ICES training Course on Design and Analysis of Statistically Sound Catch Sampling Programmes

Transcription

1 ICES training Course on Design and Analysis of Statistically Sound Catch Sampling Programmes Sara-Jane Moore

2 General Statistics - backed up by case studies

3 General Introduction to sampling theory Sampling Design Random, Stratified, Cluster Designing Sampling Surveys WKPICS & WGCATCH Case Studies, References, Irish Perspective

4 Introduction to sampling theory Pop, target pop, sampled pop, sampling frame Because the sample is a subset of the population, we desire to collect the sample such that it Is obtained cost-effectively (time and money) Is representative of the population Can be used to estimate the population characteristics of interest precisely (low variability) and accurately (unbiased) Can calculate estimates of the precision of the estimators of the population parameters Population Target Population Study Population Sample

5 Sampling Frames Illegal or undocumented catch

6 Steps in The Planning of Surveys Define the target population Commercial catch/trip of NEA cod from Barents Sea by Norwegian vessels for a given year Define the sampling frame All vessels/trips that can be sampled Define the population characteristics to be estimated from the sample mean length and distribution of ages of all fish in the total commercial catch of NEA cod from Barents Sea by Norwegian vessels for a given year and identify the equivalent survey information to be collected in the sample lengths and ages of sampled NEA cod in the Barents Sea by Norwegian vessels

7 Sampling Designs Simple Random Sampling Procedure Stratified Non-Probability Sampling Probability Sampling Cluster Convenience Judgment or Purposive Simple Random Stratified Systematic Cluster

8 Random Sampling WR or WOR Simple Random Sampling/Equal Prob Sampling Selection probability Inclusion probability Unequal Probability Random Sampling Selection probability Inclusion probability

9 Estimation 3 weeks of statistics in 1 day Once a sample has been selected we need to be able to estimate some population parameters Horvitz Thompson Estimator Valid for WR and WOR sampling Hansen-Hurwitz Estimator Valid for with replacement sampling only Horvitz-Thompson Estimator (HTE) is generally more precise than the Hansen-Hurwitz Estimator (HHE) Also estimated variance of these estimators

10 Stratification Divide the population into subpopulations, called strata The strata do not overlap (mutually exclusive), i.e. an element is associated with only a single stratum Every element in the population is associated with a stratum (exhaustive)

11 Stratification WHY? Ensure good spatial coverage Natural subgroups within the population Administrative control for implementation Increase precision of the estimators

12 library(party) Stratification Weighting in Stratification Males and females, geographic, temporal How to apportion the samples to each stratum Equal sample size Proportional sample size Neyman (Optimal) Allocation: Include cost of sampling eg or time Sampling designs can vary among strata Not required to have the same design in each stratum E.g. SRSWR in one stratum and UPS in another

13 Cluster Sampling Divide the population into groups of elements, called clusters cannot list every trip taken by all commercial vessels in a fishery but can list every vessel Each vessel has a number of trips they will (or did) take Population element of interest is the trip, nested within vessel Natural cluster is the set of trips taken by a vessel, usually further refined by stating that it is the set of trips taken by a vessel within a stratum

14 Cluster Sampling Sub-sampling of clusters Single Stage Two Stage Multi Stage 4-Stage Cluster Sampling Design

15 Cluster Sampling Estimators for Cluster Sampling Horvitz Thompson Estimator Hansen-Hurwitz Estimator ratio estimator

16 Comparisons of Sampling Designs Unequal Probability Random Sampling vs Stratified Random Sampling in R SRS vs PPS WR Cluster Sampling in R

17 R R code library(teachingsampling) HH, HT Allows the user to draw probabilistic samples and make inferences from a finite population based on several sampling designs. library(lsmeans) Used in cluster sampling analysis library(samplingbook) stratamean library(party) Regression tree

18 ICES and 4s WKPICS WGCATCH WKCOSTBEN

19 Case Studies Mozambique Example of a 4- stage Cluster Sampling Design

20 Case Studies Norwegian Fishers Cluster = port-day combination PSU = port-day SSU = tourist fisher

21 References Cochran,1977 Thompson, 2002 Lohr,2010 Sampling:Design and Analysis Gary A. Nelson (2014) Cluster Sampling: A Pervasive, Yet Little Recognized Survey Design in Fisheries Vølstad et al. review of Alaska observer program 1997.pdf

22 Irish Perspective Strata-vessel*trip Refusal rates Optimum no. of fish to measure in each haul Clearly defined objectives Estimation tools Quality Indicators

23 End