Optimizer_mode and statistics gathering in 10g

The OPTIMIZER_MODE parameter has a new default value of ALL_ROWS in OracleDatabase 10g.
In Oracle Database 10g, the Optimizer uses dynamic sampling to get statistics for these tables and uses Cost Based Optimizer(CBO). The other two possible values are FIRST_ROWS_N and FIRST_ROWS.
The CHOOSE and RULE values are no longer supported by Oracle.

In Oracle Database 10g an automatic statistics gathering job is enabledby default when a database is created .This is because of the default setting STATISTICS_LEVEL=TYPICAL.
This is also true when you do database upgrade. Oracle will automatically collect statistics for alldatabase objects which are missing statistics by running an Oracle Scheduler job(GATHER_STATS_JOB) during a predefined maintenance window.
Statistics on a table are considered stale when more than 10% of the rows are changed.
The maintenance window by default is opens every night from 10:00 pm to 6:00 am and all day on weekends.This can be changed.

In 9i to gather statistics automatically on tables, you have to set MONITORING on when creating the table or using the alter table command.
In 10g MONITORING and NOMONITORING is no longer in use.It has been depreciated.

Monitoring tracks the approximate number of DMLs (INSERT, UPDATE, and DELETE)operations for the table since the last time statistics were gathered. information about how many rows are affected is maintained in the SGA, until periodically (about every 15 minutes.This can be changed) after that the background process called SMON flush the data into the data dictionary.(another use of SMON )
This data dictionary information is made AVAILABLE through the tablesDBA_TAB_MODIFICATIONS, ALL_TAB_MODIFICATIONS or USER_TAB_MODIFICATIONS views.
Oracle uses these views to identify tables with stale statistics. Whenever there is 10% change in data in a table, Oracle considers the statistics to be stale.Then it will start to collect statiscts during the maintanence window (STATISTICS_LEVEL=TYPICAL. That is the default)
Since in 10g CBO is used, having up to date statistics is so important to generate good execution plans. Automatic statistics collection is the way to go in 10g.