Book Review: â€śThe Probability of Godâ€?, by Stephen D. Unwin 

 I continue with my review of The Probability of God, by Stephen D. Unwin, which I began  here . 

 The first clue I had that this book would have anything but rigorous mathematical analysis was that I found it in the Harvardâ€™s Divinity library. As expected, the book is mainly philosophical in nature, but that doesnâ€™t mean it exceeds its mathematical scope. Indeed, it gives the reader a good introduction to Bayesian inference while being very clear about its limits. 

 The premise is simple: start with a proposition â€“ in this case, that a monotheistic God exists; select a series of evidential questions that are relevant to the investigation; and assess the evidence under each of the two mutually exclusive probabilities. 

 The considerations he takes into account are as follows: 


 Prior distribution: Is there any reason to believe God exists other than using anti-anthropic arguments? Unwin believes there is no value in the â€śwatchmakerâ€? hypothesis â€“ that the wonder and beauty we see around us is so complex that it could only have been designed by a being of higher order than our own â€“ and so chooses the simplest of priors, that there might as well be a 50-50 chance. (Unwin later demonstrates that this prior fails any reasonable sensitivity analysis â€“ stay tuned.) 

 In its rawest form, Bayesian inference takes the following form: 

 P(proptrue|evid) =		P(evid|proptrue)P(proptrue) 
			------------------------------------------------------------- 
			P(evid|proptrue)P(proptrue) + P(evid|propfalse)P(propfalse) 

 Notice that if we divide top and bottom by P(evidence|prop false), we have the following quantity on top and bottom: P(evidence|proptrue)/P(evidence|propfalse). Statisticians call this a Bayes Factor â€“ the likelihood of one model over another â€“ while Unwin, seeking to appeal to a wider audience, calls this a Divine Indicator. Iâ€™ll continue with the former. 

 He then considers six â€śquantitiesâ€? that relate to Godâ€™s existence, and how they fair under a world with God or no-God. In particular, he examines each Bayes factor, considers each piece of evidence to be independent from the others, then performs the Bayes calculation one at a time, using each subsequent posterior probability as the new prior probability. Any skeptic might question that the nature of his inquiries might be skewed under his own personal biases should remember that this is just an exercise. 

 In addition, to simplify the math, Unwin uses a scale of 1 to 3 to evaluate each piece of evidence, indicating no, weak or strong support (this is my interpretation, rather than a hard ranking system the author himself uses.) To put this into the equation, he uses a 5-level scale, setting the Bayes factor to be 0.1, 0.5, 1, 2 or 10 depending on the comparison of evidence. 

 1) The recognition that â€śgoodnessâ€? exists.  Under God, he argues, good and evil are built into the system. Without God, goodness can only be described as a pragmatic measure, so goodness wouldnâ€™t be taken in that context. Unwin starts off with a blast and gives himself a 10. P(God exists) is now 91%. 

 2) The recognition that â€śmoral evilâ€? exists. Unwin says that moral evil is inevitable in a godless universe, but that God wouldnâ€™t tolerate such a degree we have right now. Strong meets weak; the Bayes factor at this step is 0.5, leaving an 83% chance. (I find this step a little unsettling, as it immediately turns God into a humanlike figure, attaching too much specificity in my mind.) 

 3) The recognition that â€śnatural evilâ€? exists. In the wake of Hurricane Katrina, a great number of survivors in Louisiana are asking themselves what kind of a God would allow such a tragedy to happen. Unwin carries the same spirit across and claims that such a perspective makes little sense under Godâ€™s domain. No evidence versus strong gives a Bayes factor of 0.1 and a 33% chance of Godâ€™s existence. 

 4) The incidence of â€śintra-naturalâ€? miracles (such as whether praying for the Red Sox to win makes it so.) There are studies carried out routinely whether organized prayer can aid in the healing process. Never mind that these studies are highly unscientific â€“ there isnâ€™t an equal group praying against another injured person with roughly the same path to recovery, and a control group is nearly impossible to manufacture. Unwin doesnâ€™t mind the inconclusiveness of these experiments; instead he relies on personal perspective and finds that prayer has some place in the world of God but little in one without. A Bayes 
factor of 2 brings the probability of God back to 50%. 

 5) The incidence of â€śextra-naturalâ€? miracles (those examples that canâ€™t be explained by science). These sorts of miracles were observed before God, so Unwin says many other systems are good enough to explain their existence (though certainly not their cause.) Equal evidence means a Bayes factor of 1, and the probability of God holds at 50%. 

 6) Religious experiences. I find this category to be the weakest of Unwinâ€™s areas of evidence, since it immediately suggests a stacked deck. Unwin does hold back and merely suggests that what we perceive to be religious experiences â€“ perceived moments of oneness with a higher power â€“ are more likely to be justified if there is such a higher power. Unwin gives a Bayes factor of 2, bringing us to the conclusion that in his perspective, the probability of Godâ€™s existence is 67%. 

 Now many of you (including my co-authors) are bewildered as to why Iâ€™d consider this book, and this analysis, as being relevant to the practice of statistics.  To begin with â€“ or rather, end with â€“ Unwin admits that this test is extremely sensitive to the choice of prior beliefs. Under his assessment of the evidence, his prior belief in Godâ€™s existence (50%) yields the probability of Godâ€™s existence at 67%; using prior beliefs of 10% or 75%, using the same evidence, swings the result to 18% or 86% respectively. 

 As in many strong works of philosophy, the important lesson is not in the answer, but in asking the questions that lead there. These calculations lead only to the halfway point of the text, as Unwin now segues from his method of observation into a discussion of the nature of faith, and what components of probability and faith lead to what we understand as belief.