Hypothesis tests

Null hypothesis testing doesn’t apply to the Bayesian context (thankfully)

However, we can still ask questions about the probability of certain outcomes

attendance_brms

 Family: poisson 
  Links: mu = log 
Formula: daysabs ~ math + gender + prog 
   Data: attendance (Number of observations: 314) 
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 10;
         total post-warmup samples = 400

Population-Level Effects: 
             Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
Intercept        1.49      0.08     1.32     1.63        376 1.00
math            -0.01      0.00    -0.01    -0.01        401 1.00
genderMale      -0.25      0.04    -0.34    -0.16        421 0.99
progGeneral      1.27      0.08     1.11     1.43        391 1.00
progAcademic     0.85      0.07     0.70     0.99        404 1.00

Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample 
is a crude measure of effective sample size, and Rhat is the potential 
scale reduction factor on split chains (at convergence, Rhat = 1).

hypothesis(attendance_brms, 'genderMale < -.2')

Hypothesis Tests for class b:
              Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
1 (genderMale)-(-.2) < 0    -0.05      0.04     -Inf     0.03        5.9      0.86     
---
'*': The expected value under the hypothesis lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(attendance_brms, 'progGeneral/progAcademic > 1')

Hypothesis Tests for class b:
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
1 (progGeneral/prog... > 0     0.51      0.09     0.37      Inf        Inf         1    *
---
'*': The expected value under the hypothesis lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.