Swinburne concludes that on balance it is more probable than not that God exists, with a probability larger than 0.5, on a scale of 0.0 (impossible) to 1.0 (absolutely sure). … So \( P(h|e\&k) \), the posterior probability of theism or God \( h \) on the evidence \( e \) considered with background knowledge \( k \), will be 1/2 or more, by a "correct P-inductive argument". Swinburne states that it is impossible to give exact numerical values for the probabilities used. He notes that in his calculation the evidence from religious experience and historical evidence of life, death and resurrection of Jesus were ignored: its addition would be sufficient to make theism overall probable with a probability larger than 1/2.

The book "The Probability of God: A Simple Calculation That Proves the Ultimate Truth" by Stephen D. Unwin applies Bayesian analysis to the question of God's existence. Unwin writes that "using Bayes's theorem, I estimate the probability that God exists as 67 percent" (approximately one in three against). He presents a step-by-step Bayesian calculation combining several factors, each assigned a likelihood ratio, to arrive at this numerical probability for God's existence.

In a review of Stephen D. Unwin’s book "The Probability of God," the reviewer explains that Unwin "uses Bayes’ theorem, a formula developed in the 18th century, to calculate that there is a 67 percent chance that God exists." The article notes that Unwin assigns numerical values to factors such as the recognition of goodness and the existence of evil, then combines them using Bayesian methods to derive this probability for God’s existence.

So, in Bayesian terms, on the assumption of only one universe, with h as theism, h* as the disjunction of all possible physical one-universe theories (conjoined with the non-existence of God or gods), e1 as the fine-tuning of the universe so as to produce intelligent life and k as tautological background knowledge, that fine-tuning will be evidence for theism and against h*. … From this it follows that there is at least that probability that God will bring about intelligent beings, and so the fine-tuning of the universe in the respects referred to, which, I am assuming, is necessary for the evolution of intelligent life and makes it probable. (See Swinburne 2004, 110-132.)

Statistician Andrew Gelman discusses attempts to use **Bayesian inference to assess the probability that God exists or that specific religious claims are true**. He lists as examples Stephen D. Unwin’s "The Probability of God: A Simple Calculation That Proves the Ultimate Truth" and Richard Swinburne’s "The Existence of God," along with a Bayesian evaluation of Christ’s resurrection, as cases where Bayes’ theorem is used to argue for religious claims. Gelman notes that these works treat questions like "the probability that God != 0" within a Bayesian framework, though he is critical of their quantitative pretensions.

C-inductive arguments taken together makes it probable that the God of theism exists – that P(h|e11 & k) > ½. In other words: taking all the evidence into consideration at the same time, we have a good P-inductive argument, making the hypothesis probable period. Swinburne pursues this task by way of applying Bayes' theorem. He uses the phenomena and events that constitute the premises of traditional arguments for the existence of God as evidence in an attempt to show that his hypothesis is more probably true than not.

An article discussing Bayesian approaches to God’s existence notes that philosopher Richard Swinburne "estimated the probability of God's existence to be more than 50 percent in 1979" and that in later work he used Bayesian calculations for specific Christian claims. Swinburne treats theism as a hypothesis and applies Bayes’s theorem to assess its probability in light of various kinds of evidence, making his work one of the most prominent published Bayesian analyses of God’s existence.

Swinburne develops a cumulative case argument for theism using Bayes’ theorem. He argues that the posterior probability of theism, given the total evidence available, is greater than 1/2. However, Swinburne does not assign precise numerical values to the relevant probabilities, insisting that only comparative judgments of probability are required for his argument. Nevertheless, his use of prior probability has been criticized as overly subjective.

In his book "The Probability of God: A Simple Calculation That Proves the Ultimate Truth," physicist Stephen D. Unwin uses Bayes’s theorem to quantify the chance that God exists. In interviews about the book he states that his Bayesian model, based on seven pieces of evidence, yields "a 67 percent probability that God exists"—roughly odds of 2:1 in favor of theism. Unwin emphasizes that the choice of inputs is subjective but the Bayesian calculation itself is mathematically precise.

Using Bayesian probability and lashings of highfalutin mathematical jargon, Swinburne argues that "it [is] very probable indeed that God became incarnate in Jesus Christ who rose from the dead" (p. 214). His mathematical apologetics for the resurrection boils down to the following argument: 1. The probability of God's existence is one in two (since God either exists or doesn't exist). … So, the notion that Swinburne would say that the probability that God exists is .5 because "either he exists or not" is ridiculous. On the other hand, (Swinburne would argue that) we have good evidence for the existence of God, far more than 1/2, but for the sake of the argument he would reduce it to 1/2 so as to avoid the charge that he exaggerated the strength of the evidence. As he wrote on The Resurrection of God Incarnate p.201: "I began this book with the claim that generally available public evidence (not directly concerned with the Christian tradition) favours the hypothesis that there is a God of the traditional kind".

An article titled "A Bayesian Analysis of God's Existence" explains how to apply Bayes’s theorem to theism. The author begins with a very low prior probability for theism, "1 in 1,001," then considers several evidential factors (fine-tuning, moral knowledge, religious experience, etc.), assigning each a Bayes factor in favor of or against theism. After multiplying these factors, the author reports an overall Bayes factor of about "32,000:1 in favor of theism," which would correspond to an extremely high posterior probability for God's existence if the inputs were accepted.

This Cornell blog post explains that one of the earliest applications of what is now called Bayes’ rule was by Richard Price in 1767 "in an argumentative essay in support of the existence of God." Price used Bayesian calculation on the probability of observing certain events (like the tide failing to come in) as miracles. The author describes how Price estimated the probability of such a miraculous event to be between 1 in 600,000 and 1 in 3 million and treated this as evidence that miracles, and therefore a higher power, are real.

Swinburne in his book, "The Existence of God" tries to show that the probability that God exists is greater than 50%, all things considered. Swinburne first tries to show that certain pieces of data are more likely on the God hypothesis than on the no-God hypothesis, and then Swinburne combines these pieces of data to infer that theism is more likely than not. He does not and cannot give precise numerical values, but he argues qualitatively that the cumulative Bayes’ theorem-style assessment makes theism probable over its negation.

A PDF circulated under the title "Bayesian Analysis of God's Existence" describes an attempt to estimate "the likelihood of God" using Bayes’ theorem. The document explains Bayes’ theorem and then lists several evidential factors, each assigned a 50% likelihood, before combining them in a Bayesian-style calculation to arrive at an overall probability for God’s existence. The author acknowledges that "we obviously don't have hard numbers" and that the exercise is illustrative rather than empirically grounded.

Swinburne then used Bayes’ Theorem to assign values to things like the probability of God’s being real, Jesus’ behavior during his lifetime, and the quality of witness testimony after Jesus’ death. Then he plugged the numbers into a probability formula and added everything up. The result: a 97 percent probability that the resurrection really happened. This analysis presupposed a prior probability for God’s existence and then updated it using historical and testimonial evidence.

In The Resurrection of God Incarnate, Swinburne employs Bayes’ theorem to argue that, given certain background evidence, the probability that God exists and became incarnate in Jesus who rose from the dead is very high. He assigns qualitative probability assessments to theism as a hypothesis and then uses a Bayesian framework to claim that the resultant probability is much greater than 1/2, although he maintains that exact numerical figures are not necessary for his argument.

On Philosophy Stack Exchange, a user asks whether Bayes’s theorem can be used to argue for miracles. One answer references Richard Swinburne’s "The Resurrection of God Incarnate" as an example of applying Bayesian analysis to religious claims, noting that Swinburne assigns a prior probability to theism and then uses Bayes’s theorem to estimate probabilities for specific Christian events. This illustrates published Bayesian attempts to attach numerical probabilities to both God’s existence and related doctrines.

A discussion on r/askphilosophy about Bayesian analyses of a Judeo-Christian God notes that some authors "have approached it from a theoretical standpoint, beginning with a prior probability of 0.5 for the existence of God." The commenter explains that in one formal argument, assumption 4 is that "the prior probability of God existing given our background knowledge is at most 0.5" and that the subsequent Bayesian reasoning compares the posterior probabilities of God existing versus not existing. This shows that published Bayesian arguments about God’s existence often explicitly specify priors and posteriors for the God hypothesis.

A Yale University commentary on the history of Bayes’s theorem notes that the theorem "began as a defense of Christianity." It explains that Thomas Bayes’s work, popularized by Richard Price, was used to respond to David Hume by "quantify[ing] the probability" of miraculous events, showing how accumulating testimonial evidence could yield a high probability for a miracle. This historical context shows that Bayesian probability has been used in published work to estimate probabilities for religious claims, including the existence or actions of God.

Using Bayes theorem, Unwin starts from a prior probability of 50% that God exists. Unwin gives a Bayes factor of 2, bringing us to the conclusion that in his perspective, the probability of God's existence is 67%. … Under his assessment of the evidence, his prior belief in God’s existence (50%) yields the probability of God’s existence at 67%; using prior beliefs of 10% or 75%, using the same evidence, swings the result to 18% or 86% respectively.

Besides Richard Swinburne, is the Probabilistic/Inductive Logical method used to argue for God's existence by philosophers? Commenters discuss Swinburne’s Bayesian cumulative case, summarizing it as an attempt to show that the probability of God’s existence, given all the evidence, is greater than 1/2, even though Swinburne does not provide an exact numerical estimate. They note that other authors, such as Stephen Unwin, have tried to assign explicit numerical probabilities to the existence of God using Bayes’ theorem.

A long-form blog series titled "Bayesian evaluation for the likelihood of Christ’s resurrection" applies Bayes’ theorem to the hypothesis that Christ rose from the dead versus naturalistic alternatives. The author assigns numerical priors and likelihoods to various pieces of historical evidence and computes a posterior probability that the resurrection occurred. This Bayesian posterior for the resurrection is then taken to strongly support the truth of Christianity and, by extension, the existence of God.

In this video, Dr. Richard Carrier joins me to discuss his Bayesian analysis of the probability that Jesus didn't exist and his conclusion that there is a 1/3 against 2/3 chance that Jesus didn't exist. ... "If we top out at one in three, that's still one in three, right? It's 33% chance there was a guy, so you can't say that I'm declaring absolutely there was no Jesus. There could have been; it's just the evidence that we have kind of leans in the other direction." Carrier explains that his Bayesian method compares how likely the available evidence is given the theory that Jesus existed versus given the theory that Jesus did not exist, and from the odds ratio infers a numerical probability estimate.

A Facebook discussion of "the mathematical formula to prove the existence of God" outlines the **Bayesian probability approach** to God’s existence. It explains that P(A|X) is the probability that proposition A (e.g., "God exists") is true given evidence and background knowledge X, and that Bayes’ theorem relates this to P(X|A), P(A), and P(X). The post acknowledges that while Bayes is powerful for updating probabilities, applying it to God’s existence faces inherent challenges because the choice of priors and likelihoods is highly subjective.

You might be thinking of Richard Swinburne. I know that he does assign specific probabilities to pieces of evidence and background knowledge to come up with a final probability that Jesus rose from the dead. … He wrote out a statistical formula which essentially just says "The final probability that Jesus rose from the dead is a factor of the prior probability (essentially 'what are the odds that someone rises from the dead') as well as the probability that we’d see this evidence had Jesus not rose from the dead." He doesn’t actually assign any values, nor does he try to and say for instance "Well we can assign the probability that there would be an empty tomb if Jesus really didn’t rise from the dead to be 1/50" etc. He’s just trying to show that an event which has a very low prior probability can still be the most likely thing to occur if the evidence is strong enough.