appears to be nearly optimal. Under this rule, one stops sampling as soon as the number of sperm of the least frequent recombinant type is s fewer than the number of sperm of the next least frequent type. We develop a random-walk algorithm and some heuristic formulas for assessing the performance of this rule. Since the broader goal of linkage analysis is to order many more than three loci, we propose a trisection strategy for ordering a new locus relative to an existing ordered set of loci. The crux of the trisection strategy is to restrict attention to the smallest block of ordered loci among which the new locus can fall and to divide this block into thirds for the next comparison. This trisection strategy is optimal in the sense that it has the best worse-case performance of any strategy. When it is applied sequentially to order a collection of loci, it is only nearly optimal, as we demonstrate by specific counter-example. However, it does become asymptotically optimal as the size of the collection increases.

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Bayesian sequential methods for choosing the best multinomial cell: some simulation results

Cited by 2 publications

References 4 publications

Bayesian sequential estimation of the proportion of damage in maize seeds

Bayesian sequential estimation of the proportion of damage in maize seeds

Multilocus ordering strategies based on sperm typing

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