Asian shares inched cautiously higher on Tuesday as investors wagered Australia would become the latest country in the region to inject more policy stimulus into its economy. Liquidity was lacking with markets in Japan, South Korea and Thailand on holiday and little in the way of major economic data on the docket for Tuesday. Australia’s main index (.AXJO) rose 1.1 percent as investors waited to see if the country’s central bank would cut interest rates to a record low of 2.0 percent as many expect.