What's in a Bayesian Model?

Mô hình Hồi quy Bayesian với rstanarm

Jake Thompson

Psychometrician, ATLAS, University of Kansas

Posterior distributions

  • Posterior distributions sampled in groups called chains
  • Each sample in a chain is an iteration
Mô hình Hồi quy Bayesian với rstanarm

Mô hình Hồi quy Bayesian với rstanarm

Mô hình Hồi quy Bayesian với rstanarm

Changing the number and length of chains

stan_model <- stan_glm(kid_score ~ mom_iq, data = kidiq,
  chains = 3, iter = 1000, warmup = 500)
Mô hình Hồi quy Bayesian với rstanarm
summary(stan_model)

Model Info:

 function:     stan_glm
 family:       gaussian [identity]
 formula:      kid_score ~ mom_iq
 algorithm:    sampling
 priors:       see help('prior_summary')
 sample:       1500 (posterior sample size)
 observations: 434
 predictors:   2

Estimates:
                mean    sd      2.5%    25%     50%     75%     97.5%
(Intercept)      25.8     6.0    14.1    21.7    25.6    29.9    37.5
mom_iq            0.6     0.1     0.5     0.6     0.6     0.7     0.7
sigma            18.3     0.6    17.2    17.9    18.3    18.7    19.6
mean_PPD         86.9     1.3    84.5    86.0    86.9    87.7    89.2
log-posterior -1885.4     1.2 -1888.4 -1885.9 -1885.1 -1884.5 -1884.0

Diagnostics:
              mcse Rhat n_eff
(Intercept)   0.2  1.0  1500 
mom_iq        0.0  1.0  1500 
sigma         0.0  1.0  1500 
mean_PPD      0.0  1.0  1500 
log-posterior 0.0  1.0   619 

For each parameter, mcse is Monte Carlo standard error, n_eff is a crude measure of effective sample size, and Rhat is the potential scale reduction factor on split chains (at convergence Rhat=1).
Mô hình Hồi quy Bayesian với rstanarm

Mô hình Hồi quy Bayesian với rstanarm

How many iterations?

  • Fewer iterations = shorter estimation time
  • Not enough iteration = convergence problems
Mô hình Hồi quy Bayesian với rstanarm

Let's practice!

Mô hình Hồi quy Bayesian với rstanarm

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