# Presentation: 228058

## The Interplay Between Research Innovation and Federal Statistical Practice

- Stephen E. Fienberg
- Department of Statistics
- Center for Automated Learning & Discovery
- Carnegie Mellon University
- Pittsburgh PA

## Some Themes

- Methodological innovation comes from many places and in different colors and  flavors.
- Importance of cross-fertilization.
- Cycle of innovation.
- Examples: Bayesian inference, Log-linear models, Missing data and imputation, X-11-ARIMA.

## Some Themes (cont.)

- Statistical thinking for non-statistical problems:
- e.g., disclosure limitation.
- Putting several innovations to work simultaneously:
- New proposal for census adjustment.
- New challenges

## Methodological Innovation in Statistics 

- Comes from many places and in different colors and flavors:
- universities:
- statisticians.
- other methodologists.
- government agencies.
- Private industry.
- nonprofits, e.g., NISS.
- committees at the NRC.

## Role of Statistical Models

- “All models are wrong, but some models are useful.”  John Tukey?
- Censuses and surveys attempt to describe and measure stochastic phenomena:
- 1977 conference story.
- U.S. census coverage assessment:
-  “Enumeration”.
-  Accuracy and Coverage Evaluation (ACE) survey.
-  Demographic Analysis.

## Importance of Cross-Fertilization

- Between government and academia.
- Among fields of application:
- e.g., agriculture, psychology, computer science
- Between methodological domains e.g., sample surveys and experimental design:
**Jan van den Brakel Ph.D. thesis, EUR**
- Using other fields to change statistics e.g., cognitive aspects of survey design:
**Krosnick and Silver; Conrad and Shober**

## Cycle of Innovation

- Problem need
- Formal formulation and abstraction
- implementation on original problem
- Generalizations across domains
- General statistical theory
- Reapplication to problem and development of extensions
- reformulation

## Example 1: Bayesian Inference

- Laplace
- role of inverse probability.
- ratio-estimation for population estimation.
- Empirical Bayes and shrinkage (borrowing strength) - hierarchical models.
- NBC election night prediction model.
- Small area estimation.
**Elliott and Little on census adjustment**
**Singh, Folsom, and Vaish**

## Example 2: Log-linear Models

- Deming-Stephan iterative proportional fitting algorithm (raking).
- Log-linear models and MLEs:
- margins are minimal sufficient statistics.
- implications for statistical reporting.
- Some generalizations: generalized IPF, graphical models, exponential families.
- Model-based inference for raking.

## Graphical & Decomposable Log-linear Models

- Graphical models defined in terms of simultaneous conditional independence relationships or absence of edges in graph.
- _Example_:
- Decomposable models correspond  to triangulated graphs.

## Example 3: Missing Data and Imputation

- Missing data problems in survey and censuses.
- solutions: cold deck and hot deck imputation
- Rubin 1974 framework representing missingness as random variable.
- 1983 CNSTAT Report, Madow et al (3 vol.).
- Rubin (1997) - Bayesian approach of multiple imputation.
- NCHS and other agency implementations
-     **session on imputation and missing data**

## Example 4: X-11-ARIMA

- BLS seasonal adjustment methods:
- X-11 and seasonal factor method (Shishkin et al., 1967)
- ARIMA methods a la Box-Jenkins (1970):
- Cleveland and Tiao (1976).
- X-11 + ARIMA =X-11/ARIMA (Dagum, 1978).
- Levitan Commission Report (1979).
- X-12-ARIMA.
**Burck and Salama**

## Statistical Thinking for Non-Statistical Problems 

- Disclosure limitation was long thought of as non-statistical problem.
- Duncan and Lambert (1986, 1989) and others explained statistical basis.
- New methods for bounds for table entries as well as new perturbation methods are intimately linked to log-linear models.
**NISS Disclosure Limitation Project - Karr and Sanil**

## Query System Illustration (k=3)

***Challenge:*****  Scaling up approach for large *****k*****.**** **

## Bounds for Entries in k-Way Contingency Table

- Explicit formulas for sharp bounds if margins correspond to cliques in decomposable graph. (**Dobra and Fienberg , 2000)**
***Upper bound:***** minimum of relevant margins.**
***Lower bound:***** maximum of zero, or sum of relevant margins minus separators.**
**Example: **
**cliques are**** ****{14}, {234}, **
**        ****{345}, {456}, {567}**
**separators are {4}, {34}, **
**                    ****{45}, {56}**

## More Bound Results

- Log-linear model related extensions for
-  reducible graphical case.
- if all (*k*-1) dimensional margins fixed.
- General “tree-structured” algorithm.**  Dobra (2000)**
- Applied to 16-way table in a recent test.
- Relationship between bounds results and methods for perturbing tables.
- Measures of risk and their role.

## NISS Table Server: 8-Way Table

## Census Estimation

- 2000 census adjustment model uses variant of dual systems estimation, combining census and ACE data,  to correct for
- omissions.
- erroneous enumerations (subtracted out before DSE is applied).
- DSE is based on log-linear model of independence.
**UK and US papers on DSE adjustment methods**

## Dual Systems Setup

**   ****	****In ****	****Out  ****	****  Total**
** ****In  ****	*****a ******	******b****** ******	******      ******n******1***
**Out       *****c ******	******d*****??****        *****N -n******1***
**  ****Total       *****n******2****** ******	******N - n******2    ******N*****??**

***N = n******1****** n******2****/****a***

**^**

**Census**

**Dual Systems Setup**

## Putting Several Innovations to Work Simultaneously

- Third system for each block based on administrative records - ***StARS/AREX***
- Log-linear models allow us to model dependence between census and ACE:
- in all ***K*** blocks have census and AREX data.
- in sample of ***k*** blocks also have ACE data.
- missing data on ACE in remaining ***K-k*** blocks.

## Triple System Approach

- Administrative List
-              P 		           A
-              Sample	        Sample
-             P	  A	        P	A
-        P       58       12          69       41     * n* = 268
-        A       11       43          34         -

- Census

**Triple System Approach**

- Example of small minority stratum from 1988 St. Louis census dress rehearsal.

## New Bayesian Model

- Bayesian triple-systems model:
- correction for EEs in census and administrative records.
- missing ACE data in *K-k* blocks.
- dependencies (heterogeneity) among lists.
- smoothing across blocks and/or strata using something like logistic regression model.
- Revised block estimates to borrow strength across blocks *and* from new source.

## New Challenges

## Challenges of Multiple-Media Survey Data 

**Example:**  Wright-Patterson A.F. Base Sample Survey
- Demographic data PLUS three 3-dimensional full-body laser surface scans per respondent.
- Interest in “functionals” measured from scans.
- Ultimately will have 50 MB of data for each of 10,000 individuals in U.S. and The Netherlands/Italy.

## Some Methodological Issues With Image Data

- Data storage and retrieval.
- Data reduction, coding, and functionals:
- design vs. model-based inference.
- Disclosure limitation methodology.

## Standing Statistics On Its Head