Addressed the following issues from the review of the patch:

1. The PERSISTENT FOR clause of the ANALYZE command overrides
the setting of the system variable use_stat_tables: 
with this clause ANALYZE unconditionally collects persistent
statistics.
2. ANALYZE collects persistent statistics only for tables of
the USER category. So it never collects persistent statistics
for system tables.  

mysql-test/r/statistics.result

@@ -1016,11 +1016,73 @@ test	t1	idx1	2	NULL
 test	t1	idx4	1	6.2000
 test	t1	idx4	2	NULL
 test	t1	idx4	3	NULL
-DROP TABLE t1,t2;
 DELETE FROM mysql.table_stats;
 DELETE FROM mysql.column_stats;
 DELETE FROM mysql.index_stats;
+ANALYZE TABLE mysql.column_stats PERSISTENT FOR ALL;
+Table	Op	Msg_type	Msg_text
+mysql.column_stats	analyze	error	Invalid argument
+ANALYZE TABLE mysql.column_stats;
+Table	Op	Msg_type	Msg_text
+mysql.column_stats	analyze	status	OK
+SELECT * FROM mysql.table_stats;
+db_name	table_name	cardinality
+SELECT * FROM mysql.column_stats;
+db_name	table_name	column_name	min_value	max_value	nulls_ratio	avg_length	avg_frequency
+SELECT * FROM mysql.index_stats;
+db_name	table_name	index_name	prefix_arity	avg_frequency
 set use_stat_tables='never';
+ANALYZE TABLE t1 PERSISTENT FOR ALL;
+Table	Op	Msg_type	Msg_text
+test.t1	analyze	status	Table is already up to date
+SELECT * FROM mysql.table_stats;
+db_name	table_name	cardinality
+test	t1	40
+SELECT * FROM mysql.column_stats;
+db_name	table_name	column_name	min_value	max_value	nulls_ratio	avg_length	avg_frequency
+test	t1	a	0	49	0.0000	4.0000	1.0000
+test	t1	c	aaaa	dddddddd	0.1250	6.6571	7.0000
+test	t1	d	1989-03-12	1999-07-23	0.1500	3.0000	8.5000
+test	t1	e	0.01	0.112	0.2250	8.0000	6.2000
+test	t1	f	1	5	0.2000	1.0000	6.4000
+test	t1	b	NULL	NULL	0.2000	17.1250	NULL
+SELECT * FROM mysql.index_stats;
+db_name	table_name	index_name	prefix_arity	avg_frequency
+test	t1	PRIMARY	1	1.0000
+test	t1	idx3	1	8.5000
+test	t1	idx2	1	7.0000
+test	t1	idx2	2	2.3846
+test	t1	idx1	1	NULL
+test	t1	idx1	2	NULL
+test	t1	idx4	1	6.2000
+test	t1	idx4	2	NULL
+test	t1	idx4	3	NULL
+SELECT * FROM mysql.table_stats;
+db_name	table_name	cardinality
+test	t1	40
+SELECT * FROM mysql.column_stats;
+db_name	table_name	column_name	min_value	max_value	nulls_ratio	avg_length	avg_frequency
+test	t1	a	0	49	0.0000	4.0000	1.0000
+test	t1	c	aaaa	dddddddd	0.1250	6.6571	7.0000
+test	t1	d	1989-03-12	1999-07-23	0.1500	3.0000	8.5000
+test	t1	e	0.01	0.112	0.2250	8.0000	6.2000
+test	t1	f	1	5	0.2000	1.0000	6.4000
+test	t1	b	NULL	NULL	0.2000	17.1250	NULL
+SELECT * FROM mysql.index_stats;
+db_name	table_name	index_name	prefix_arity	avg_frequency
+test	t1	PRIMARY	1	1.0000
+test	t1	idx3	1	8.5000
+test	t1	idx2	1	7.0000
+test	t1	idx2	2	2.3846
+test	t1	idx1	1	NULL
+test	t1	idx1	2	NULL
+test	t1	idx4	1	6.2000
+test	t1	idx4	2	NULL
+test	t1	idx4	3	NULL
+DELETE FROM mysql.table_stats;
+DELETE FROM mysql.column_stats;
+DELETE FROM mysql.index_stats;
+DROP TABLE t1,t2;
 set names utf8;
 CREATE DATABASE world;
 use world;

mysql-test/t/statistics.test

@@ -397,14 +397,39 @@ ANALYZE TABLE t1;
 SELECT * FROM mysql.column_stats;
 SELECT * FROM mysql.index_stats;
 
-DROP TABLE t1,t2;
-
 DELETE FROM mysql.table_stats;
 DELETE FROM mysql.column_stats;
 DELETE FROM mysql.index_stats;
 
+ANALYZE TABLE mysql.column_stats PERSISTENT FOR ALL;
+
+ANALYZE TABLE mysql.column_stats;
+
+SELECT * FROM mysql.table_stats;
+SELECT * FROM mysql.column_stats;
+SELECT * FROM mysql.index_stats;
+
 set use_stat_tables='never';  
 
+
+ANALYZE TABLE t1 PERSISTENT FOR ALL;
+
+SELECT * FROM mysql.table_stats;
+SELECT * FROM mysql.column_stats;
+SELECT * FROM mysql.index_stats;
+
+
+SELECT * FROM mysql.table_stats;
+SELECT * FROM mysql.column_stats;
+SELECT * FROM mysql.index_stats;
+
+
+DELETE FROM mysql.table_stats;
+DELETE FROM mysql.column_stats;
+DELETE FROM mysql.index_stats;
+
+DROP TABLE t1,t2;
+
 set names utf8;
 
 CREATE DATABASE world;

sql/sql_admin.cc

@@ -650,6 +650,12 @@ static bool mysql_admin_table(THD* thd, TABLE_LIST* tables,
       TABLE *tab= table->table;
       Field **field_ptr= tab->field;
 
+      if (lex->with_persistent_for_clause &&
+          tab->s->table_category != TABLE_CATEGORY_USER)
+      {
+        compl_result_code= result_code= HA_ADMIN_INVALID;
+      }
+
       if (!lex->column_list)
       { 
         uint fields= 0;
@@ -711,7 +717,9 @@ static bool mysql_admin_table(THD* thd, TABLE_LIST* tables,
 
     if (compl_result_code == HA_ADMIN_OK &&
         operator_func == &handler::ha_analyze && 
-	thd->variables.use_stat_tables > 0)
+        table->table->s->table_category == TABLE_CATEGORY_USER &&
+        (thd->variables.use_stat_tables > 0 ||
+         lex->with_persistent_for_clause)) 
     {
       if (!(compl_result_code=
             alloc_statistics_for_table(thd, table->table)) &&

sql/sql_lex.cc

@@ -458,6 +458,7 @@ void lex_start(THD *thd)
   lex->set_var_list.empty();
   lex->param_list.empty();
   lex->view_list.empty();
+  lex->with_persistent_for_clause= FALSE;
   lex->column_list= NULL;
   lex->index_list= NULL;
   lex->prepared_stmt_params.empty();

sql/sql_lex.h

@@ -2452,6 +2452,7 @@ struct LEX: public Query_tables_list
     this command.
   */
   bool parse_vcol_expr;
+  bool with_persistent_for_clause; // uses PERSISTENT FOR clause (in ANALYZE)
 
   enum SSL_type ssl_type;			/* defined in violite.h */
   enum enum_duplicates duplicates;

sql/sql_yacc.yy

@@ -7258,7 +7258,10 @@ opt_persistent_stat_clause:
           /* empty */
           {}        
         | PERSISTENT_SYM FOR_SYM persistent_stat_spec  
-          {}
+          { 
+            THD *thd= YYTHD;
+            thd->lex->with_persistent_for_clause= TRUE;
+          }
         ;
 
 persistent_stat_spec: