Bayesian Improved Surname Geocoding

• BISG is a probabilistic imputation method that uses surname and geographic data to estimate a posterior distribution over racial or ethnic categories.
• It relies on a naive Bayes formulation with conditional independence assumptions, combining empirical inputs from surname and Census geolocation data.
• BISG is widely used in applications like voting, public health, and fair lending, though its accuracy varies by individual classification versus aggregate inference.

Bayesian Improved Surname Geocoding (BISG) is a probabilistic imputation method for inferring race or ethnicity from an individual’s surname and geolocation when self-reported protected-class data are unavailable, missing, or legally restricted. In its standard form, BISG is a naive Bayes model: it combines surname-based race information with race-by-geography information to produce a posterior distribution over racial or ethnic categories, rather than treating race as directly observed (Imai et al., 2022, Osoba et al., 25 Jun 2026). BISG has become a common proxy in applications spanning voting, public health, fair lending, insurance, and Responsible AI fairness measurement, but a large recent literature shows that its usefulness depends sharply on the task: individual classification, aggregate composition estimation, survey sampling, and downstream disparity estimation do not place the same demands on the method (Decter-Frain, 2022, Xin et al., 17 Mar 2026).

1. Bayesian formulation

In the standard formulation, BISG estimates race $R$ from surname $S=s$ and geography $G=g$ by

$$P(r \mid s,g)= \frac{P(r \mid s)\,P(g \mid r)}{\sum_{r'}P(r' \mid s)\,P(g \mid r')}.$$

Equivalent forms written in the literature replace $P(g\mid r)$ with $P(r\mid g)$ and the marginal $P(r)$, but the substantive structure is the same: surname evidence and geolocation evidence are multiplied and then normalized across categories (Imai et al., 2022, Greengard et al., 2023). The simplifying assumption is conditional independence,

$S \perp G \mid R,$

so that surname and geography are assumed independent once race is fixed (Greengard et al., 2023, Osoba et al., 25 Jun 2026).

The categories used by BISG vary by application. Several implementations use five mutually exclusive groups—White, Black, Hispanic, Asian, and Other—while other production and fairness-measurement settings use six U.S. Office of Management and Budget-style categories such as White, Black, Hispanic or Latino, American Indian or Alaska Native, Asian or Pacific Islander, and Multiple (Rosenman et al., 2022, Osoba et al., 25 Jun 2026). This category dependence is not ancillary: it shapes the source tables, the calibration problem, and the meaning of downstream disparity estimates.

BISG is often extended to include first names. In Bayesian Improved First Name and Surname Geocoding (BIFSG), the posterior becomes

$$P(r \mid s,f,g) = \frac{P(r \mid s)\,P(f \mid r)\,P(g \mid r)}{\sum_{r'} P(r' \mid s)\,P(f \mid r')\,P(g \mid r')},$$

or equivalent variants using $P(r\mid f)$ and $S=s$0 under analogous conditional-independence assumptions (Rosenman et al., 2022, Xin et al., 17 Mar 2026). BIFSG preserves the BISG logic while adding another race-informative name component.

2. Empirical inputs and name dictionaries

BISG is only as informative as its empirical inputs. Standard implementations instantiate surname information from Census surname tables and geography information from Census racial composition tables, with geography aggregated at levels such as census block, census tract, county, state, or ZIP Code Tabulation Area (ZCTA) (Imai et al., 2022, Badrinarayanan et al., 2024). A recurrent distinction in the literature is between $S=s$1, which asks how race is distributed among bearers of surname $S=s$2, and $S=s$3, which asks how surnames are distributed within race $S=s$4.

The public name-dictionary literature substantially broadened the empirical base for BISG-style imputation. One large resource compiles dictionaries for first, middle, and last names from voter files in six Southern states—Alabama, Florida, Georgia, Louisiana, North Carolina, and South Carolina—using self-reported race/ethnicity at voter registration for the overwhelming majority of voters (Rosenman et al., 2022). These dictionaries contain roughly 993,000 first names, 1.09 million middle names, and 1.42 million last names, and they store race-specific counts $S=s$5 that can be normalized row-wise to obtain $S=s$6 or column-wise to obtain $S=s$7 (Rosenman et al., 2022).

The practical importance of these dictionaries is twofold. First, they expand coverage well beyond the Census surname list. Second, they make BIFSG-style inference feasible at scale when first and middle names are available. In the leave-one-out evaluation reported for the six-state dictionaries, adding the new name data lowered misclassification from 16.7% to 13.2% (Rosenman et al., 2022). Related work also emphasizes that the Census surname table covers about 90% of the U.S. population, leaving approximately 10% of people with surnames absent from the standard list; these unmatched surnames are disproportionately Hispanic and Asian, so the omitted-mass problem is substantively nonrandom (Dasanaike et al., 24 Apr 2026, Li, 2023).

The dependence on external tables explains both the portability and the fragility of BISG. It is portable because no labeled race data are required in the target dataset. It is fragile because representativeness, regional portability, and temporal stability of the source tables become central modeling assumptions (Rosenman et al., 2022).

3. Variants, corrections, and calibrated extensions

A large methodological literature keeps the BISG structure but alters one of its weakest components: zero counts, missing names, miscalibration, or exogeneity failures.

Variant	Key modification	Source
BIFSG	Adds first-name information to surname and geography	(Imai et al., 2022)
fBISG	Replaces plug-in geography counts with full posterior inference	(Imai et al., 2022)
Calibrated BISG	Adds surname-by-geolocation margins and rakes to known totals	(Greengard et al., 2023)
eBISG	Uses embeddings to estimate race priors for names missing from Census tables	(Dasanaike et al., 24 Apr 2026)
BRS	Surname-only analogue used when geography may violate exogeneity	(Fisher et al., 18 Nov 2025)

The fully Bayesian Improved Surname Geocoding method, or fBISG, was introduced to address one of the canonical Census-data failures in standard BISG: zero counts for minority groups in some Census blocks (Imai et al., 2022). In six Southern-state voter files, about 2.8% of voters lived in Census blocks where the 2010 Census said there were zero members of their self-reported race, and the problem was much worse for minorities: about 20% for Asians and 30% for Other (Imai et al., 2022). Standard BISG can therefore assign zero posterior probability to a person’s true race. fBISG replaces the brittle plug-in geography prior with a Dirichlet-multinomial posterior over geographic race shares, thereby smoothing hard zeros and propagating uncertainty (Imai et al., 2022).

A separate line of work shows that standard BISG is biased because surname and geolocation are not conditionally independent within racial and ethnic categories in real U.S. data (Greengard et al., 2023). The proposed remedy augments BISG with the observed surname-by-geolocation joint distribution from state voter files and then uses raking to enforce consistency with the voter-file surname-by-geolocation margin and a statewide race distribution from the CPS Voter Supplement (Greengard et al., 2023). Empirically, the paper reports mean absolute error of about 4% for raking versus about 10% for BISG in Florida 2020, about 3% versus about 7% in North Carolina 2020, and about 3% versus about 5% in North Carolina 2010 (Greengard et al., 2023).

Embedding-powered BISG, or eBISG, addresses the missing-surname problem without changing the downstream Bayesian update. For surnames absent from the Census list, standard BISG defaults to an uninformative generic prior, so the posterior collapses to geography alone (Dasanaike et al., 24 Apr 2026). eBISG replaces that fallback with a name-specific prior estimated from pretrained text embeddings and neural networks. The strongest gains are reported for Hispanic and Asian voters with omitted surnames, precisely the groups for which standard BISG is least informative (Dasanaike et al., 24 Apr 2026).

In fair-lending settings, another extension discards geography rather than enriching it. A surname-only posterior, called BRS (“Bayes Rule on Surname”), is proposed when geography may violate the exogeneity condition required for consistent disparity estimation, since BISG can fail if geography has a direct effect on approval beyond race (Fisher et al., 18 Nov 2025). This suggests that “better race prediction” and “better race-disparity identification” are not the same objective.

4. Uses in disparity estimation, fairness measurement, and sampling

BISG is routinely used when analysts need group-disaggregated measurement but do not directly observe race. In this role, the key choice is whether to convert BISG probabilities into hard labels or to use the posterior probabilities directly. A large fairness-measurement literature advocates the latter. In weighted estimators, the unobserved group indicator $S=s$8 is replaced with the imputed group probability $S=s$9. For example, the weighted false negative rate estimator is

$G=g$0

and analogous replacements are used for false positive rate, selection rate, error rate, and output-rate disparities (Wastvedt et al., 2024). This approach treats BISG as a probabilistic demographic signal rather than a hard classifier.

In privacy-preserving fairness infrastructure, BISG is the demographic-estimation engine but not the final labeling rule. The Privacy-Preserving Probabilistic Race/Ethnicity Estimation (PPRE) system combines BISG with a sparse Self-ID survey set, local differential privacy, secure two-party computation, and additive homomorphic encryption to enable fairness measurement on U.S. LinkedIn members without assigning a persistent race label to any individual (Badrinarayanan et al., 2024, Osoba et al., 25 Jun 2026). The system applies probabilistic clipping when a race probability exceeds threshold $G=g$1, with $G=g$2 chosen so that 90% of the maximum probability entries in the BISG data lie below $G=g$3 (Badrinarayanan et al., 2024). The resulting weighted fairness estimators are linear in the test values, which makes them compatible with encrypted aggregation (Osoba et al., 25 Jun 2026).

BISG has also been used as a sampling engine rather than an estimation covariate. In a survey of Jewish Americans, BISG probabilities were incorporated into a stratified Poisson design so that units with higher estimated minority-membership probability were sampled more aggressively (Chasalow et al., 6 May 2026). For a target sample of 50,000, the expected Jewish yield was about 1.9% under simple random sampling, about 2.7% under geography-only stratified sampling, about 3.6% under geography stratified plus filtering, and 58.6% under BISG Poisson sampling with filtering (Chasalow et al., 6 May 2026). The observed Jewish-identification rate among respondents was 56.9%, close to the predicted 58.6% (Chasalow et al., 6 May 2026).

These uses share a common feature: BISG is most effective when treated as a source of probabilistic information for aggregate inference or design, not as a definitive individual-level label.

5. Bias, calibration, and inferential distortion

The principal controversy in the BISG literature is no longer whether it predicts race “well enough” in a generic classification sense, but how its error structure interacts with downstream estimands. A central recent result is that proxy race does not merely add noise in regression-based fairness audits; it changes the estimand itself (Xin et al., 17 Mar 2026). If true race is represented by a dummy-coded regressor matrix $G=g$4 and proxy race by $G=g$5, then the proxy coefficient for category $G=g$6 satisfies

$G=g$7

Each proxy-group coefficient is therefore a weighted mixture of multiple true group effects (Xin et al., 17 Mar 2026). Under neutral and reversible misclassification, the variability in fitted values must shrink, which provides an intuition for why proxy-based audits often pull group differences toward the overall mean, especially toward the majority group (Xin et al., 17 Mar 2026).

The North Carolina voter–insurance study identifies two distinct distortion mechanisms. The first is intrinsic mixing: when true-race coefficients are mapped through the BIFSG confusion structure, minority-group coefficients are mechanically compressed toward the White baseline. The second is structured proxy error: misclassification varies with ZIP-level racial composition and socioeconomic conditions, and the residual misclassification component remains correlated with pricing residuals after controls (Xin et al., 17 Mar 2026). As a result, full proxy-based regressions can either attenuate or amplify disparities relative to analyses based on self-reported race (Xin et al., 17 Mar 2026).

Related work in clinical fairness auditing reaches a similar conclusion from a different angle. The bias of weighted BISG-based fairness metrics depends on the mismatch between true and imputed group membership within the confusion-matrix cells relevant to the chosen metric, not just on global classification accuracy (Wastvedt et al., 2024). The proposed response is a sensitivity-analysis framework parameterized by $G=g$8 and $G=g$9, which quantify error in the specific numerator and denominator cells of the metric (Wastvedt et al., 2024).

In disparity estimation more generally, simple thresholding and weighting are often too naive. In a validation study based on North Carolina voter-file data, the true Black–White Democratic registration gap was 54.6 percentage points, the standard BISG weighting estimator gave 24.1 points, thresholding gave 32.5 points, and BIRDiE yielded 47.9 points with the saturated model and 48.5 points with the mixed-effects model (McCartan et al., 2023). A later frequentist treatment reaches the same critique and replaces heuristic BISG-based estimators with OLS and MLE under a conditional-independence/exogeneity assumption; in Los Angeles HMDA data, OLS with an income-stratified prior reduced RMSE in the Black/White adverse-impact ratio from 10.639 percentage points to 2.158 percentage points, a 79.7% reduction (Fisher et al., 18 Nov 2025).

Uncertainty quantification adds another layer. The dual-bootstrap literature shows that ordinary standard errors understate uncertainty because they treat the race-imputation model as fixed, but in BISG the variance component is often modest relative to bias because the method is trained on very large Census inputs (Lu et al., 2024). The paper’s bottom-line conclusion is explicit: for BISG, bias is likely more important than variance (Lu et al., 2024).

6. Empirical performance, alternatives, and interpretation

Benchmarking studies consistently find that BISG is strong as a transparent baseline but not state of the art for individual classification. In out-of-state voter-file benchmarks using California, Florida, North Carolina, and Georgia, machine learning consistently outperformed BISG at individual classification, while BISG and machine learning methods exhibited divergent biases for estimating regional racial composition, and performance varied substantially across states (Decter-Frain, 2022). This state dependence is itself important: validation in Florida does not guarantee similar behavior in California, Georgia, or North Carolina (Decter-Frain, 2022).

Recent neural and ensemble models widen the performance gap. In one held-out validation study, LSTM+Geo achieved 88.7% accuracy, compared with 86.4% for standalone LSTM, 86.8% for BIFSG, and 82.9% for BISG; the strongest ensemble reached 89.4% accuracy (Chalavadi et al., 30 Apr 2025). The same paper reports that LSTM+Geo reduced the rate at which non-White individuals were misclassified as White, with White FPR 19.3% versus 24.6% for a name-only LSTM and 41.8% for BISG (Chalavadi et al., 30 Apr 2025). Another paper reports that LLMs achieved up to 84.7% accuracy on balanced Florida and North Carolina samples, outperforming BISG at 68.2%, and reduced the income bias in which minorities in wealthier neighborhoods are systematically misclassified as White (Dasanaike, 29 Jan 2026).

These comparisons do not make BISG obsolete, but they sharpen its interpretation. BISG remains useful because it is interpretable, low-cost, deployable without labeled race data in the target dataset, and compatible with probabilistic aggregation, privacy-preserving pipelines, and survey design (Osoba et al., 25 Jun 2026, Chasalow et al., 6 May 2026). At the same time, the literature repeatedly cautions against treating BISG as ground truth or as a neutral replacement for self-reported race in regression-based disparity analysis (Xin et al., 17 Mar 2026, Wastvedt et al., 2024).

The strongest contemporary consensus is therefore task-specific. For aggregate fairness measurement, probabilistic auditing, or sample design, BISG can be informative and operationally valuable. For individual classification, richer machine-learning methods frequently perform better. For causal or regulatory disparity estimation, naive plug-in use of BISG probabilities or hard BISG labels can be seriously misleading unless the error structure, identifying assumptions, and calibration properties are analyzed directly (McCartan et al., 2023, Fisher et al., 18 Nov 2025). One paper states the operational caution in the strongest terms: these methods “are not sufficiently accurate to aid in decisions regarding any one individual record,” and using them “in a transactional process to identify race for decision-making purposes would be reckless” (Chalavadi et al., 30 Apr 2025).