The Japan Times article has the basic information but I'll add a quote from an e-mail announcement put out by the Kumamoto City International Foundation (Kumamoto City International Center):

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■“Hifuri-shinji” (shrine ritual) at Aso Shrine
“Hifuri-shinji” is a traditional ceremony which celebrates the marriage of deities.
People twirl flaming torches to celebrate. You can see beautiful loops of light.
Day and Time: Sat.,21st. Mar.
18:00~20:00
Place: Aso Shrine
Cost: free
Access: JR Kumamoto Station (boarding) → JR Miyaji Station (kick off)
*about 15 minutes on foot from the station, or please take Sanko Bus and get off “Aso Jinjya-mae”
For more information: Aso Shrine (TEL: 0967-22-0064) *Japanese language only
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http://www.japantimes.co.jp/events/2015/03/02/things-to-do/traditional-festivals-things-to-do/hifuri-shinji-aso-shrine/