How can you use Bayesian models to update program evaluation findings?

1 What are Bayesian models?

Bayesian models are a type of statistical models that use Bayes' theorem to update the probability of a hypothesis based on new data and prior beliefs. Bayes' theorem is a mathematical formula that calculates the conditional probability of a hypothesis given some evidence, by multiplying the prior probability of the hypothesis and the likelihood of the evidence, and dividing by the marginal probability of the evidence. Bayesian models allow you to express your uncertainty and assumptions about the parameters and outcomes of your program evaluation, and to revise them as you collect more data.

2 How do Bayesian models differ from traditional models?

Traditional models, also known as frequentist models, are another type of statistical models that use hypothesis testing and confidence intervals to infer the significance and effect size of a program evaluation. Traditional models rely on fixed assumptions and parameters, and do not account for prior knowledge or beliefs. They also use p-values and alpha levels to reject or fail to reject a null hypothesis, which can be misleading or misinterpreted. Bayesian models, on the other hand, use posterior probabilities and credible intervals to estimate the plausibility and range of a hypothesis, which can be more intuitive and informative.

3 How to apply Bayesian models to program evaluation data?

To apply Bayesian models to your program evaluation data, you need to follow three steps: specify a model, assign prior distributions, and update with data. First, you need to specify a model that describes the relationship between your program variables, such as inputs, outputs, outcomes, and impacts. For example, you can use a linear regression model to predict the impact of a training program on employee performance. Second, you need to assign prior distributions that reflect your beliefs or expectations about the parameters of your model, such as the coefficients, intercepts, and variances. For example, you can use a normal distribution to assign a mean and a standard deviation to each parameter. Third, you need to update your model with your data, using Bayes' theorem, to obtain posterior distributions that represent your updated beliefs or estimates about the parameters of your model. For example, you can use a software package like R or Python to perform Bayesian inference and calculate the posterior distributions.

4 How to interpret and communicate Bayesian models?

To interpret and communicate your Bayesian models, you need to use posterior probabilities and credible intervals. Posterior probabilities are the probabilities of your hypotheses given your data and prior distributions. They can help you compare and rank different hypotheses, and assess their plausibility and uncertainty. For example, you can say that there is a 95% probability that the training program has a positive impact on employee performance. Credible intervals are the intervals that contain a certain percentage of the posterior distribution. They can help you estimate the range and precision of your hypotheses, and identify outliers and anomalies. For example, you can say that the 95% credible interval for the impact of the training program is between 0.2 and 0.8 standard deviations.

5 What are the benefits and challenges of Bayesian models?

Bayesian models have several benefits and challenges for program evaluation. Incorporating prior knowledge and beliefs into your analysis, as well as updating them as more data is collected, is one of the advantages of Bayesian models. Additionally, they provide more intuitive and informative measures of uncertainty and evidence than traditional models, and can handle complex and nonlinear models better. Furthermore, they can facilitate learning and adaptation, and support decision making and policy making based on your program evaluation findings. However, Bayesian models also require more computational resources and time, can encounter convergence and sensitivity issues, depend on the choice and quality of prior distributions, and may be unfamiliar or misunderstood by some stakeholders.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?