STATISTICAL METHODS
Bayesian & Computational Methods
Statistical Consulting for Priors and Resampling
Our Bayesian statistics consulting covers models that combine prior information with data and computational methods that estimate uncertainty by resampling, simulation or imputation, from Bayesian regression and the bootstrap to missing data.
Bayesian & Computational Methods is the family of approaches that estimate parameters and their uncertainty by combining prior information with the data, or by simulating, resampling and imputing when a closed-form solution is unavailable or its assumptions are doubtful. Within Statistical Methods, these methods are separated by what is being estimated, whether prior information is used, whether the sampling unit and its dependence can be preserved, and how much of the data are missing. OnlineSPSS is a specialist statistical consultancy for academic, clinical and professional research, and these analyses are carried out in-house by PhD-level statisticians.
METHODS IN THIS CATEGORY
Bayesian & Computational Analysis Methods
Six methods: Bayesian analysis and regression for prior-informed inference, bootstrapping and Monte Carlo simulation as resampling and simulation methods, and missing data analysis with multiple imputation.
01
Bayesian Analysis
Combines a prior with the likelihood to give a posterior distribution, reported with credible intervals and checked by predictive checks.
Priors
Posterior inference
02
Bayesian Regression
Places explicit priors on regression coefficients, which can stabilize estimates in small samples, sparse outcomes or correlated predictors.
Regression priors
Posterior
03
Bootstrapping
Estimates the sampling variability of a statistic by resampling the independent units, giving percentile or BCa confidence intervals.
Resampling
Bootstrap CIs
04
Missing Data Analysis
Assesses how much is missing and why, and what each assumption allows, before a method for the incomplete data is chosen.
Missingness
MCAR, MAR, MNAR
05
Monte Carlo Simulation
Evaluates a method or a design by repeated random draws from a specified data-generating process, for power, bias and coverage.
Simulation
Power and bias
06
Multiple Imputation
Replaces each missing value with several plausible values, analyzes every completed dataset and pools the results with Rubin's rules.
Imputation
Rubin's rules
METHOD COMPARISON
Choosing Between Methods in This Family
Start from what is uncertain: a parameter that needs prior information, the variability of a statistic, the behavior of a method, or values that are missing. A conventional model is sometimes the better answer.
| Research situation | Typical method |
|---|---|
| Prior information combined with the data, credible intervals | Bayesian Analysis |
| Regression with priors on coefficients, small or sparse data | Bayesian Regression |
| Interval for a statistic without a convenient formula | Bootstrapping |
| Missingness to be assessed before choosing a method | Missing Data Analysis |
| Power, bias or coverage of a design or estimator | Monte Carlo Simulation |
| Plausible MAR missingness, uncertainty propagated | Multiple Imputation |
COMMON ANALYTICAL ISSUES
Common Issues We See in Bayesian & Computational Methods
Most problems here arise before the software runs, in how the priors were chosen, which unit was resampled and what was assumed about the missing values.
Priors Chosen Mechanically Default priors are often accepted without asking what they imply on the outcome scale. Prior predictive checks expose implausible values before fitting, and sensitivity to the prior should be shown.
Convergence Treated as Validity A sampler can converge to the posterior of a model that does not fit the data. Convergence diagnostics show that the computation worked; posterior predictive checks show whether the model reproduces the data.
Resampling the Wrong Unit Resampling rows is wrong when observations are paired, clustered or repeated. The bootstrap and simulation studies must preserve the real sampling unit and its dependence, or the intervals mislead.
Missing Values Filled Once Deleting cases, single imputation, or codes such as 99 left in the data understate uncertainty or distort estimates. The uncertainty from the missing values has to be carried into the final results.
Unsure whether a Bayesian, resampling or imputation approach fits? We can review the question, design and data and confirm an appropriate approach.
ANALYTICAL SUPPORT
From Method Selection to Reportable Results
Within our Quantitative Data Analysis service, Bayesian statistics consulting and computational methods are carried from specification to a documented, reproducible analysis.
Method Specification We confirm the estimand, the sampling unit and the prior or missingness question, and document why a Bayesian, resampling, simulation or imputation approach fits the design.
Assumptions & Diagnostics Priors are checked on the outcome scale, samplers by R-hat and effective sample size, fit by predictive checks, resampling units against the design and missingness against the data.
Effect Estimates & Uncertainty Results are reported as posterior summaries with credible intervals, bootstrap intervals with the method named, or pooled estimates under Rubin's rules, and not as a bare p-value.
Publication-Ready Outputs Tables, figures and methods text follow APA 7, the Bayesian Analysis Reporting Guidelines or the journal's requirements, with seeds, settings and code supplied for reruns.
SOFTWARE
Statistical Software for Computational Analysis
Each analysis is run in the software that suits the method, from MCMC samplers to resampling and imputation routines, with scripts and seeds provided where applicable.
RESEARCH DISCIPLINES
Computational Methods Across Research Fields
Bayesian, resampling and imputation methods appear wherever data are sparse, incomplete or hierarchical, and each field brings its own priors, designs and reporting conventions.
RESEARCHER VOICE
What Researchers Say
Feedback from two researchers, one weighing whether a Bayesian model added value over a conventional analysis, and one whose mixed designs needed methods and reporting matched to the field.
“We were considering a Bayesian approach but needed clarity on priors, uncertainty, and whether the model added value over a conventional analysis. The assessment was technically strong without becoming academic for its own sake, and it gave us a clear computational plan we could reproduce.”
“Our projects mix surveys, clustered samples, policy data, and qualitative material, so a one-size-fits-all statistical approach does not work. The team understood the design issues immediately and helped us choose methods and reporting that made sense for education and social research.”
OnlineSPSS provides the agreed methodological, analytical and statistical reporting support and claims no intellectual contribution. The research question, interpretation, conclusions and authorship remain with the researcher or research team.
FREQUENTLY ASKED QUESTIONS
Questions About Bayesian & Computational Methods
Short answers to what researchers ask before a project in this family, from choosing a method to confidentiality and the assessment process.
How do I choose between a Bayesian, resampling and imputation approach?
The choice follows the problem, not the label. Prior information, small or sparse data and the wish for direct probability statements point to a Bayesian model. An interval for a statistic with no convenient formula points to the bootstrap, and missing values call for an assessment of missingness first, then multiple imputation or a likelihood-based model. Where a standard model answers the question, a conventional analysis is often the more transparent choice.
Can resampling or imputation repair a small or unrepresentative sample?
No. The bootstrap reproduces the sample it is given, so it cannot correct bias, non-representativeness or too few observations, and imputation rests on assumptions about why values are missing that the observed data cannot fully test. Both quantify uncertainty under stated assumptions and do not add information. If an analysis has already been run and questioned, Independent Statistical Review re-examines the method and its reporting.
How do you protect my research data and confidentiality?
Research data, code and project details are handled confidentially, and project information is not published. Researcher names and institutions are not used publicly without permission. An NDA is available where required and can be arranged before sensitive materials are shared.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analytical work, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope rather than being quoted in advance.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need to Confirm the Right
Computational Method?
Share your research question, study design and data. We review the prior, sampling unit or missingness question and confirm the approach before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014