Two-phase Stratified Sampling Research Articles

Order-Restricted Bayesian Estimation of the Age Composition of a Population of Atlantic Cod

The management of a commercial fishery often requires estimates of the age composition. These estimates are typically based on age and length data obtained from sampling the commercial landings from the fishery and the catches from a research vessel survey. We use data from annual research cruises of Georges Bank conducted by the Canadian Department of Fisheries and Oceans to show how inferences for Atlantic cod (Gadus morhua) can be improved. Traditionally, two-phase stratified sampling is used with fish length (or weight) as the stratification variable. Letting Pi . denote the proportion of fish belonging to length stratum i, and π ij denote the proportion of fish belonging to age class j in stratum i, we use Bayesian methods to estimate P.j = π i πij , the proportion of fish that are age j. Specifications of smoothness, expressed as unimodal order relations among the π ij (within and between the length strata), are incorporated into the prior distributions. Uncertainty about both the locations of the modes and the unimodality itself are included as part of the probabilistic specification. With computations facilitated by using the Gibbs sampler, we show that the smoothness conditions provide very large gains in precision. For the data analyzed in this article, one can obtain similar precision by using (a) a conventional analysis or (b) an analysis with order restrictions and a sample of half the size in (a). We also show that better estimates of the age composition provide improved estimates of the quantities used by fisheries managers to forecast the catches from cohorts of fish.

Optimal Two-Phase Stratified Sampling for Estimation of the Age Composition of a Fish Population

The provision of biological advice for the management of a commercial fish stock requires, among other things, an estimate of the age composition. This estimate is usually obtained from length and age information collected by sampling the commercial landings associated with that fish stock. The sampling methods used and the types of problems encountered are discussed by Quinn et al. (1983) and Stevenson (1983). The final stage of the sample design is typically a two-phase stratified sample of a large catch from a commercial vessel (Quinn et al., 1983; Stevenson, 1983; Southward, (1976). At the first phase, a large simple random sample (SRS) of size n' is selected, and each fish is assigned to a stratum consisting of all fish having lengths in a specified range. Denote by nf the number of sampled fish in length stratum i. At the second phase a SRS of size ni is chosen from stratum i (i = 1, . . ., I). Each of these ni fish is aged with nij fish found to be agej (j = 1, ... , J). The problems are: (i) estimation of IPj: j = 1, . .. , J), where P.j is the population proportion of age j fish; (ii) given n' and In': i = 1, . . ., I }, how to select Ini: i = 1, .. , I }; and (iii) for a specified cost function and given budget, how to select n'. Smith and Sedransk (1982) provide methods for (i) and (ii). For (ii), their approach is flexible in that currently used or proposed allocation schemes are shown to be optimal under appropriate specifications. In the current paper we: (i) review the Smith-Sedransk methodology, (ii) show how to determine the optimal value of n', and (iii) exhibit potential gains from using two-phase sampling. In Section 3 we give a numerical illustration of the

Stratified sampling compared with two-phase stratified cluster sampling for timber volume estimation.

Two sampling methods were compared on orthophotos (scale 1:10 000) of a rectangular 12 855-ha area of intensively managed Norway spruce forest in Upper Austria. Trees other than spruce >40 yr old were ignored. 'Method 1' used stratified cluster sampling to determine the area proportion of spruce in the total area: 2 clusters of 5 circular 0.05-ha photo plots were randomly selected within each of 8 rectangular sub-blocks in each of 72 blocks into which the area was 'stratified' (systematically divided). Vol. was determined by 2-phase sampling: (i) 2 clusters were randomly selected in each block, and the % crown cover of spruce was determined in each photo plot; (ii) one photo plot was selected in each block (all crown cover classes being represented) for subsequent vol. determination on 72 plots in the field. 'Method 2' used areas of mature spruce on forest management maps, which were copied on to the orthophotos and then divided into 2 nearly equal strata of higher and lower density whose areas were measured by planimeter. Ten field plots were located in each stratum and enumerated in order to determine the s.d. of each stratum and hence the number of additional random field plots required; the total number of field plots was 55. The 2 methods required the same number of man-days (36), method 1 requiring less office work and more field work and computation. If the sampling intensity was reduced, method 1 became less time-consuming than method 2 (except in the field) for the same vol. error. However, method 2 with sampling errors only in vol., is preferred over method 1 which has sampling errors in both area and volume. (Abstract retrieved from CAB Abstracts by CABI’s permission)

Optimum allocation in Bayesian stratified two-phase sampling when there arem-attributes

The problem of optimally allocating a sample amongk-strata at the second phase of a two-phase sampling procedure when the sampling is for proportion has been discussed byNewbold [1971] and then by the author [Khan, 1972].

Optimum Allocation in Stratified Two-Phase Sampling for Proportions

Optimum Allocation in Stratified Two-Phase Sampling for Proportions

Optimum allocation in stratified two-phase sampling for proportions

Optimum allocation in stratified two-phase sampling for proportions

Bayesian Stratified Two-Phase Sampling Results: k Characteristics

Bayesian Stratified Two-Phase Sampling Results: k Characteristics

Bayesian stratified two-phase sampling results: k characteristics

In a previous paper (1968), we obtained some results concerning the optimum allocation of sampling effort among several strata at the second phase of a two-phase sampling procedure, using information obtained from the first phase. One variable, or characteristic, was involved. Here we extend our results to the case of k characteristics.

Some Bayesian stratified two-phase sampling results

In this paper we obtain some results concerning the optimum allocation of sampling effort among k strata at the second phase of a two-phase sampling procedure, using information obtained from the first phase. Two different approaches are employed; a Bayesian posterior analysis and a Bayesian preposterior analysis. Two different allocation methods are derived and illustrated with some numerical examples, for cases where some or all of the nuisance parameters are unknown. The problem when all nuisance parameters are known has been discussed by Ericson (1965).