diff --git a/contrib/postgres_fdw/deparse.c b/contrib/postgres_fdw/deparse.c
index 95247656504..dfdf78d11e9 100644
--- a/contrib/postgres_fdw/deparse.c
+++ b/contrib/postgres_fdw/deparse.c
@@ -2367,14 +2367,57 @@ deparseAnalyzeSizeSql(StringInfo buf, Relation rel)
 	appendStringInfo(buf, "::pg_catalog.regclass) / %d", BLCKSZ);
 }
 
+/*
+ * Construct SELECT statement to acquire the number of rows of a relation.
+ *
+ * Note: we just return the remote server's reltuples value, which might
+ * be off a good deal, but it doesn't seem worth working harder.  See
+ * comments in postgresAcquireSampleRowsFunc.
+ */
+void
+deparseAnalyzeTuplesSql(StringInfo buf, Relation rel)
+{
+	StringInfoData relname;
+
+	/* We'll need the remote relation name as a literal. */
+	initStringInfo(&relname);
+	deparseRelation(&relname, rel);
+
+	appendStringInfoString(buf, "SELECT reltuples FROM pg_catalog.pg_class WHERE oid = ");
+	deparseStringLiteral(buf, relname.data);
+	appendStringInfoString(buf, "::pg_catalog.regclass");
+}
+
 /*
  * Construct SELECT statement to acquire sample rows of given relation.
  *
  * SELECT command is appended to buf, and list of columns retrieved
  * is returned to *retrieved_attrs.
+ *
+ * We only support sampling methods we can decide based on server version.
+ * Allowing custom TSM modules (like tsm_system_rows) might be useful, but it
+ * would require detecting which extensions are installed, to allow automatic
+ * fall-back. Moreover, the methods may use different parameters like number
+ * of rows (and not sampling rate). So we leave this for future improvements.
+ *
+ * Using random() to sample rows on the remote server has the advantage that
+ * this works on all PostgreSQL versions (unlike TABLESAMPLE), and that it
+ * does the sampling on the remote side (without transferring everything and
+ * then discarding most rows).
+ *
+ * The disadvantage is that we still have to read all rows and evaluate the
+ * random(), while TABLESAMPLE (at least with the "system" method) may skip.
+ * It's not that different from the "bernoulli" method, though.
+ *
+ * We could also do "ORDER BY random() LIMIT x", which would always pick
+ * the expected number of rows, but it requires sorting so it may be much
+ * more expensive (particularly on large tables, which is what what the
+ * remote sampling is meant to improve).
  */
 void
-deparseAnalyzeSql(StringInfo buf, Relation rel, List **retrieved_attrs)
+deparseAnalyzeSql(StringInfo buf, Relation rel,
+				  PgFdwSamplingMethod sample_method, double sample_frac,
+				  List **retrieved_attrs)
 {
 	Oid			relid = RelationGetRelid(rel);
 	TupleDesc	tupdesc = RelationGetDescr(rel);
@@ -2422,10 +2465,35 @@ deparseAnalyzeSql(StringInfo buf, Relation rel, List **retrieved_attrs)
 		appendStringInfoString(buf, "NULL");
 
 	/*
-	 * Construct FROM clause
+	 * Construct FROM clause, and perhaps WHERE clause too, depending on the
+	 * selected sampling method.
 	 */
 	appendStringInfoString(buf, " FROM ");
 	deparseRelation(buf, rel);
+
+	switch (sample_method)
+	{
+		case ANALYZE_SAMPLE_OFF:
+			/* nothing to do here */
+			break;
+
+		case ANALYZE_SAMPLE_RANDOM:
+			appendStringInfo(buf, " WHERE pg_catalog.random() < %f", sample_frac);
+			break;
+
+		case ANALYZE_SAMPLE_SYSTEM:
+			appendStringInfo(buf, " TABLESAMPLE SYSTEM(%f)", (100.0 * sample_frac));
+			break;
+
+		case ANALYZE_SAMPLE_BERNOULLI:
+			appendStringInfo(buf, " TABLESAMPLE BERNOULLI(%f)", (100.0 * sample_frac));
+			break;
+
+		case ANALYZE_SAMPLE_AUTO:
+			/* should have been resolved into actual method */
+			elog(ERROR, "unexpected sampling method");
+			break;
+	}
 }
 
 /*
diff --git a/contrib/postgres_fdw/expected/postgres_fdw.out b/contrib/postgres_fdw/expected/postgres_fdw.out
index 1a2c2a665c6..c0267a99d26 100644
--- a/contrib/postgres_fdw/expected/postgres_fdw.out
+++ b/contrib/postgres_fdw/expected/postgres_fdw.out
@@ -11779,3 +11779,28 @@ SELECT * FROM prem2;
 
 ALTER SERVER loopback OPTIONS (DROP parallel_commit);
 ALTER SERVER loopback2 OPTIONS (DROP parallel_commit);
+-- ===================================================================
+-- test for ANALYZE sampling
+-- ===================================================================
+CREATE TABLE analyze_table (id int, a text, b bigint);
+CREATE FOREIGN TABLE analyze_ftable (id int, a text, b bigint)
+       SERVER loopback OPTIONS (table_name 'analyze_rtable1');
+INSERT INTO analyze_table (SELECT x FROM generate_series(1,1000) x);
+ANALYZE analyze_table;
+SET default_statistics_target = 10;
+ANALYZE analyze_table;
+ALTER SERVER loopback OPTIONS (analyze_sampling 'invalid');
+ERROR:  invalid value for string option "analyze_sampling": invalid
+ALTER SERVER loopback OPTIONS (analyze_sampling 'auto');
+ANALYZE analyze_table;
+ALTER SERVER loopback OPTIONS (SET analyze_sampling 'system');
+ANALYZE analyze_table;
+ALTER SERVER loopback OPTIONS (SET analyze_sampling 'bernoulli');
+ANALYZE analyze_table;
+ALTER SERVER loopback OPTIONS (SET analyze_sampling 'random');
+ANALYZE analyze_table;
+ALTER SERVER loopback OPTIONS (SET analyze_sampling 'off');
+ANALYZE analyze_table;
+-- cleanup
+DROP FOREIGN TABLE analyze_ftable;
+DROP TABLE analyze_table;
diff --git a/contrib/postgres_fdw/option.c b/contrib/postgres_fdw/option.c
index fa80ee2a55e..b5890c92a13 100644
--- a/contrib/postgres_fdw/option.c
+++ b/contrib/postgres_fdw/option.c
@@ -210,6 +210,23 @@ postgres_fdw_validator(PG_FUNCTION_ARGS)
 						 errmsg("sslcert and sslkey are superuser-only"),
 						 errhint("User mappings with the sslcert or sslkey options set may only be created or modified by the superuser.")));
 		}
+		else if (strcmp(def->defname, "analyze_sampling") == 0)
+		{
+			char	   *value;
+
+			value = defGetString(def);
+
+			/* we recognize off/auto/random/system/bernoulli */
+			if (strcmp(value, "off") != 0 &&
+				strcmp(value, "auto") != 0 &&
+				strcmp(value, "random") != 0 &&
+				strcmp(value, "system") != 0 &&
+				strcmp(value, "bernoulli") != 0)
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+						 errmsg("invalid value for string option \"%s\": %s",
+								def->defname, value)));
+		}
 	}
 
 	PG_RETURN_VOID();
@@ -257,6 +274,10 @@ InitPgFdwOptions(void)
 		{"keep_connections", ForeignServerRelationId, false},
 		{"password_required", UserMappingRelationId, false},
 
+		/* sampling is available on both server and table */
+		{"analyze_sampling", ForeignServerRelationId, false},
+		{"analyze_sampling", ForeignTableRelationId, false},
+
 		/*
 		 * sslcert and sslkey are in fact libpq options, but we repeat them
 		 * here to allow them to appear in both foreign server context (when
diff --git a/contrib/postgres_fdw/postgres_fdw.c b/contrib/postgres_fdw/postgres_fdw.c
index b9268e32dde..8b21b7ecbe8 100644
--- a/contrib/postgres_fdw/postgres_fdw.c
+++ b/contrib/postgres_fdw/postgres_fdw.c
@@ -4973,11 +4973,60 @@ postgresAnalyzeForeignTable(Relation relation,
 	return true;
 }
 
+/*
+ * postgresCountTuplesForForeignTable
+ *		Count tuples in foreign table (just get pg_class.reltuples).
+ */
+static double
+postgresCountTuplesForForeignTable(Relation relation)
+{
+	ForeignTable *table;
+	UserMapping *user;
+	PGconn	   *conn;
+	StringInfoData sql;
+	PGresult   *volatile res = NULL;
+	volatile double reltuples = -1;
+
+	/*
+	 * Get the connection to use.  We do the remote access as the table's
+	 * owner, even if the ANALYZE was started by some other user.
+	 */
+	table = GetForeignTable(RelationGetRelid(relation));
+	user = GetUserMapping(relation->rd_rel->relowner, table->serverid);
+	conn = GetConnection(user, false, NULL);
+
+	/*
+	 * Construct command to get page count for relation.
+	 */
+	initStringInfo(&sql);
+	deparseAnalyzeTuplesSql(&sql, relation);
+
+	/* In what follows, do not risk leaking any PGresults. */
+	PG_TRY();
+	{
+		res = pgfdw_exec_query(conn, sql.data, NULL);
+		if (PQresultStatus(res) != PGRES_TUPLES_OK)
+			pgfdw_report_error(ERROR, res, conn, false, sql.data);
+
+		if (PQntuples(res) != 1 || PQnfields(res) != 1)
+			elog(ERROR, "unexpected result from deparseAnalyzeTuplesSql query");
+		reltuples = strtod(PQgetvalue(res, 0, 0), NULL);
+	}
+	PG_FINALLY();
+	{
+		if (res)
+			PQclear(res);
+	}
+	PG_END_TRY();
+
+	ReleaseConnection(conn);
+
+	return reltuples;
+}
+
 /*
  * Acquire a random sample of rows from foreign table managed by postgres_fdw.
  *
- * We fetch the whole table from the remote side and pick out some sample rows.
- *
  * Selected rows are returned in the caller-allocated array rows[],
  * which must have at least targrows entries.
  * The actual number of rows selected is returned as the function result.
@@ -5000,9 +5049,14 @@ postgresAcquireSampleRowsFunc(Relation relation, int elevel,
 	ForeignServer *server;
 	UserMapping *user;
 	PGconn	   *conn;
+	int			server_version_num;
+	PgFdwSamplingMethod method = ANALYZE_SAMPLE_AUTO;	/* auto is default */
+	double		sample_frac = -1.0;
+	double		reltuples;
 	unsigned int cursor_number;
 	StringInfoData sql;
 	PGresult   *volatile res = NULL;
+	ListCell   *lc;
 
 	/* Initialize workspace state */
 	astate.rel = relation;
@@ -5030,20 +5084,147 @@ postgresAcquireSampleRowsFunc(Relation relation, int elevel,
 	user = GetUserMapping(relation->rd_rel->relowner, table->serverid);
 	conn = GetConnection(user, false, NULL);
 
+	/* We'll need server version, so fetch it now. */
+	server_version_num = PQserverVersion(conn);
+
+	/*
+	 * What sampling method should we use?
+	 */
+	foreach(lc, server->options)
+	{
+		DefElem    *def = (DefElem *) lfirst(lc);
+
+		if (strcmp(def->defname, "analyze_sampling") == 0)
+		{
+			char	   *value = defGetString(def);
+
+			if (strcmp(value, "off") == 0)
+				method = ANALYZE_SAMPLE_OFF;
+			else if (strcmp(value, "auto") == 0)
+				method = ANALYZE_SAMPLE_AUTO;
+			else if (strcmp(value, "random") == 0)
+				method = ANALYZE_SAMPLE_RANDOM;
+			else if (strcmp(value, "system") == 0)
+				method = ANALYZE_SAMPLE_SYSTEM;
+			else if (strcmp(value, "bernoulli") == 0)
+				method = ANALYZE_SAMPLE_BERNOULLI;
+
+			break;
+		}
+	}
+
+	foreach(lc, table->options)
+	{
+		DefElem    *def = (DefElem *) lfirst(lc);
+
+		if (strcmp(def->defname, "analyze_sampling") == 0)
+		{
+			char	   *value = defGetString(def);
+
+			if (strcmp(value, "off") == 0)
+				method = ANALYZE_SAMPLE_OFF;
+			else if (strcmp(value, "auto") == 0)
+				method = ANALYZE_SAMPLE_AUTO;
+			else if (strcmp(value, "random") == 0)
+				method = ANALYZE_SAMPLE_RANDOM;
+			else if (strcmp(value, "system") == 0)
+				method = ANALYZE_SAMPLE_SYSTEM;
+			else if (strcmp(value, "bernoulli") == 0)
+				method = ANALYZE_SAMPLE_BERNOULLI;
+
+			break;
+		}
+	}
+
+	/*
+	 * Error-out if explicitly required one of the TABLESAMPLE methods, but
+	 * the server does not support it.
+	 */
+	if ((server_version_num < 95000) &&
+		(method == ANALYZE_SAMPLE_SYSTEM ||
+		 method == ANALYZE_SAMPLE_BERNOULLI))
+		ereport(ERROR,
+				(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				 errmsg("remote server does not support TABLESAMPLE feature")));
+
+	/*
+	 * For "auto" method, pick the one we believe is best. For servers with
+	 * TABLESAMPLE support we pick BERNOULLI, for old servers we fall-back to
+	 * random() to at least reduce network transfer.
+	 */
+	if (method == ANALYZE_SAMPLE_AUTO)
+	{
+		if (server_version_num < 95000)
+			method = ANALYZE_SAMPLE_RANDOM;
+		else
+			method = ANALYZE_SAMPLE_BERNOULLI;
+	}
+
+	/*
+	 * If we've decided to do remote sampling, calculate the sampling rate. We
+	 * need to get the number of tuples from the remote server, but skip that
+	 * network round-trip if not needed.
+	 */
+	if (method != ANALYZE_SAMPLE_OFF)
+	{
+		reltuples = postgresCountTuplesForForeignTable(relation);
+
+		/*
+		 * Remote's reltuples could be 0 or -1 if the table has never been
+		 * vacuumed/analyzed.  In that case, disable sampling after all.
+		 */
+		if ((reltuples <= 0) || (targrows >= reltuples))
+			method = ANALYZE_SAMPLE_OFF;
+		else
+		{
+			/*
+			 * All supported sampling methods require sampling rate,
+			 * not target rows directly, so we calculate that using
+			 * the remote reltuples value. That's imperfect, because
+			 * it might be off a good deal, but that's not something
+			 * we can (or should) address here.
+			 *
+			 * If reltuples is too low (i.e. when table grew), we'll
+			 * end up sampling more rows - but then we'll apply the
+			 * local sampling, so we get the expected sample size.
+			 * This is the same outcome as without remote sampling.
+			 *
+			 * If reltuples is too high (e.g. after bulk DELETE), we
+			 * will end up sampling too few rows.
+			 *
+			 * We can't really do much better here - we could try
+			 * sampling a bit more rows, but we don't know how off
+			 * the reltuples value is so how much is "a bit more"?
+			 *
+			 * Furthermore, the targrows value for partitions is
+			 * determined based on table size (relpages), which can
+			 * be off in different ways too. Adjusting the sampling
+			 * rate here might make the issue worse.
+			 */
+			sample_frac = targrows / reltuples;
+
+			/*
+			 * Ensure the sampling rate is between 0.0 and 1.0, even after the
+			 * 10% adjustment above.  (Clamping to 0.0 is just paranoia.)
+			 */
+			sample_frac = Min(1.0, Max(0.0, sample_frac));
+		}
+	}
+
 	/*
 	 * Construct cursor that retrieves whole rows from remote.
 	 */
 	cursor_number = GetCursorNumber(conn);
 	initStringInfo(&sql);
 	appendStringInfo(&sql, "DECLARE c%u CURSOR FOR ", cursor_number);
-	deparseAnalyzeSql(&sql, relation, &astate.retrieved_attrs);
+
+	deparseAnalyzeSql(&sql, relation, method, sample_frac, &astate.retrieved_attrs);
 
 	/* In what follows, do not risk leaking any PGresults. */
 	PG_TRY();
 	{
 		char		fetch_sql[64];
 		int			fetch_size;
-		ListCell   *lc;
 
 		res = pgfdw_exec_query(conn, sql.data, NULL);
 		if (PQresultStatus(res) != PGRES_COMMAND_OK)
@@ -5130,8 +5311,15 @@ postgresAcquireSampleRowsFunc(Relation relation, int elevel,
 	/* We assume that we have no dead tuple. */
 	*totaldeadrows = 0.0;
 
-	/* We've retrieved all living tuples from foreign server. */
-	*totalrows = astate.samplerows;
+	/*
+	 * Without sampling, we've retrieved all living tuples from foreign
+	 * server, so report that as totalrows.  Otherwise use the reltuples
+	 * estimate we got from the remote side.
+	 */
+	if (method == ANALYZE_SAMPLE_OFF)
+		*totalrows = astate.samplerows;
+	else
+		*totalrows = reltuples;
 
 	/*
 	 * Emit some interesting relation info
@@ -5139,7 +5327,7 @@ postgresAcquireSampleRowsFunc(Relation relation, int elevel,
 	ereport(elevel,
 			(errmsg("\"%s\": table contains %.0f rows, %d rows in sample",
 					RelationGetRelationName(relation),
-					astate.samplerows, astate.numrows)));
+					*totalrows, astate.numrows)));
 
 	return astate.numrows;
 }
diff --git a/contrib/postgres_fdw/postgres_fdw.h b/contrib/postgres_fdw/postgres_fdw.h
index a11d45bedfc..9074fa30520 100644
--- a/contrib/postgres_fdw/postgres_fdw.h
+++ b/contrib/postgres_fdw/postgres_fdw.h
@@ -134,6 +134,18 @@ typedef struct PgFdwConnState
 	AsyncRequest *pendingAreq;	/* pending async request */
 } PgFdwConnState;
 
+/*
+ * Method used by ANALYZE to sample remote rows.
+ */
+typedef enum PgFdwSamplingMethod
+{
+	ANALYZE_SAMPLE_OFF,			/* no remote sampling */
+	ANALYZE_SAMPLE_AUTO,		/* choose by server version */
+	ANALYZE_SAMPLE_RANDOM,		/* remote random() */
+	ANALYZE_SAMPLE_SYSTEM,		/* TABLESAMPLE system */
+	ANALYZE_SAMPLE_BERNOULLI	/* TABLESAMPLE bernoulli */
+} PgFdwSamplingMethod;
+
 /* in postgres_fdw.c */
 extern int	set_transmission_modes(void);
 extern void reset_transmission_modes(int nestlevel);
@@ -211,7 +223,10 @@ extern void deparseDirectDeleteSql(StringInfo buf, PlannerInfo *root,
 								   List *returningList,
 								   List **retrieved_attrs);
 extern void deparseAnalyzeSizeSql(StringInfo buf, Relation rel);
+extern void deparseAnalyzeTuplesSql(StringInfo buf, Relation rel);
 extern void deparseAnalyzeSql(StringInfo buf, Relation rel,
+							  PgFdwSamplingMethod sample_method,
+							  double sample_frac,
 							  List **retrieved_attrs);
 extern void deparseTruncateSql(StringInfo buf,
 							   List *rels,
diff --git a/contrib/postgres_fdw/sql/postgres_fdw.sql b/contrib/postgres_fdw/sql/postgres_fdw.sql
index 94fe69ed3b6..c37aa803836 100644
--- a/contrib/postgres_fdw/sql/postgres_fdw.sql
+++ b/contrib/postgres_fdw/sql/postgres_fdw.sql
@@ -3938,3 +3938,39 @@ SELECT * FROM prem2;
 
 ALTER SERVER loopback OPTIONS (DROP parallel_commit);
 ALTER SERVER loopback2 OPTIONS (DROP parallel_commit);
+
+-- ===================================================================
+-- test for ANALYZE sampling
+-- ===================================================================
+
+CREATE TABLE analyze_table (id int, a text, b bigint);
+
+CREATE FOREIGN TABLE analyze_ftable (id int, a text, b bigint)
+       SERVER loopback OPTIONS (table_name 'analyze_rtable1');
+
+INSERT INTO analyze_table (SELECT x FROM generate_series(1,1000) x);
+ANALYZE analyze_table;
+
+SET default_statistics_target = 10;
+ANALYZE analyze_table;
+
+ALTER SERVER loopback OPTIONS (analyze_sampling 'invalid');
+
+ALTER SERVER loopback OPTIONS (analyze_sampling 'auto');
+ANALYZE analyze_table;
+
+ALTER SERVER loopback OPTIONS (SET analyze_sampling 'system');
+ANALYZE analyze_table;
+
+ALTER SERVER loopback OPTIONS (SET analyze_sampling 'bernoulli');
+ANALYZE analyze_table;
+
+ALTER SERVER loopback OPTIONS (SET analyze_sampling 'random');
+ANALYZE analyze_table;
+
+ALTER SERVER loopback OPTIONS (SET analyze_sampling 'off');
+ANALYZE analyze_table;
+
+-- cleanup
+DROP FOREIGN TABLE analyze_ftable;
+DROP TABLE analyze_table;
diff --git a/doc/src/sgml/postgres-fdw.sgml b/doc/src/sgml/postgres-fdw.sgml
index 527f4deaaa2..6c943184850 100644
--- a/doc/src/sgml/postgres-fdw.sgml
+++ b/doc/src/sgml/postgres-fdw.sgml
@@ -326,6 +326,41 @@ OPTIONS (ADD password_required 'false');
     frequently updated, the local statistics will soon be obsolete.
    </para>
 
+   <para>
+    The following option controls how such an <command>ANALYZE</command>
+    operation behaves:
+   </para>
+
+   <variablelist>
+
+    <varlistentry>
+     <term><literal>analyze_sampling</literal> (<type>text</type>)</term>
+     <listitem>
+      <para>
+       This option, which can be specified for a foreign table or a foreign
+       server, determines if <command>ANALYZE</command> on a foreign table
+       samples the data on the remote side, or reads and transfers all data
+       and performs the sampling locally. The supported values
+       are <literal>off</literal>, <literal>random</literal>,
+       <literal>system</literal>, <literal>bernoulli</literal>
+       and <literal>auto</literal>. <literal>off</literal> disables remote
+       sampling, so all data are transferred and sampled locally.
+       <literal>random</literal> performs remote sampling using the
+       <literal>random()</literal> function to choose returned rows,
+       while <literal>system</literal> and <literal>bernoulli</literal> rely
+       on the built-in <literal>TABLESAMPLE</literal> methods of those
+       names. <literal>random</literal> works on all remote server versions,
+       while <literal>TABLESAMPLE</literal> is supported only since 9.5.
+       <literal>auto</literal> (the default) picks the recommended sampling
+       method automatically; currently it means
+       either <literal>bernoulli</literal> or <literal>random</literal>
+       depending on the remote server version.
+      </para>
+     </listitem>
+    </varlistentry>
+
+   </variablelist>
+
   </sect3>
 
   <sect3>