NOTE: This is a condensed excerpt from my forthcoming (2014) commentary on Philippians.
The paradoxical nature of the result stated in 1:14 should not be missed. The natural response to persecution would be to cower in fear and reduce one’s public visibility. We see such a response in the days following the crucifixion of Jesus; his followers gathered behind locked doors because they feared they might be next (John 20:19). Yet less than six weeks later they boldly and publicly preach the gospel to Jews gathered from across the Roman Empire to celebrate Pentecost. The difference was the gift of the Spirit (Acts 2:1-4). Although Paul does not explicitly mention the Spirit here, he will soon do so in connection with his own situation (Phil 1:19). Only the Spirit can transform the natural response of cowardice in the face of persecution into greater boldness to proclaim the very message that provokes persecution. Such boldness is not the product of greater human effort, but is rather fueled by confidence/trust in the Lord. Paul makes the connection between trust in the Lord and sharing the gospel explicit in 2 Corinthians 4:13-14—”Since we have the same spirit of faith according to what has been written, ‘I believed, and so I spoke,’ we also believe, and so we also speak, knowing that he who raised the Lord Jesus will raise us also with Jesus and bring us with you into his presence.” There appears to be a proportional relationship between one’s boldness in speaking the gospel fearlessly and trust in the Lord. Lack of boldness may signal a lack of confidence/trust in the Lord.
 Here in 2 Corinthians 4:13-14 Paul quotes from Psalm 116:10, where the psalmist verbally expresses his faith in the midst of persecution; for more on this citation, see G. K. Beale and D. A. Carson, Commentary on the New Testament Use of the Old Testament (Grand Rapids: Baker, 2007), 764-65.