So, what is my bias in the way I think about these experiences? I do believe that in all likelihood, the supernatural doesn't exist. I believe the natural world/cosmos is all there is. So, my bias is each and every one of these experiences probably have a natural explanation. I have read thousand of these experiences (premonitions, fulfilled prophecies, answered prayers, near-death experiences, astral projections, Voodoo curses, ghost encounters, feeling touched by dead relatives, divining rod, ESP, alien sightings, etc), and I have never encountered an experience for which I could not come up with at least one idea of how it may have happened naturally using nothing more than known processes such as: confirmation bias, illusory correlations, faulty memory reconstructions, hallucinations, etc. The problem is these events don't happen under careful, skeptical scientific observation. Every time scientists have made careful observations, the supernatural thing that supposedly can't be scientifically explained never happens. I guess ESP is camera shy. LOL.
Susan Blackmore, a scientific researcher who graduated from Oxford I believed set out to prove her skeptical professors wrong by proving these supernatural things were real. She began researcher as a believer because she had experienced what is commonly called astral projection. She spent decades of her career trying to show something non-natural was going on. Eventually, she became convinced by her own research that there isn't any evidence of things going on that cannot be understood through a natural worldview.
James Randi is a guy offering $1,000,000 to any one who will submit their supernatural powers (ESP, divining rod, etc) to his scientific examination and pass some tests that would prove they have some supernatural ability. No one has ever claimed that million dollars.
I don't believe that what we have to explain is what the person claims happened. We have to explain what actually happened, and the only way we can know what actually happened is if we have carefully collected scientific data on the event, which we almost never have. Human memories are suspect, human interpretations of their experiences are suspect, human perceptions are suspect, and human sensations are suspects. We know that they all have been wrong from time to time. So, we cannot use that faulty anecdotal data to establish extraordinary claims. It takes extraordinary evidence to support extraordinary claims.
It is clear that these types of human experiences happen quite often. It is not clear that they are what they seem to be, even what they seem to be to the participant of the experience.
Even when we cannot think of any natural way to explain an event all that leaves us with is an unexplained event. We have no reason to jump to a "God did it" accusation. Theoretically, there are nearly an infinite number of possible explanations (i.e., Gremlins did it, Fairies did it, Good witches from the other side did it, Magnetic impulses from negative energy did it, etc). But, not one of those things is an explanation at all. In order for any of them to be an explanation, we would have to understand HOW such a signal to come home was generated and how it traveled and how it is received, etc). Without that one cannot have an explanation, at best one only has an accusation. For us to acknowledge that science has an explanation, we expect science to take us step by step and show us how such a thing could happen using known physical forces. If science can't do that, we say science does not have an explanation. We have to hold all of these religious "explanations" to the same standard.
Just because we can't think of a natural way to explain an experience that doesn't mean that it wasn't naturally caused. Now, to be fair, just because we can't think of a supernatural way to explain an experience that doesn't mean that it wasn't supernaturally caused. But, here is the advantage of the natural explanation - every phenomena that we have ever looked at that was formerly believed to be supernatural in origin has turned out to have natural causes (thunder, storms, death, diversity in species, planetary orbits, etc). Nothing has ever been found to have a divine/demonic/fairy dust explanation. Furthermore, natural explanations not only use natural forces and processes which we know exist, they also use natural elements (atoms, cells, genes, etc) which we know exist. Supernatural explanations would use elements that we don't even know if they exist (gods, angels, spirits) and forces or processes that we don't know exist (immaterial entities interacting with material substance, spirits leaving bodies, telepathic communication through unknown mediums, etc).
By the way, I have had countless of these experiences that might be hard to explain naturally. I don't deny I had the experiences, but I do question the interpretation I gave them at the time (that they were acts of God, etc). For me, anecdotal evidence (aka personal experience) will never be sufficient to reliably tell me about the nature of existence. In short, I do not trust my interpretations of my personal experiences at all.
Permit me to speculate on what may be the natural causes of premonitions. Our bodies are bombarded with a lot of stimulation all throughout the day. Signals are being sent to our brain constantly, but we are only consciously aware of a tiny bit. For instance, if you are wearing shoes, the whole time you have been reading this post, your brain has been receiving messages from the receptors in your foot that there is pressure being exerted on the top of your foot by your shoe and you were completely unaware of those messages until I just brought our attention to it. So, fact number one - our unconscious mind is receiving and processing signals it receives from the environment without our conscious awareness. Two, our brains are exceptionally good at recognizing patterns or associations between things. For instance, a stirring in the bushes usually indicates there is an animal in the bushes even though we can't see them. Three, there are subtle signals of danger or health problems that we may perceive just below our conscious awareness. Example, our joints might ache before a storm comes due to changes in air pressure. Now, sometimes those joints aches may be strong enough that we become consciously aware of them, and if so we will credit them as the reason we think a storm is coming, but if those ache signals are processed only by an unconscious mind, we may only have the sense (or premonition) a storm is coming, but have no idea why we think that (because the explanation isn't something we are consciously aware of.
OK, so we know that dogs can be trained to smell low blood sugar in their owners and can alert their owners to that fact so the owners can eat something, etc. And we know some dogs can smell cancerous skin cells and identify which moles are cancerous and which are benign. So, there is a physical chemical being released by the body of someone with low blood sugar and someone with skin cancer that dogs can pick up on in their conscious minds. Our noses aren't as good as a dog's, but in theory our noses could pick up on the chemicals being released by a person with low blood sugar, etc, but the signal be so weak that we are not consciously aware of it. Then, our unconscious could give us the feeling (premonition) that something bad is about to happen to the person even though we don't know why we feel that way because the real reason is outside of our conscious awareness. There could be other clues for other physical ailments. For instance, half the face of a person having a stroke might relax, and although we do not consciously notice it, our subconscious might.
So, a wife says goodbye to her husband and heads to the mall for some shopping. She is not consciously aware of anything wrong, but she gets a strong feeling (premonition) that something bad is happening at home so she rushes home to find her husband going into shock due to low blood sugar. It may have been that when she was leaving the house her unconscious mind smelled the chemicals that indicated sickness.
This hypothesis of mind could generate scientific tests: can humans detect the scent of low blood sugar, etc. All this post is to show that there could be natural explanations for some premonitions.