Detect is a synonym of Observe. Observe is a synonym of Celebrate. Spirit can be used for Celebrate. Spirit is related to Holy. 
Apologize entails/necessarily involves Admit. Admit is related to Allow. 
Detect <--Synonym--> Observe <--Synonym--> Celebrate <--UsedFor-- Spirit <--RelatedTo--> Holy 
Apologize --Entails--> Admit <--RelatedTo--> Allow 