title: Does Bloom Filter false positive rate increase on intersections/unions?
body: <p>Didn't find anything on this, so I hope that my question will find the answer here.</p>
  
  <p><strong>Problem set:</strong></p>
  
  <p>Everything belongs to uplift mining with bloom filters.</p>
  
  <p>I have thousands of bloom filters with some max capacity M, amount of items in each filter N.  </p>
  
  <p>For the case <strong>N won't ever reach M</strong> in any case at any stage.</p>
  
  <p>Probability of false positives P - 0.001%</p>
  
  <p>In my problem I need to incrementally perform from several to ±5 incremental intersections, </p>
  
  <p>like <em>A ∩ B ∩ C ∩ D...</em></p>
  
  <p>such operation will be performed for arbitrary big number (or small depending on my cost function)of different set combinations of different lengs</p>
  
  <p><em>A ∩ B;  A ∩ J ∩ K;  T ∩ W ∩ ... ∩ Z; etc.</em></p>
  
  <p>All received (new) intersection as a bloomfilters (BF∩i), will be combined by union operation,</p>
  
  <p><em>BF1 U BF2 U ... U BFi</em></p>
  
  <hr>
  
  <p><strong>Questions:</strong></p>
  
  <p>Will such operations on bloom filters affect the false positive rate for the ultimate, combined bloom filter (union of multiple intersections) as I might have many of them?</p>
  
  <p>How can I estimate possible accuracy/precision loss (or rather false positive rate increase) for my case? </p>
  
  <p>Will be very thankful for any hint or direction to a relevant material!</p>