BRIN (Block Range INdexes) in PostgreSQL are designed for large tables where data is naturally ordered. They are highly efficient in terms of storage space and are suitable when the table rows are physically sorted in a way that correlates with the indexed columns.

Example: If you have a large table with time-series data ordered by a timestamp column, a BRIN index would be ideal.

CREATE INDEX idx_brin_timestamp ON big_table USING BRIN (timestamp_column);

Use Case: BRIN indexes are perfect for very large datasets with a natural ordering, such as log data, time-series data, or geographical data where rows are ordered by location.

To troubleshoot performance issues with PostgreSQL BRIN indexes, consider the following tips:

1. Proper Data Order: BRIN indexes are most effective when the data is physically ordered in the database in a way that correlates with the indexed column.
2. Appropriate Page Range: Adjust the pages_per_range parameter to match the data distribution. Smaller ranges can improve accuracy but may increase index size.
3. Regular Maintenance: Use the VACUUM command to update the BRIN index and keep it in sync with the table data.
4. Monitoring Index Usage: Use EXPLAIN to ensure that queries are effectively using the BRIN index.
5. Reindexing: Periodically reindex to manage index bloat and improve performance.
6. Analyzing Data Patterns: Understand your data's distribution and access patterns to determine if BRIN is the right choice.

By summarizing ranges of values, BRIN indexes allow PostgreSQL to quickly determine which disk blocks need to be visited, significantly speeding up queries on large tables. They are less effective on small tables or where data isn't ordered.