BSTVC | Make Space and Time Explainable.

Turn spatiotemporal heterogeneityinto interpretable evidence.

Conventional global regression reduces complex spatiotemporal relationships to a single coefficient, while black-box GeoAI often explains predictions only after the fact. BSTVC (Bayesian Spatiotemporally Varying Coefficients) takes a different path—unifying local effects, global key-driver identification, dynamic prediction, and uncertainty quantification within a transparent Bayesian framework to reveal where, when, and why relationships change.

Local Effects.Global Insight.Dynamic Prediction.
No CodeReproducibleBayesian White BoxThe first open-source tool for spatiotemporal interpretability analysis.
3Response Types
Continuous · Binary · Count
50 / 95Bayesian Credible Intervals
Uncertainty-Informed Interpretation
12Empirical Studies
2018–Present · Health & Medical Geography
1 GBUpload Limit
Large Panels and Maps

01 / WHY BSTVC

Interpretability is more than
an importance ranking.

Where. When. Why.

Why does the same factor have different effects across places and periods?

Explore the GeoAI Paradigm

A global regression uses one coefficient for every place and period, creating a potential stationarity bias. BSTVC returns relationships to their geographic context while quantifying effect magnitude, direction, and uncertainty.

01

Global Stationarity Assumption

A single coefficient assumes the same relationship everywhere and at all times, potentially obscuring local health–environment mechanisms.

GLOBAL POSTERIOR · β
02

Spatiotemporally Nonstationary Relationships

Identify spatial and temporal heterogeneity simultaneously while preserving the geographic meaning of local relationships.

LOCAL COEFFICIENT FIELD · β(s, t)
03

Evidence-Based Interpretation

Use credible intervals, model assessment, and STVPI show effect magnitude, evidential stability, and the most important drivers.

CREDIBLE EVIDENCE · 95%
SPATIOTEMPORAL
INTERPRETABILITY

02 / THREE RESEARCH TASKS

From local mechanisms to global attribution,
then to dynamic prediction.

Iβ(s, t)
LOCAL INTERPRETABILITY · CORE FUNCTION

Local Spatiotemporal Interpretability

Use STVC/STIVC to estimate the direction, magnitude, and uncertainty of covariate effects across places and periods—showing where, when, and how an effect operates.

TCs · SCs · 50/95% CREDIBLE INTERVALS
IIΣ%
GLOBAL INTERPRETABILITY · CORE FUNCTION

Global Spatiotemporal Interpretability

Use STVPI to quantify each factor’s relative spatiotemporal contribution and identify key drivers and their spatial and temporal sources of variation.

STVPI · RELATIVE CONTRIBUTION · ATTRIBUTION
IIIŷt+1
DYNAMIC PREDICTION · CORE FUNCTION

Dynamic Spatiotemporal Prediction

Use STVI/STIVI and related models for missing-value imputation, spatiotemporal smoothing, and forecasting to construct continuous, reliable spatiotemporal data.

PREDICTION · IMPUTATION · SMOOTHING

03 / GEOAI PARADIGM

Two geographic laws.
One white-box framework.

Go beyond asking why a model predicted an outcome: determine where the relationship occurs, when it changes, and how stable the evidence is.

FIRST LAWSpatial Autocorrelation

Nearby entities tend to be more closely related. BSTVC represents spatial or spatiotemporal dependence across data, process, and parameter levels.

SECOND LAWSpatial Heterogeneity

Phenomena and variable relationships differ across places. Local coefficients directly characterize this spatial and spatiotemporal nonstationarity.

INTERPRETABLE MODELSDATA → STRUCTURE → EVIDENCE
ANTE-HOC / INTRINSIC INTERPRETABILITY INTRINSIC INTERPRETABILITY

Definition:Explanatory variables, effect structures, and evidence outputs are specified before model fitting. Interpretation follows directly from model parameters and their posterior distributions, not from an external approximation added after training.

WHITE BOX / INTERPRETATION PATHObserved data Y → model structure Xβ(s, t) → posterior evidence

Interpretation comes directly from model structure and parameters, rather than an external approximation added after training.

The Model Structure Is the Explanation

Regression coefficients, credible intervals, and variance partitioning all arise directly from the Bayesian white-box model; mechanisms and predictions share the same statistical framework.

BSTVC CORE PARADIGM
POST-HOC / EXTERNAL EXPLANATION

Explaining a Black Box with External Tools

The explanation is produced after training and usually approximates model behavior; it is not equivalent to a mechanism intrinsic to the statistical structure.

EXTERNAL EXPLANATION TOOL
LOCAL + GLOBAL + DYNAMIC

From Local Mechanisms and Global Attribution to Dynamic Prediction

BSTVC organizes three research tasks into a continuous evidence chain: determine where, when, and how factors operate; compare the relative contributions of key drivers; then perform imputation, smoothing, and prediction within the same Bayesian framework.

01 / LOCALβ(s, t)
Local Spatiotemporal Interpretability

Locate effect direction, magnitude, and uncertainty for every place and period.

STVC · STIVC → coefficient surfaces
02 / GLOBALΣ%
Global Spatiotemporal Interpretability

Compare candidate-factor contributions and identify key drivers and their temporal–spatial sources.

STVPI → variance partitioning
03 / DYNAMICŷ(t+1)
Dynamic Spatiotemporal Prediction

Perform missing-value imputation, smoothing, and forecasting in one posterior framework.

STVI · STIVI → posterior prediction
INTERACTIVE SCIENTIFIC DIAGRAM

04 / MODEL SYSTEM

One System for interpretation and prediction.

From intercepts to coefficients, independent variation to space–time interactions, and spatial cross-sections to spatiotemporal panels—the research question determines the model scale.

HOW TO CHOOSE
Predict only the spatiotemporal dynamics of Y?STVI / STIVI
Interpret local effects of X?STVC / STIVC / BSVC
Compare relative factor contributions?STVPI
Dynamic Predictionŷ
STVI

Spatiotemporally Varying Intercepts

Characterizes the response variable’s spatiotemporal evolution for missing-value imputation, smoothing, and dynamic prediction.

DATA
Spatiotemporal panel Y(s, t)
BOUNDARY
Focuses on response dynamics; does not interpret local X effects
BAYESIAN WHITE-BOX MODEL
Interaction-Aware Predictiont×s
STIVI

Spatiotemporally Interacting Varying Intercepts

Adds space–time interaction to a varying-intercept structure to represent coupled spatial and temporal dynamics.

DATA
Panel Y(s, t) with space–time interaction
BOUNDARY
For complex dynamic prediction; not a substitute for varying-coefficient attribution
BAYESIAN WHITE-BOX MODEL
Core Modelβst
RECOMMENDED FIRST MODEL · STVC
STVC

Spatiotemporally Varying Coefficients

Fits local spatiotemporal coefficients for explanatory variables to identify temporal and spatial nonstationarity in their relationships.

DATA
Y(s, t) + multiple X(s, t)
BOUNDARY
Spatial and temporal effects vary independently
BAYESIAN WHITE-BOX MODEL
Model Extensionβ×
STIVC

Spatiotemporally Interacting Varying Coefficients

Uses a space–time interaction assumption to reveal more complex local effect mechanisms and evolutionary patterns.

DATA
Hierarchical or interaction-based spatiotemporal panel
BOUNDARY
Requires an explicit SSH/TSH interaction assumption
BAYESIAN WHITE-BOX MODEL
Spatial Cross-Sectionβs
BSVC

Bayesian Spatially Varying Coefficients

Identifies spatially heterogeneous relationships and local driving patterns in single-time-point or spatial cross-sectional data.

DATA
Single-period spatial cross-section Y(s), X(s)
BOUNDARY
Explains spatial heterogeneity without estimating temporal change
BAYESIAN WHITE-BOX MODEL
Global AttributionΣ%
STVPI

Spatiotemporal Variance Partitioning Index

Transforms model results into relative contribution percentages to identify key factors and their temporal and spatial sources.

DATA
BSTVC posterior variance components
BOUNDARY
For relative contribution; not a substitute for interpreting local coefficient direction
BAYESIAN WHITE-BOX MODEL
CORE 01 / STVCSpace–Time Independent Nonstationarity

Simultaneously quantifies spatially and temporally heterogeneous associations between Y and multiple X variables while incorporating spatial and temporal autocorrelation.

CORE 02 / STIVCSpace–Time Interaction Nonstationarity

Defines interaction random effects through spatial stratified heterogeneity (SSH) or temporal stratified heterogeneity (TSH), supporting two-level coupled data such as county–province or day–month structures while controlling model complexity.

CORE 03 / STVPIRelative Spatiotemporal Importance

Uses variance partitioning to express heterogeneous effects as interpretable percentages, screening key factors while distinguishing temporal and spatial sources of contribution.

05 / METHOD ADVANTAGES

BSTVC Advantages:
Comparable, Quantifiable, Reproducible.

Its advantages arise not only from local regression, but from the combination of unified full-map modeling, Bayesian uncertainty, and a complete evidence chain.

01

Unified Full-Map Modeling

Fits all local parameters in one complete Bayesian hierarchical framework rather than separating map units into unrelated small models.

02

Directly Comparable Local Coefficients

Unified data, process, and parameter levels make regression coefficients statistically comparable across places and periods.

0350/95

Explicit Uncertainty Quantification

Local predictions, TCs, and SCs include 50% inner and 95% outer credible intervals.

04β→Σ

Integrated Local–Global Interpretation

Identify nonstationary spatiotemporal effects from local coefficients, then compare factor contributions using STVPI.

05

Three Response Types

Supports continuous (log-Gaussian), binary (logistic), and count (Poisson) responses within one system.

06UI

No-Code Desktop Workflow

Connects data conversion, field checks, spatial-order alignment, model fitting, result export, and visualization guidance.

LOCALβ(s, t)Heterogeneous Effect Mechanisms

TCs · SCs · CI

GLOBALΣ%Key-Driver Identification

STVPI · attribution

DYNAMICŷDynamic Spatiotemporal Prediction

impute · smooth · forecast

ONE METHOD SERIESAnalyze Factors → Identify Key Drivers → Predict Dynamically

From local mechanism interpretation and global key-driver identification to dynamic prediction, BSTVC connects research questions, statistical evidence, and decision-ready communication in one coherent methodology.

06 / EMPIRICAL WORKFLOW

A Real-Case-Driven
desktop modeling workflow.

Each response type is demonstrated with a real software interface. Import and validate data first, then check spatial order, configure parameters, run the model, and export results.

MODEL SPECIFICATION PRINCIPLEChoose the likelihood and link function from the response range, distributional properties, and data-generating mechanism—not researcher preference.

  1. 01Data InputTable + Complete Map
  2. 02Validate AlignmentFields + Spatial Order
  3. 03Configure ParametersY / X / Time / Space
  4. 04Run ModelsBSTVC / BSVC
  5. 05Export ResultsSix Excel Output Types
ACTUAL DESKTOP SCREEN
Real interface screenshot · Source: BSTVC Desktop User Guide
Real interface screenshot · Source: BSTVC Desktop User Guide
log-Gaussian RESPONSE

Global Health-Adjusted Life Expectancy (HALE)

2000–2020 · 177 COUNTRIES AND TERRITORIES

SUITABLE FORExplaining why continuous indicators—such as life expectancy, resource quantities, concentrations, and rates—vary across places and periods.Gaussian likelihood on log-transformed response · identity link

INPUT
TestData_Continuous. csv + complete TestMap_Continuous Shapefile set
RESPONSE
Y = HALE
EXPLANATORY X
High BMI, health expenditure, natural environment, health behavior, PM2.5, and related covariates
OUTPUT
TCs · SCs · STVPI · local predictions and credible intervals
View Data and Parameter Specifications
RESPONSE CHECK / ContinuousAVOID MIS-SPECIFICATION

Do not treat strongly skewed or overdispersed counts, or 0/1 outcomes, as continuous variables. Transform data and inspect distributions when appropriate.

Download Three Example Datasets ↓

07 / READ THE OUTPUT

Read
the spatiotemporal evidence chain.

Do not interpret a coefficient in isolation. Combine TCs, SCs, STVPI, local predictions, credible intervals, and model assessment to build an interpretable conclusion.

Real case result · Source: BSTVC Desktop User Guide
Real case result · Source: BSTVC Desktop User Guide
01 / RESULT

Map Local Effect Direction and Magnitude

02 / HOW TO READ

Spatial regression coefficients are exported by map unit for visualization in R, ArcGIS, ArcGIS Pro, or QGIS. Use consistent classes, color scales, and spatial extents across covariate maps.

RECOMMENDED: ArcGIS Pro / QGIS / R sf
SPATIAL NONSTATIONARITYLOCAL EFFECTMAPPING
03 / INTERPRETATION

Assess direction and magnitude first, then the inner and outer credible intervals; finally integrate model assessment, mapped patterns, and substantive context.

Bayesian credible intervals express posterior parameter uncertainty and should not be mechanically equated with frequentist significance tests or reduced to significant/non-significant labels.
DIC / WAICModel Fit

Lower values generally indicate better fit.

↓ LOWER IS GENERALLY BETTER
EFF / PD2Model Complexity

Quantifies effective parameters and model complexity.

↔ INTERPRET WITH MODEL FIT
LS / AUCPredictive Performance

Evaluates accuracy and discrimination by response type.

LS → 0 · AUC ↑
TCs / SCsLocal Relationships

Reads temporal and spatial nonstationary effects separately.

DIRECTION + MAGNITUDE + CrI
SCIENTIFIC FIGURE01 / 01

08 / SELECTED PUBLICATIONS

A methods-to-applications
evidence chain.

From methodological development to validation in health, social, and environmental settings, representative studies continue to test and extend the interpretive capabilities and application boundaries of the BSTVC model family.

2018
Scientific Reports

Estimating Missing Values in China’s Official Socioeconomic Statistics Using Progressive Spatiotemporal Bayesian Hierarchical Modeling.

Provincial panel, China1991—2011Socioeconomic statistical imputation
DOI
01
2019
Science of the Total Environment

Exploring Spatiotemporal Nonstationary Effects of Climate Factors on Hand, Foot, and Mouth Disease Using Bayesian STVC.

Counties in Sichuan Province36 monthsInfectious disease and climate–health
DOI
02
2020
Annals of GIS

Spatiotemporally Varying Coefficients Model: A Bayesian Local Regression to Detect Spatial and Temporal Nonstationarity.

County panel, China2008—2017STVC methods and validation
DOI
03
2022
International Journal of Disaster Risk Reduction

Spatiotemporal Disparities in Regional Public Risk Perception of COVID-19 Using Bayesian STVC Series Models.

366 Chinese citiesCOVID-19 periodPublic risk perception
DOI
04
2022
Journal of Cleaner Production

Spatiotemporal Heterogeneity in Associations of National Population Ageing with Socioeconomic and Environmental Factors.

189 countries and territories20 yearsGlobal population ageing
DOI
05
2024
BMC Public Health

Revealing Spatiotemporal Inequalities, Hotspots, and Determinants in Healthcare Resource Distribution.

2,308 Chinese countiesLong-term panelHealthcare resource equity
DOI
06
METHOD EVOLUTION2018—2026Eight years of methodological development and multi-setting applications underpin today’s open-source system. Hover over a year to explore the associated papers, patents, and software.
2018Bayesian STVI

Missing-value estimation and disease-risk mapping.

2019Bayesian STVC

Local effects, downscaling, and landslide applications.

2020General STVC Framework

Established a generalizable Bayesian local spatiotemporal regression framework.

2021Cross-Domain Expansion

Continued validation in tourism, disasters, and software systems.

2022STIVC + STVPI

Space–time interactions and relative contributions unified.

2023Research Translation

Methods translated into patents and visual modeling systems.

2024Health Geography Special Issue

Expanded health-geography research and large-scale county healthcare studies.

2025First Open-Source R Package ReleaseOPEN SOURCE

BSTVC-R released openly, alongside studies of multiple resources, maternal and child health, and efficiency.

2026BSTVC Desktop

R package, desktop tool, and knowledge ecosystem opened together.

2026 / RESEARCH EVIDENCEBSTVC Desktop5 representative outputs
Article

Hao, M., et al. Spatiotemporal Patterns of Age at Menarche or Spermarche in Chinese Children and Adolescents and Socioeconomic and Environmental Determinants: Findings from a Series of Nation-Wide Surveys, 1995 to 2019. Environment & Health (2026).

DOI
Data Article

Tang, Z., et al. A Long-term Consistent Socioeconomic Dataset of Chinese Cities Generated by Bayesian Spatiotemporal Modeling with Multi-source Earth Observations. Earth System Science Data Discussions (2026): 1–39.

DOI
Article

Chen, A., Xue, J., Tang, X., et al. A Joint Multimetric Spatiotemporal Evaluation of Maternal Healthcare Services in China Considering Inequality, Geographic Clustering, and Key Factors. Modern Preventive Medicine (2026).

Open-Source Tool

BSTVC Desktop integrates data checking, model execution, result export, and user support in a visual workflow.

Method Ecosystem

BSTVC-R, the Desktop User Guide, case data, the INLA Resource Monitor, and the official website form an open research toolchain.

09 / RESEARCH APPLICATIONS

Twelve Research Cases
Connected to Real-World Questions.

2018–PRESENTMETHOD-TO-APPLICATION
12OFFICIAL CASES
189 / 2,308COUNTRIES / COUNTIES
STVC · STIVC · STVPIMODEL FAMILY
01 / 12SWIPE HORIZONTALLY TO BROWSE CASES
PRIMARY SOURCE

For complete methods, original case figures, and updates, visit the BSTVC Model Homepage ↗

DYNAMIC IDENTITY / BSTVCBSTVC Animated Logo

10 / FREE DOWNLOAD

Download BSTVC Desktop.
Make spatiotemporal relationships interpretable.

English desktop release for Windows 10/11, with direct GitHub access to the installer, source repository, reproducible case interface, and supporting tools.

https://pan.baidu.com/s/5h7zSPjXEvBINShxLVLjirA
BSTVC Desktop English interface showing the overview, core features, and workflow
BSTVC Desktop · English interface · Data preparation, modeling, and results workflow
Click to Enlarge
ENGLISH RELEASE / 2026.8.1
  • 01 Windows x64 installer
  • 02 English user interface
  • 03 Continuous-response example
  • 04 Binary-response example
  • 05 Count-response example
  • 06 Data, maps, and visualization guidance
The homepage works offline; external downloads and repositories require internet access.

11 / USER GUIDE KNOWLEDGE HUB

From Desktop to R:
build a complete research workbench.

Use the tabs to navigate data preparation, nine parameters, six output types, current limitations, R-package installation, documentation, and support.

DESKTOP + R PACKAGE GUIDE

Organize Tables and Maps into a Verifiable Spatiotemporal Panel

Files

Supports CSV, XLSX, and XLS. Import the complete Shapefile set rather than a standalone. shp file.

Spatial Order

The spatial-unit order in every time slice must match the map. The desktop app can compare, reorder, and export validated data automatically.

Fields

The table and map must use spatial identifiers with matching names and types; represent missing values consistently as NA.

Auxiliary Tool

Built-in data conversion, field conversion, and custom spatial matrices support wide-to-long reshaping and numeric field conversion.

12 / AUXILIARY TOOL

BSTVC Process Monitor Static LogoBSTVC
MONITOR

BSTVC Process Monitor:
Find the Right Thread Setting for Model Runs.

A lightweight resource monitor for BSTVC Desktop that tracks CPU, memory, and thread states during model computation to support faster, more stable settings.

WINDOWS / LOCAL ONLYv0.5.7

More Threads
Are Not Always Faster.

Different data scales, model structures, and hardware configurations have different resource sweet spots. Start with the BSTVC default of six threads, then compare eight or 12 using real trajectories from similar models.

BSTVC RECOMMENDED START6 THREADS

Start with the default six threads, then adjust using monitor results from comparable models.

BSTVC PROCESS MONITORLIVE / LOCAL
CPU TOTAL68.4%stable activity
MEMORY7.8GBpeak 8.4 GB
THREADS06current / peak 06
RESOURCE TRAJECTORYpast 60 min
TOTAL CPU MEMORY PRESSURE
PROCESS / PIDRUNTIMESTATUS
BSTVC / INLA PID 428000:18:42RUNNING
BSTVC / INLA PID 391600:11:07STOPPED
LIVE RESOURCE SIGNALS

See How BSTVC Modeling Uses Your Computer

Monitor one or more inla. exe processes and continuously record system-wide CPU, memory, threads, PID, runtime, and status. The main CPU series matches the system-wide metric shown by Windows Task Manager.

  • CPU mean / P95 / proportion above threshold
  • Current and peak thread counts and memory use
  • Distinguish multiple processes by PID, start time, and runtime
THREAD STARTING POINTS
08
Advanced ComparisonMany-Core Workstation
12
Test with CautionWatch Memory and Throttling
More threads do not guarantee faster runs; test with comparable models.
THREAD DECISION

Start with the default six threads. Try eight threads only when memory is sufficient and the task is large. Reserve 12 threads for many-core, high-memory systems and confirm stable headroom with the monitor.

OPEN-SOURCE / MIT

Published by bayesianstvc. Runs on Windows 10/11 with PowerShell 5.1 or 7 and a modern browser. View v0.5.7 Release ↗

13 / CONTACT & FEEDBACK

Contact Us
to Improve the Methods and Software.

ANONYMOUS VISITOR MAPCONNECTING / ANONYMOUS TOTAL
BSTVC organization logo
GITHUB ORGANIZATIONbayesianstvc

BSTVC ORGANIZATION

Advancing Spatiotemporal
Interpretability.

Bayesian Spatiotemporally Varying Coefficients

PRODUCT ECOSYSTEM

One framework. Multiple ways to explore.

Explore the BSTVC Organization