David Binder

ssc.ca

David Binder

David Binder

Statistics Canada (retired)

November 29, 2007

SSO 2007 Fall Seminar and Workshop

1


Examples

Sedransk: 2008

• Inference for Establishment Surveys

• Vast amount of prior data

• Highly skewed distribution

• Stratified sampling with large “certainty” stratum

• Plausible model, concordant with data

• Inference for Small Subpopulations

• Foundational reasons

• Large sample approximations necessary in frequentist

analysis, but hard to obtain

SSO 2007 Fall Seminar and Workshop

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Examples (cont’d)

• Use Bayesian framework to obtain improved survey design

• Pooling data from several sources

• Provider profiling

• Evaluation of performance of hospitals, doctors … to enhance

quality of care

• Population Based Surveys

• Situation problematical for inference for small to moderate sized

subpopulations

• Other cases where large sample approximations don’t hold

• Limiting factor is time needed to develop models

SSO 2007 Fall Seminar and Workshop

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Examples (cont’d)

Little (2007)

• Calibrated Bayes

• The goal of model-based inference is to predict the

nonsampled values

• Prediction approach captures design information with

covariates, fixed and random effects, in the prediction

• Weighters can’t ignore models

• Modelers can’t ignore weights

SSO 2007 Fall Seminar and Workshop

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Being a Closet Bayesian

• 1978, 1981 – Bayesian Cluster Analysis, Multiple

Comparisons

• 1978 – Switching Regression

• 1982 - Non-parametric Bayes approach for stratified

samples

• Including a Bayesian approach for percentile estimation

• 1989 - Empirical Bayes for time series analysis

• 1992 - Exchange paradox

SSO 2007 Fall Seminar and Workshop

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Being a Closet Bayesian

(cont’d)

• Why I chose a Bayesian approach?

• Too many parameters

• Small sample size

• Clear decision problem

• Sensitive to prior

SSO 2007 Fall Seminar and Workshop

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Being a Closet Bayesian

(cont’d)

• Why I chose a Bayesian approach? (cont’d)

• Insight into problem

• Percentile estimation from sample surveys

• Multiple comparisons

• New problem

• Estimating time series models where observations were subject to

possibly correlated survey error (also used for analyzing panel

surveys)

SSO 2007 Fall Seminar and Workshop

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General principles

• Sample size

• Number of parameters

• New statistical problems

• Sensitivity analysis yields disparate results

SSO 2007 Fall Seminar and Workshop

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General principles (cont’d)

• Frequentist vs. Likelihood-based

• Frequentist approaches can be ad hoc, unless there are optimality

principles

• Even with optimality principles, counter-examples can be

concocted where results are absurd

• A frequentist approach that does not have a Bayesian

analalogue can be unsatisfying

• When there is a Bayesian analogue, the underlying assumptions

become sharper

SSO 2007 Fall Seminar and Workshop

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General principles (cont’d)

• Purpose of the study

• Specialized vs. multi-purpose

• Robustness to violation of model assumptions

• Bayesian approach can be used, but may be difficult

• Micro data or aggregate data

SSO 2007 Fall Seminar and Workshop

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Application to Surveys

Prior

Distribution

Superpopulation

Model

Finite

Population

Sample

Estimate

(Non-informative)

SSO 2007 Fall Seminar and Workshop

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Model-based vs. Designbased

• Asymptotic design consistency

• Relevance of ADC

• Treatment of non-response

• Small domain estimation

• Time series modelling

• Researcher’s target population

• Finite vs. infinite

SSO 2007 Fall Seminar and Workshop

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Model-based vs. Design-based

(cont’d)

• Target parameters

• FPQ’s vs. Model Parameters

• Design-based properties of model-based methods

• “Proper” Multiple imputation

• Robustness to violation of model assumptions

• Design/planning issues vs. inferential issues

SSO 2007 Fall Seminar and Workshop

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Type of Application

• Social Surveys

• Should we incorporate external information in a social

survey?

• This could become an issue when results are counter-intuitive

• Suppose a tobacco use survey indicates that smoking rates have

increased and all other indicators say otherwise

SSO 2007 Fall Seminar and Workshop

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Type of Application (cont’d)

• Social Surveys (cont’d)

• Response error issues

• We may have additional information on nature of the error

• Latent variables (IRT models)

• Fuzzy data

• Grouped income

• Spatial/Temporal correlation

• Economic Surveys

• How to incorporate historical information in an economic

survey

SSO 2007 Fall Seminar and Workshop

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Type of Application (cont’d)

• Combining information from more than one survey

• or from more than one cycle of a longitudinal survey

• Meta analysis

• Bayes or Empirical Bayes

SSO 2007 Fall Seminar and Workshop

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Final Remarks

• Bayesian methods are model-based

• Bayesian/model-based methods do have an important role

to play

• These methods should be learned and be part of the

statistician’s toolbox

• Many advocates, including Little, Ghosh, Rubin, Sedransk

SSO 2007 Fall Seminar and Workshop

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Final Remarks (cont’d)

• Design-based methods should still be the dominant

approach

• This is especially true when sample sizes are large

• For inferences about model parameters, design-based

methods can also be appropriate

• Conditions for when it is appropriate is discussed extensively in

the literature

SSO 2007 Fall Seminar and Workshop

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