Bayesian Computing in the Undergraduate Statistics Curriculum

Figures & data

Table 1 Bayes table representation for learning about a discrete-valued parameter.

Model	Prior	Likelihood	Product	Posterior
λ1	p1	$L({\lambda }_1)$	$p_{1}L({\lambda }_1)$	$p_{1}L({\lambda }_1)/S$
λ2	p2	$L({\lambda }_2)$	$p_{2}L({\lambda }_2)$	$p_{2}L({\lambda }_2)/S$
…	…	…	…	…
λk	pk	$L({\lambda }_k)$	$p_{k}L({\lambda }_k)$	$p_{k}L({\lambda }_k)/S$
Sum			S

Table 2 Bayes table representation for ED example.

λ	Prior	Likelihood	Product	Posterior
3.0	0.1	57.8	5.78	0.241
3.5	0.2	46.3	9.26	0.386
4.0	0.4	19.6	7.84	0.327
4.5	0.2	5.1	1.02	0.042
5	0.1	0.9	0.09	0.004

Fig. 1 Comparison of “exact” grid and normal approximation to the marginal posterior of the slope parameter β₁ in the two-group logistic model example.

Fig. 2 Histogram of sample means of predicted samples, compared to the actual sample mean (vertical red line).

Fig. 3 The distribution of named storms over time, 1851–2015.