A Grouping Genetic Algorithm for Joint Stratification and Sample Allocation Designs

Predicting the cheapest sample size for the optimal stratification in multivariate survey design is a problem in cases where the population frame is large. A solution exists that iteratively searches for the minimum sample size necessary to meet accuracy constraints in partitions of atomic strata created by the Cartesian product of auxiliary variables into larger strata. The optimal stratification can be found by testing all possible partitions. However the number of possible partitions grows exponentially with the number of initial strata. There are alternative ways of modelling this problem, one of the most natural is using Genetic Algorithms (GA). These evolutionary algorithms use recombination, mutation and selection to search for optimal solutions. They often converge on optimal or near-optimal solution more quickly than exact methods. We propose a new GA approach to this problem using grouping genetic operators instead of traditional operators. The results show a significant improvement in solution quality for similar computational effort, corresponding to large monetary savings.Comment: 22 page

Using Particle Swarm Optimization to Determine the Optimal Strata Boundaries

Stratified random sampling is a commonly used sampling methodology especially for heterogeneous populations with outliers. Stratified sampling is preferably employed due to its capability of improving statistical precision by yielding a smaller variance of the estimator, compared with simple random sampling. In order to reduce the variance of the estimator in stratified sampling, the problems of stratum boundary determination and sample allocation must be resolved initially. This paper proposes a PSO algorithm to solving the problem of stratum boundary determination in heterogeneous populations while distributing the sample size according to Neyman allocation method. The PSO algorithm is tested on two groups of populations and a comparative study with Kozak, GA and Delanius and Hodges methods have been implemented. The numerical results show the ability of the proposed algorithm to find the optimal stratified boundaries for a set of standard populations and various standard test functions compared with other algorithms

On Constructing Optimum Strata and Determining Optimum Allocation

The problem of constructing optimum stratum boundaries (OSB) and the problem of determining sample allocation to different strata are well known in the sampling literature. To increase the efficiency in the estimates of population parameters these problems must be addressed by the sampler while using stratified sampling. There were several methods available to determine the OSB when the frequency distribution of the study (or its related) variable is known. Whereas, the problem of determining optimum allocation was addressed in the literature mostly as a separate problem assuming that the strata are already formed and the stratum variances are known. However, many of these attempts have been made with an unrealistic assumption that the frequency distribution and the stratum variances of the target variable are known prior to conducting the survey. Moreover, as both the problems are not addressed simultaneously, the OSB and the sample allocation so obtained may not be feasible or may be far from optimum. In this paper, the problems of finding the OSB and the optimum allocation are discussed simultaneously when the population mean of the study variable y is of interest and its frequency distribution f(y) or the frequency distribution f(x) of its auxiliary variable x is available. The problem is formulated as a Nonlinear Programming Problem (NLPP) that seeks minimization of the variance of the estimated population parameter of the target variable, which is subjected to a fixed total sample size. The formulated NLPP is then solved by executing a program coded in a user’s friendly software, LINGO. Two numerical examples, when the study variable or its auxiliary variable has respectively a uniform and a right-triangular distribution in the population, are presented to demonstrate the practical application of the proposed method and its computational details. The proposed technique can easily be applied to other frequency distributions

Optimal Stratification and Allocation for the June Agricultural Survey

A computational approach to optimal multivariate designs with respect to stratification and allocation is investigated under the assumptions of fixed total allocation, known number of strata, and the availability of administrative data correlated with thevariables of interest under coefficient-of-variation constraints. This approach uses a penalized objective function that is optimized by simulated annealing through exchanging sampling units and sample allocations among strata. Computational speed is improved through the use of a computationally efficient machine learning method such as K-means to create an initial stratification close to the optimal stratification. The numeric stability of the algorithm has been investigated and parallel processing has been employed where appropriate. Results are presented for both simulated data and USDA’s June Agricultural Survey. An R package has also been made available for evaluation

Heuristic Algorithm for Univariate Stratification Problem

In sampling theory, stratification corresponds to a technique used in surveys, which allows segmenting a population into homogeneous subpopulations (strata) to produce statistics with a higher level of precision. In particular, this article proposes a heuristic to solve the univariate stratification problem - widely studied in the literature. One of its versions sets the number of strata and the precision level and seeks to determine the limits that define such strata to minimize the sample size allocated to the strata. A heuristic-based on a stochastic optimization method and an exact optimization method was developed to achieve this goal. The performance of this heuristic was evaluated through computational experiments, considering its application in various populations used in other works in the literature, based on 20 scenarios that combine different numbers of strata and levels of precision. From the analysis of the obtained results, it is possible to verify that the heuristic had a performance superior to four algorithms in the literature in more than 94% of the cases, particularly concerning the known algorithms of Kozak and Lavallee-Hidiroglou.Comment: 25 pages and 7 figure

An Integrated Decision Making Framework for Medical Audit Sampling

The loss of three to ten percent of annual health care expenditures to fraudulent transactions makes medical audits paramount. In order to handle the size and complexity of medical claims, the use of analytical methods and information technology tools to aid in medical audits is necessary. In general, sampling frameworks are utilized to choose representative claims. However, these are not integrated within audit decision-making procedures. As a novelty, this paper presents an integrated decision-making framework for medical audit sampling. We propose a simple but effective optimization method that uses sampling output and enables auditors address the trade-offs between audit costs and expected overpayment recovery. We use U.S. Medicare Part B claims payment data to demonstrate the framework

A simulated annealing algorithm for joint stratification and sample allocation

This study combines simulated annealing with delta evaluation to solve the joint stratification and sample allocation problem. In this problem, atomic strata are partitioned into mutually exclusive and collectively exhaustive strata. Each partition of atomic strata is a possible solution to the stratification problem, the quality of which is measured by its cost. The Bell number of possible solutions is enormous, for even a moderate number of atomic strata, and an additional layer of complexity is added with the evaluation time of each solution. Many larger scale combinatorial optimisation problems cannot be solved to optimality, because the search for an optimum solution requires a prohibitive amount of computation time. A number of local search heuristic algorithms have been designed for this problem but these can become trapped in local minima preventing any further improvements. We add, to the existing suite of local search algorithms, a simulated annealing algorithm that allows for an escape from local minima and uses delta evaluation to exploit the similarity between consecutive solutions, and thereby reduces the evaluation time. We compared the simulated annealing algorithm with two recent algorithms. In both cases, the simulated annealing algorithm attained a solution of comparable quality in considerably less computation time

Oceanographic barriers, divergence, and admixture : phylogeography and taxonomy of two putative subspecies of short-finned pilot whale

Funding:Commander, U.S. Pacific Fleet Environmental Readiness Division and NMFS Pacific Islands Fisheries Science Center; NMFS West Coast Region; Scripps Institution of Oceanography Edna Bailey Sussman Research Fellowship; and Woods Hole Oceanographic Institution.Genomic phylogeography plays an important role in describing evolutionary processes and their geographic, ecological, or cultural drivers. These drivers are often poorly understood in marine environments, which have fewer obvious barriers to mixing than terrestrial environments. Taxonomic uncertainty of some taxa (e.g., cetaceans), due to the difficulty in obtaining morphological data, can hamper our understanding of these processes. One such taxon, the short‐finned pilot whale, is recognized as a single global species but includes at least two distinct morphological forms described from stranding and drive hunting in Japan, the “Naisa” and “Shiho” forms. Using samples (n = 735) collected throughout their global range, we examine phylogeographic patterns of divergence by comparing mitogenomes and nuclear SNP loci. Our results suggest three types within the species: an Atlantic Ocean type, a western/central Pacific and Indian Ocean (Naisa) type, and an eastern Pacific Ocean and northern Japan (Shiho) type. mtDNA control region differentiation indicates these three types form two subspecies, separated by the East Pacific Barrier: Shiho short‐finned pilot whale, in the eastern Pacific Ocean and northern Japan, and Naisa short‐finned pilot whale, throughout the remainder of the species' distribution. Our data further indicate two diverging populations within the Naisa subspecies, in the Atlantic Ocean and western/central Pacific and Indian Oceans, separated by the Benguela Barrier off South Africa. This study reveals a process of divergence and speciation within a globally‐distributed, mobile marine predator, and indicates the importance of the East Pacific Barrier to this evolutionary process.PostprintPeer reviewe