Markov Chain Monte Carlo (MCMC) for Biologists

By Dr. Zubair Khalid, DVM, MS, PhD · 2026-08-22

Key Takeaways

MCMC methods enable the estimation of posterior distributions for complex biological models where analytical solutions are intractable, by generating iterative samples that converge to the target distribution.
Rigorous convergence diagnostics, including trace plot inspection for parameter trends and R-hat statistics below 1.01, are critical before interpreting posterior summaries like means or credible intervals.
The biological relevance of MCMC results is contingent on appropriate model specification and justifiable prior choices; convergence alone does not validate the model's suitability for the biological question.
Common MCMC algorithms in biology include Metropolis-Hastings for general sampling, Gibbs sampling for conditional distributions, and Hamiltonian Monte Carlo (HMC) and No-U-Turn Sampler (NUTS) for efficient exploration of high-dimensional parameter spaces, such as in phylogenetic inference.
Key workflow steps involve defining the biological model (likelihood), selecting biologically informed priors, running multiple chains, verifying convergence with diagnostics, and transparently reporting all settings and results.
Failure patterns like poor mixing (high autocorrelation, low effective sample size) or non-convergence (slow drift, high R-hat) necessitate specific troubleshooting, such as adjusting proposal distributions, increasing iterations, or reparameterizing the model.

Quick Answer

MCMC methods let biologists estimate posterior distributions for complex models when analytical solutions are unavailable, using iterative sampling that converges to the target distribution.
Start with trace plot inspection and R-hat diagnostics below 1.01 for all parameters before interpreting any posterior summaries.
MCMC results depend on model specification and prior choices, so convergence does not guarantee that the model itself is appropriate for the biological question.

What MCMC Actually Does in Biological Research

Markov Chain Monte Carlo methods are computational tools that generate samples from probability distributions that are too complex to describe mathematically. In biological research, these distributions typically represent the uncertainty around model parameters after observing data. The Markov property means each new sample depends only on the current state, not on the full history of previous samples. Monte Carlo refers to using random sampling to approximate numerical results.

For a biologist fitting a nonlinear growth curve, estimating heritability from pedigree data, or reconstructing a phylogenetic tree, the posterior distribution often has no closed form. MCMC provides a way to draw samples from that distribution without knowing its exact shape. The samples accumulate into a histogram that approximates the true posterior, and summary statistics such as means, medians, and credible intervals come from that empirical distribution.

The core idea is a random walk through parameter space. The algorithm proposes new parameter values, decides whether to accept or reject them based on how well they explain the data, and records the accepted values. Over time, the chain spends more time in regions of high probability and less time in regions of low probability. The resulting sequence of samples is the Markov chain, and the distribution of those samples approximates the target posterior.

The most common MCMC algorithm in biological applications is the Metropolis-Hastings algorithm. It works by proposing a new parameter value from a proposal distribution, then accepting it with a probability that depends on the ratio of the posterior densities at the proposed and current values. The Gibbs sampler is a special case where each parameter is updated in turn from its conditional distribution given all other parameters. Hamiltonian Monte Carlo and its extension, the No-U-Turn Sampler, use gradient information to explore high-dimensional parameter spaces more efficiently.

Why Biologists Need MCMC

Bayesian statistical methods have become standard in many areas of biology because they provide a coherent framework for incorporating prior knowledge and quantifying uncertainty. The posterior distribution combines the likelihood of the observed data with prior beliefs about the parameters. This posterior is the complete answer to a statistical inference problem, but it is rarely available in closed form.

Consider a study of bacterial growth rates under different antibiotic concentrations. The researcher wants to estimate the growth rate parameter and its uncertainty for each concentration. A simple linear regression might be adequate, but if the relationship is nonlinear or if there are hierarchical effects across experimental batches, the model becomes too complex for analytical solutions. MCMC allows the researcher to fit these models and obtain full posterior distributions for every parameter.

Phylogenetics is another major application. Reconstructing evolutionary relationships from sequence data requires searching over tree topologies and branch lengths. The space of possible trees is enormous, and the posterior distribution over trees cannot be computed directly. MCMC methods are used to sample from this distribution and estimate the probability of different tree topologies.

Population genetics, epidemiology, and ecology all use MCMC for similar reasons. Models of population growth, disease transmission, and species interactions are typically nonlinear and have multiple parameters that interact. MCMC is the computational engine that makes Bayesian inference feasible for these models.

The National Library of Medicine provides access to biomedical books and research-method references that cover the statistical foundations of these approaches. Researchers can use these resources to understand the mathematical basis of MCMC and to identify appropriate methods for their specific biological questions.

Core Principles of MCMC

The Target Distribution

The target distribution is the posterior distribution of the model parameters given the data. It is proportional to the likelihood of the data times the prior distribution of the parameters. The constant of proportionality is the marginal likelihood, which is often impossible to compute directly. MCMC avoids this problem because the algorithms only require the unnormalized posterior, which is the product of the likelihood and the prior.

The Markov Property

A Markov chain has the property that the next state depends only on the current state, not on the sequence of states that preceded it. This property is what makes the chain tractable. The transition probabilities from one state to the next define the chain, and under certain conditions the chain will converge to a stationary distribution that is the target distribution.

Convergence and Burn-in

The chain starts at some initial value, which may be far from the high-probability region of the posterior. The early samples, called the burn-in period, are not representative of the target distribution and should be discarded. After burn-in, the chain is said to have converged if it is sampling from the stationary distribution. The length of the burn-in period depends on the model and the starting values.

Autocorrelation and Effective Sample Size

Samples from a Markov chain are not independent. Each sample is correlated with the samples that came before it. This autocorrelation reduces the amount of information in the chain. The effective sample size is the number of independent samples that would provide the same amount of information as the correlated chain. A chain with high autocorrelation has a low effective sample size and requires more iterations to achieve the same precision.

Trace Plots

A trace plot shows the value of a parameter against the iteration number. A well-behaved chain looks like a hairy caterpillar, with the parameter value moving around the posterior mean and no obvious trends or long periods in one region. A chain that has not converged may show a trend, such as a slow drift from the starting value, or it may be stuck in one region of parameter space.

The MCMC Workflow for Biological Data

Step 1: Define the Model

The first step is to write down the likelihood function, which describes how the data were generated given the parameters. This requires a biological model of the process under study. For example, a logistic growth model for a bacterial population has parameters for the carrying capacity and the growth rate. The likelihood describes the probability of observing the measured population sizes given those parameters.

Step 2: Choose Priors

The prior distribution encodes the biological knowledge about the parameters before seeing the data. Priors can be informative, based on previous experiments or published values, or weakly informative, which provide some regularization but do not dominate the data. The choice of prior matters, especially with small sample sizes, and should be justified in the methods section of any report.

Step 3: Run the Chain

The MCMC algorithm is run for a number of iterations. The number of chains is also important. Multiple chains with different starting points are recommended to check that all chains converge to the same distribution. The chains should be run long enough to produce a sufficient effective sample size for the parameters of interest.

Step 4: Check Convergence

Convergence diagnostics are used to assess whether the chains have reached the stationary distribution. The R-hat statistic compares the variance between chains to the variance within chains. Values close to 1.0 indicate convergence. The effective sample size should be large enough to provide stable estimates of posterior quantiles.

Step 5: Summarize the Posterior

Once convergence is confirmed, the posterior samples are used to compute summary statistics. The posterior mean or median is a point estimate, and the credible interval provides a range of plausible values. The posterior distribution can also be used to compute the probability that a parameter exceeds a threshold, which is often the biologically relevant question.

Step 6: Report the Results

The results should be reported with the model specification, the priors, the MCMC settings, and the convergence diagnostics. This transparency allows other researchers to reproduce the analysis and assess its validity. The EQUATOR Network provides reporting guidelines for various study types, and researchers should select the appropriate guideline for their study design.

At a Glance

MCMC Component	Purpose	Common Biological Application	Key Diagnostic
Metropolis-Hastings	General purpose sampling for low-dimensional models	Estimating growth rates from time series data	Trace plot inspection
Hamiltonian Monte Carlo	Efficient sampling for high-dimensional models	Phylogenetic inference and hierarchical models	R-hat and effective sample size
Gibbs Sampler	Sampling from conditional distributions	Mixed models with multiple variance components	Autocorrelation plot

Convergence Diagnostics in Practice

R-hat Statistic

The R-hat statistic, also called the potential scale reduction factor, compares the variance between multiple chains to the variance within each chain. If the chains have converged to the same distribution, the between-chain variance should be similar to the within-chain variance, and R-hat should be close to 1.0. A common threshold is R-hat below 1.01 for all parameters, though some fields use a more lenient threshold of 1.1.

Effective Sample Size

The effective sample size is the number of independent samples that the chain is equivalent to. It is calculated from the autocorrelation of the chain. A chain with high autocorrelation has a low effective sample size. For most biological applications, an effective sample size of at least 100 is needed for stable estimates of the posterior mean, and more is needed for stable estimates of the tails of the distribution.

Trace Plot Inspection

Trace plots should be examined visually for every parameter. A chain that is mixing well will show a dense band of values with no long-term trends. A chain that is stuck in one region will show a flat line for many iterations, followed by a jump to another region. This behavior indicates poor mixing and the chain may not have converged.

Autocorrelation Plots

Autocorrelation plots show the correlation between samples at different lags. A chain with low autocorrelation will have a plot that drops quickly to zero. A chain with high autocorrelation will show a slow decay, indicating that the samples are highly dependent and the effective sample size is low.

Common Failure Patterns

Poor Mixing

A chain that mixes poorly moves slowly through the parameter space and has high autocorrelation. This can be caused by a proposal distribution that is too narrow, which leads to many rejected proposals, or too wide, which leads to many proposals that are far from the current state and are rejected. The result is a chain that stays in one region for a long time.

Non-convergence

A chain that has not converged is still moving toward the stationary distribution. This can be caused by a starting point that is far from the high-probability region, or by a model that is too complex for the amount of data. The trace plot will show a trend, and the R-hat statistic will be high.

Label Switching

In mixture models, the components of the mixture are exchangeable, and the chain may switch between different labelings of the components. This is a common problem in biological applications such as clustering gene expression data. The posterior distribution is symmetric, and the chain may not converge to a single labeling.

Multimodality

The posterior distribution may have multiple modes, which are regions of high probability separated by regions of low probability. A single chain may get stuck in one mode and never explore the other modes. Multiple chains with different starting points can help, but they may still miss modes if the starting points are in the same region.

Practical Implementation Steps

Choose the Software

Several software packages are available for MCMC analysis. The choice depends on the model complexity and the user's programming experience. Some packages are designed for specific applications, such as phylogenetics, while others are general-purpose.

Write the Model Code

The model must be written in the syntax of the chosen software. This includes the likelihood, the priors, and the parameters. The model code should be checked for errors and tested on simulated data before running on real data.

Run the Chains

Run multiple chains with different starting points. The number of chains and the number of iterations will depend on the model and the data. The chains should be run long enough to achieve the desired effective sample size.

Check the Diagnostics

After the chains are run, the diagnostics should be checked. The R-hat statistic should be below the threshold, and the effective sample size should be sufficient. The trace plots should be inspected visually.

Summarize the Posterior

Once the diagnostics are acceptable, the posterior samples are used to summarize the parameters. The posterior mean, median, and credible intervals are reported. The posterior can also be used to calculate the probability of a parameter being in a certain range.

Report the Analysis

The analysis should be reported with enough detail for another researcher to reproduce it. This includes the model specification, the priors, the MCMC settings, the diagnostics, and the software version. The reporting guidelines from the EQUATOR Network can help ensure that the report is complete and transparent.

Records and Measurements

Keeping a Record of MCMC Runs

For reproducibility, the MCMC settings should be recorded. This includes the random seed, the number of chains, the number of iterations, the burn-in, and the thinning interval. The software version and the model code should also be recorded.

Storing the Posterior Samples

The posterior samples should be stored in a format that can be read by the analysis software. The samples are the raw output of the MCMC and are needed for any subsequent analysis. The storage format should be documented.

Documenting the Model

The model should be documented in a way that is understandable to other researchers. This includes the biological assumptions, the likelihood, the priors, and the parameters. The documentation should be sufficient for another researcher to implement the model.

Common Failure Patterns

Overconfident Intervals

The posterior intervals can be too narrow if the model is misspecified or if the priors are too informative. The intervals reflect the model and the priors, and if the model is wrong, the intervals will be wrong. The model should be checked with posterior predictive checks, which simulate new data from the posterior and compare it to the observed data.

Underestimation of Uncertainty

The posterior intervals can be too narrow if the model does not account for all sources of uncertainty. For example, if the measurement error is not included in the model, the posterior intervals will be too narrow. The model should include all known sources of uncertainty.

Sensitivity to Priors

The posterior can be sensitive to the choice of priors, especially when the data are sparse. A sensitivity analysis should be conducted to assess the impact of the priors on the results. The analysis should be reported.

Limitations of MCMC

Computational Cost

MCMC can be computationally expensive, especially for complex models with many parameters. The chains may need to be run for a long time to achieve convergence and a sufficient effective sample size. The computational cost can be a limiting factor for large datasets.

Model Misspecification

MCMC provides the posterior distribution for the specified model. If the model is misspecified, the posterior will be the posterior for the wrong model. The model should be checked with posterior predictive diagnostics.

Interpretation of the Posterior

The posterior distribution is a statement about the parameters given the model and the data. It is not a statement about the true value of the parameter. The posterior is conditional on the model, and the model is a simplification of the biological process.

Safety and Regulatory Context

MCMC is a statistical method and does not have direct safety or regulatory implications. However, the results of MCMC analyses can be used in regulatory submissions, such as drug efficacy or environmental risk assessments. The results should be reported transparently and the methods should be reproducible.

The National Institutes of Health provides guidance on data management and sharing policies for research that it funds. The data and the analysis code should be shared to allow the other researchers to reproduce the results. The NIH grants and funding pages provide information on the requirements for data sharing.

Professional Escalation Criteria

If the MCMC chains do not converge, or if the effective sample size is too low, the results should not be used for inference. The model should be revised, or the MCMC settings should be changed. If the problem persists, a statistician should be consulted.

If the posterior is sensitive to the priors, the results should be interpreted with caution. The sensitivity analysis should be reported, and the results should be presented with the caveat that the posterior is prior-dependent.

If the model is misspecified, the posterior is not a valid statement about the biological process. The model should be revised, and the analysis should be repeated.

A Practical Decision Framework for MCMC Troubleshooting in Biological Models

When an MCMC analysis produces unsatisfactory results, the immediate reaction is often to increase the number of iterations or adjust the proposal distribution. These responses can waste computational time and may not address the underlying problem. A structured decision framework helps you identify the specific failure mode, select the appropriate corrective action, and document the process for reproducibility. This section provides a step-by-step framework that you can apply when your chains show signs of poor mixing, non-convergence, or insufficient effective sample size.

Step 1: Classify the Failure Pattern

Before changing any settings, examine your trace plots and diagnostics to classify the problem. The classification determines which corrective action is appropriate. Three primary failure patterns appear in biological MCMC applications.

Pattern A: Slow Drift with No Stabilization

The trace plot shows a gradual trend from the starting value toward some region, but the chain never settles into a stable band. The R-hat statistic remains above 1.01 even after many iterations. This pattern indicates that the chain has not yet reached the stationary distribution. The burn-in period was too short, or the starting values were too far from the high-probability region.

Pattern B: High Autocorrelation with Stable Mean

The trace plot shows a dense band around a stable mean, but the autocorrelation plot decays slowly. The effective sample size is low even though the chain appears to have converged. This pattern indicates that the chain is exploring the posterior but moving slowly. The proposal distribution is too narrow, causing many small steps that are highly correlated with each other.

Pattern C: Multiple Distinct Regions with Jumps

The trace plot shows the chain spending long periods in one region, then jumping to another region. This pattern can indicate a multimodal posterior or a problem with the model specification. In mixture models, this may be label switching. In other models, it may indicate that the posterior has multiple modes that are separated by low-probability regions.

Step 2: Apply the Corrective Action

Each failure pattern requires a different corrective action. The table below summarizes the recommended actions for each pattern.

Failure Pattern	Primary Corrective Action	Secondary Action	When to Escalate
Slow drift with no stabilization	Increase burn-in and run more iterations	Use multiple chains with dispersed starting values	If R-hat stays above 1.01 after doubling iterations
High autocorrelation with low effective sample size	Adjust the proposal distribution width	Increase the number of iterations	If effective sample size stays below 100 after adjustments
Stuck regions with no mixing	Reparameterize the model	Use a different MCMC algorithm	If the chain still does not mix after reparameterization

Step 3: Document the Decision Process

For each corrective action, record the following information in your analysis log.

The failure pattern you observed
The corrective action you applied
The number of iterations before and after the change
The R-hat and effective sample size before and after the change
The random seed used for each run

This documentation is essential for reproducibility. The National Institutes of Health data management and sharing policy requires that research data and analysis code be shared for research that it funds. Your analysis log is part of the documentation that allows other researchers to reproduce your results.

Step 4: Verify the Correction

After applying a corrective action, do not simply check the R-hat statistic. Run the full set of diagnostics, including trace plots, autocorrelation plots, and effective sample size calculations. The correction is successful only when all diagnostics are acceptable.

Step 5: Escalate When Necessary

If the corrective action does not resolve the problem, escalate to a statistician. The escalation criteria are specific and should be applied consistently.

Escalate if R-hat remains above 1.01 for any parameter after 100,000 iterations
Escalate if the effective sample size remains below 100 for any parameter of interest
Escalate if the chain continues to show the same failure pattern after two corrective actions

A Record System for MCMC Runs

A systematic record system is essential for reproducible MCMC analysis. The record system captures the model specification, the MCMC settings, and the diagnostics for each run. This system allows you to compare runs, identify the source of problems, and provide the information needed for publication and data sharing.

The MCMC Run Log

Create a run log with one entry for each MCMC run. Each entry should include the following fields.

Run identifier
Date and time
Model version
Data version
Random seed
Number of chains
Number of iterations per chain
Burn-in length
Thinning interval
Proposal distribution settings
Software and version
R-hat for each parameter
Effective sample size for each parameter
Trace plot file name
Autocorrelation plot file name

The run log is a living document that you update with each run. It provides a complete history of the analysis and allows you to trace the effect of each change.

The Model Version Log

The model code changes over time as you fix errors and improve the specification. The model version log records the changes and the date of each change. Each version has a unique identifier that is referenced in the run log.

The Data Version Log

The data may change during the analysis, for example when you correct errors or add new observations. The data version log records the changes and the date of each change. Each data version has a unique identifier that is referenced in the run log.

Storing the Posterior Samples

The posterior samples are the raw output of the MCMC and are needed for any subsequent analysis. Store the samples in a format that can be read by the analysis software. The storage format should be documented in the run log.

The Analysis Report

The analysis report is the final document that summarizes the MCMC analysis. The report includes the model specification, the priors, the MCMC settings, the diagnostics, and the results. The report should be written so that another researcher can reproduce the analysis.

Troubleshooting Method for Persistent MCMC Problems

Some MCMC problems persist even after the corrective actions described above. This troubleshooting method provides a systematic approach to identify the root cause of persistent problems.

Step 1: Check the Model Code

The first step is to check the model code for errors. A common error is a parameter that is not constrained to the correct range. For example, a variance parameter that is allowed to be negative will cause the chain to fail. Another common error is a likelihood function that is not correctly specified.

Step 2: Test on Simulated Data

The next step is to test the model on simulated data. Generate data from the model with known parameter values, then fit the model to the simulated data. If the MCMC does not recover the known parameter values, the model code has an error.

Step 3: Simplify the Model

If the model passes the simulated data test but still has problems with the real data, simplify the model. Remove parameters that are not essential. The simplified model may converge more easily.

Step 4: Change the Parameterization

The parameterization of the model can affect the MCMC performance. For example, a parameter that is constrained to be positive can be reparameterized using a log transformation. This change can improve the mixing of the chain.

Step 5: Change the MCMC Algorithm

If the model is correctly specified and the parameterization is appropriate, change the MCMC algorithm. A Hamiltonian Monte Carlo algorithm may perform better than Metropolis-Hastings for a model with many parameters.

Step 6: Consult a Statistician

If the problem persists after all of these steps, consult a statistician. The statistician can identify the root cause of the problem and recommend a solution.

Common Failure Patterns in Biological MCMC Applications

The failure patterns described in the decision framework appear in specific biological applications. The following examples illustrate the patterns and the corrective actions.

Failure Pattern in a Growth Curve Model

A researcher fits a logistic growth model to bacterial population data. The trace plot for the growth rate parameter shows a slow drift from the starting value. The R-hat statistic is 1.15 after 50,000 iterations. The corrective action is to increase the burn-in period and run more chains with dispersed starting points. The researcher runs 10 chains with starting points spread across the plausible range of the growth rate parameter. After 100,000 iterations, the R-hat is below 1.01.

Failure Pattern in a Hierarchical Model

A researcher fits a hierarchical model to gene expression data from multiple experimental batches. The trace plot for the batch variance parameter shows a stable band, but the effective sample size is only 50. The corrective action is to increase the thinning interval and run more iterations. The researcher increases the thinning interval from 1 to 10 and runs 1,000,000 iterations. The effective sample size increases to 500.

Failure Pattern in a Mixture Model

A researcher fits a mixture model to gene expression data. The trace plot for the component means shows the chain jumping between two regions. The corrective action is to reparameterize the model to constrain the component means to be ordered. The chain then mixes well and the R-hat statistic is below 1.01.

Welfare and Safety Context

MCMC is a statistical method and does not have direct welfare or safety implications. However, the results of MCMC analyses can be used in regulatory submissions, such as drug efficacy or environmental risk assessments. The results should be reported transparently and the methods should be reproducible.

The Committee on Publication Ethics core practices provide guidance on the responsible conduct of research, including data handling and reporting. The core practices emphasize the importance of accurate reporting of methods and results. The EQUATOR Network provides reporting guidelines for various study types. Researchers should select the appropriate guideline for their study design and follow it when reporting the MCMC analysis.

The National Institutes of Health provides guidance on data management and sharing policies for research that it funds. The data and the analysis code should be shared to allow other researchers to reproduce the results. The NIH grants and funding pages provide information on the requirements for data sharing.

Professional Escalation Criteria

The professional escalation criteria are the conditions under which you should stop the analysis and consult a statistician. The criteria are defined to prevent the use of invalid results.

Escalate When the Chain Does Not Converge

If the R-hat statistic remains above 1.01 for any parameter after 100,000 iterations, the chain has not converged. The results are not valid for inference. Consult a statistician.

Escalate When the Effective Sample Size Is Too Low

If the effective sample size is below 100 for any parameter of interest, the posterior estimates are not stable. The results are not valid for inference. Consult a statistician.

Escalate When the Model Is Misspecified

If the posterior predictive checks indicate that the model is misspecified, the posterior is not a valid statement about the biological process. The model should be revised, and the analysis should be repeated. If the model cannot be revised, consult a statistician.

Escalate When the Posterior Is Sensitive to Priors

If the posterior is sensitive to the choice of priors, the results should be interpreted with caution. The sensitivity analysis should be reported, and the results should be presented with the caveat that the posterior is prior-dependent. If the sensitivity is extreme, consult a statistician.

Records and Measurements

Keeping a Record of MCMC Runs

Storing the Posterior Samples

Documenting the Model

Frequently Asked Questions

What is the difference between MCMC and regular Monte Carlo?

Regular Monte Carlo draws independent samples from a known distribution. MCMC draws dependent samples from an unknown distribution by constructing a Markov chain that has the target distribution as its stationary distribution. The samples are correlated, which reduces the effective sample size.

How long should I run an MCMC chain?

The chain should be run long enough to achieve convergence and a sufficient effective sample size. The required length depends on the model and the data. The chain should be run until the R-hat is below the threshold and the effective sample size is sufficient for the parameters of interest.

What is the burn-in period?

The burn-in period is the initial part of the chain that is discarded because it is not representative of the target distribution. The chain starts at an initial value that may be far from the high-probability region, and the burn-in is the time it takes to reach the stationary distribution.

What is the effective sample size?

The effective sample size is the number of independent samples that would provide the same amount of information as the correlated samples from the chain. It is calculated by dividing the number of samples by the autocorrelation. A low effective sample size indicates that the chain is highly autocorrelated.

How do I choose the priors?

The priors should be based on the biological knowledge before seeing the data. Priors can be informative, based on published data, or weakly informative, which provide broad constraints. The choice of the prior should be justified and reported.

What is the difference between a credible interval and a confidence interval?

A credible interval is a Bayesian interval that contains the parameter with a certain probability, given the model and the data. A confidence interval is a frequentist interval that contains the parameter with a certain probability over repeated sampling. The two intervals have different interpretations.

What is the posterior predictive check?

A posterior predictive check simulates the data from the posterior distribution and compares the simulated data to the observed data. If the simulated data are similar to the observed data, the model is a good fit. If the simulated data are different, the model is misspecified.

What should I do if my chains do not converge?

If the chains do not converge, the model should be checked for errors, and the MCMC settings should be changed. The proposal distribution may need to be adjusted, or the number of iterations may need to be increased. If the problem persists, a statistician should be consulted.

Frequently Asked Questions

What is the difference between MCMC and regular Monte Carlo?

How long should I run an MCMC chain?

What is the burn-in period?

What is the effective sample size?

How do I choose the priors?

What is the difference between a credible interval and a confidence interval?

What is the posterior predictive check?

What should I do if my chains do not converge?

Related Bioinformatics Guides

Related Clinical & Scientific Guides

References and Further Reading

Research Methods Resources. National Library of Medicine.
EQUATOR Network. EQUATOR Network.
Core Practices. Committee on Publication Ethics.
NIH Grants and Funding. National Institutes of Health.
ORCID for Researchers. ORCID.
Data Management and Sharing Policy. National Institutes of Health.
NCBI Data Resources. National Center for Biotechnology Information.
EMBL-EBI Training. European Bioinformatics Institute.
Practical guidelines for Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC).. Open research Europe, 2023.
A biologist's guide to Bayesian phylogenetic analysis.. Nature ecology & evolution, 2017.
Efficient design of synthetic gene circuits under cell-to-cell variability.. BMC bioinformatics, 2023.

This article is educational and does not replace validated analysis plans, institutional policy, clinical interpretation, or specialist review.