keep the checkboxes of mass action checked for some items, by default

Question

In my Grid.php of custom module, I added the following code (excerpt) to enable mass action.

protected function _prepareMassaction(){
    $this->setMassactionIdField('entity_id');
    $this->getMassactionBlock()->setFormFieldName('some_thing');
    // options code here
    return $this;
}

I want the checkboxes of mass action to be checked by default for some items based on a variable which holds the field entity_id of the items in an array.

I am trying to show the checked items as shown in the below image even after page reload:

How to do this?