Fudging on the Resurrection Calculus

➘ A Critique of “Paulogia…It’s Time To Stop”

Part I – Foundations
1. Mapping the Five Levers
2. HRM & Maximal Data: Framing the Model
3. The Tiger Analogy and Independence Assumptions
Part II – Evidence Walkthrough
4. Evidence 1: Crucifixion (Neutral Update)
5. Evidence 2: Post-Mortem Appearances (The Swing Point)
Critical Problems
Conclusion
6. Evidence 3: Conversion of Skeptics (James and Paul)
Critical Problems
Conclusion
Part III – Likelihood Transfer & Testimony
7. Likelihood Ratio for Mundane Details
Conclusion
Part IV – Priors & Theism
8. “More Accurate Priors” (Theistic Chain)
Critical Problems
Corrected Perspective
Conclusion
9. Modern Miracles as Priors
Critical Problems
Corrected Perspective
Conclusion
Part V – Synthesis
10. Swing Audit (Log-Odds Budget)
Where the Swing Comes From
Corrected Swing
Conclusion
11. Corrected Posterior Bands
(a) Article’s Assumptions
(b) Minimal Corrections
(c) Full Corrections
Conclusion
12. Counter-Conclusion
Critical Reversal
Skeptical Conclusion

The article under review attempts to use Bayesian reasoning to show that the resurrection of Jesus is highly probable. By starting from a skeptical prior and updating with Gospel evidence, it claims to arrive at a posterior probability of roughly 88%. On the surface, the mathematics appear rigorous, and the rhetorical force is strong: if even cautious Bayesian calculation leads to belief, then skepticism seems irrational.

But a closer look reveals that the swing toward high probability is not the result of neutral Bayesian updating. It comes from a series of modeling choices that bias the outcome. Five levers are at work:

Placing the Historical Reportage Model (HRM) into background knowledge instead of testing it.
Suppressing $P(E\mid H_{Alt})$ by assigning near-zero likelihoods to naturalistic explanations.
Transferring credibility from mundane details to miracle claims.
Treating dependent testimonies as if they were independent.
Inflating priors with theological assumptions without paying targeting penalties.

This critique will follow the article section by section, mirroring its structure but exposing where the Bayesian machinery is misused. Along the way, we will foreshadow the aggregate picture: once the five levers are corrected, the posterior probability of the resurrection collapses back to insignificance.

Our approach will be explicitly Bayesian. Equations will be given in full, and after each, an annotation will explain the meaning in plain English. We will also anticipate the final audit, where the log-odds contributions of each evidence item are tallied. Readers will then see that almost all of the supposed swing comes from a single inflated step—the appearance reports—and that once naturalistic alternatives are acknowledged, the resurrection hypothesis remains astronomically unlikely.

This is not a rejection of Bayesian reasoning. On the contrary, it is a defense of Bayesian reasoning against misuse. Properly applied, Bayesian analysis confirms what critical historians already recognize: the resurrection is not the best explanation of the evidence, but a product of theological bias embedded in the model.

Part I – Foundations

1. Mapping the Five Levers

The dramatic swing toward a high posterior probability for the resurrection in the article is not the result of neutral Bayesian mechanics. Instead, it rests on five modeling choices that function as levers. When these levers are pushed in the author’s preferred direction, the conclusion is predetermined.

To frame this, recall Bayes’ theorem in odds form:

$\frac{P(H_{Res}\mid E)}{P(H_{Alt}\mid E)} = \frac{P(H_{Res})}{P(H_{Alt})} \times \frac{P(E\mid H_{Res})}{P(E\mid H_{Alt})}$

Annotation: This equation expresses the posterior odds of the resurrection hypothesis $H_{Res}$ versus any alternative $H_{Alt}$ given evidence $E$ . The posterior is equal to the prior odds multiplied by the likelihood ratio.

The article’s approach manipulates both terms on the right-hand side: the prior odds and the likelihood ratio. Five key levers explain where the manipulation occurs:

HRM Preloading
Instead of treating the Historical Reportage Model (HRM)—that the Gospels are sincere reportage—as a hypothesis to be tested, the article builds HRM into the background knowledge $k$ . This bypasses scrutiny by granting reliability at the outset.
Suppression of $P(E\mid H_{Alt})$
Alternative explanations such as memory distortion, legendary growth, redaction, or psychological phenomena are artificially assigned near-zero likelihoods. For example:

$P(E\mid H_{Alt}) \approx 0.0001$

Annotation: By making the probability of observing the testimonies under non-resurrection scenarios vanishingly small, the denominator of the likelihood ratio collapses, producing an inflated Bayes factor.

Testimony Transfer
Accuracy in mundane details (geography, names, cultural features) is permitted to “bleed” into the credibility of miraculous claims. But properly:

$P(\text{Author Testifying Honestly}\mid E_{mundane}) \not= P(\text{Miracle Occurred}\mid E_{mundane})$

Annotation: The probability that the author is sincere given accurate mundane details is not equal to the probability that the miracle itself occurred. The article conflates these.

False Independence
Multiple reports are treated as though independent when in fact they are clustered and interdependent (shared sources, oral traditions). Instead of modeling dependence, the article assumes:

$P(E_{1},E_{2},...,E_{n}\mid H) = \prod_{i=1}^{n} P(E_{i}\mid H)$

Annotation: This formula multiplies probabilities as if testimonies are independent. In reality, correlation between reports makes this unjustified, shrinking the effective sample size.

Theistic Prior Sweetening
The prior is inflated by layering metaphysical assumptions: theism, incarnation, and divine purpose. Rather than a neutral prior, the chain becomes:

$P(\text{Resurrection}) = P(\text{Theism}) \times P(\text{Incarnation}\mid \text{Theism}) \times P(\text{Resurrection}\mid \text{Incarnation})$

Annotation: This formula stacks theological assumptions into the prior, producing an inflated baseline probability before the evidence is even considered.

Together, these five levers explain the apparent movement of probability in the article’s Bayesian walkthrough. Remove or adjust them, and the resurrection hypothesis remains buried under its vanishing prior.

2. HRM & Maximal Data: Framing the Model

The article introduces the Historical Reportage Model (HRM) and places it within the background knowledge $k$ . This means that instead of treating HRM as a hypothesis subject to confirmation or disconfirmation, the model assumes from the outset that the Gospel accounts are sincere reportage.

Bayesian reasoning depends on the conditionalization of evidence on hypotheses. The general form is:

$P(H\mid E,k) = \frac{P(H\mid k)\times P(E\mid H,k)}{P(E\mid k)}$

Annotation: The posterior probability of a hypothesis $H$ given evidence $E$ and background $k$ is equal to its prior probability given $k$ multiplied by the likelihood of the evidence if $H$ were true, all normalized by the total probability of the evidence.

By placing HRM inside $k$ , the article effectively writes:

$P(H_{Res}\mid E, HRM) = \frac{P(H_{Res}\mid HRM)\times P(E\mid H_{Res},HRM)}{P(E\mid HRM)}$

Annotation: This formula treats the reportage reliability of the Gospels as already part of background knowledge. Consequently, every update of the resurrection hypothesis $H_{Res}$ is conditioned on the assumption that the Gospel testimony is sincere and historically structured.

The proper comparison would instead keep HRM as a hypothesis to be tested alongside alternatives:

$\frac{P(HRM\mid E)}{P(H_{Alt}\mid E)} = \frac{P(HRM)}{P(H_{Alt})}\times \frac{P(E\mid HRM)}{P(E\mid H_{Alt})}$

Annotation: This equation shows how the sincerity of the Gospel authors (HRM) should itself be tested against alternative accounts, such as redaction, legend, or fabrication. Only then can one meaningfully weigh the resurrection hypothesis.

By embedding HRM in $k$ , the article eliminates this comparison. It moves from “are the Gospels sincere reportage?” to “given that the Gospels are sincere reportage, how likely is the resurrection?” This is circular, since the sincerity of reportage is one of the contested questions.

For clarity, we distinguish two modeling tracks:

Track A: HRM-as-background. The resurrection is tested assuming sincerity.
Track B: HRM-as-hypothesis. The resurrection is tested while also testing whether the Gospels are reliable reportage.

The divergence between Track A and Track B will become evident in later sections, when the Bayes factors appear to grow large only under Track A.

3. The Tiger Analogy and Independence Assumptions

The article introduces a “tiger in the street” analogy to illustrate the power of multiple testimonies to overwhelm a low prior probability. If many people independently testify to seeing a tiger downtown, the cumulative likelihood ratio can move a prior from negligible to substantial.

Formally, if each testimony is treated as conditionally independent, then:

$P(E_{1},E_{2},...,E_{n}\mid H) = \prod_{i=1}^{n} P(E_{i}\mid H)$

Annotation: This equation states that under the assumption of independence, the probability of observing a sequence of testimonies is equal to the product of the probabilities of each testimony given the hypothesis $H$ . This produces exponential growth in evidential weight as the number of testimonies increases.

In the tiger case, such independence is reasonable. Different witnesses report in real time, and the probability of hallucination or coordinated deception is small. But when this logic is applied to the resurrection, the independence assumption collapses.

The resurrection testimonies come from a small, tightly connected community, with shared oral traditions and textual dependence (e.g., Mark as a source for Matthew and Luke). Treating them as independent testimonies is not justified. The correct model incorporates correlation:

$P(E_{1},E_{2},...,E_{n}\mid H) \not= \prod_{i=1}^{n} P(E_{i}\mid H)$

Annotation: This inequality indicates that the testimonies are not conditionally independent. Instead of multiplying each as if they were separate datapoints, one must account for their dependence.

One way to capture this is through an effective sample size. If testimonies are highly dependent, then $n$ reported accounts may have an effective size much closer to $1$ . For example:

$n_{effective} = \frac{(\sum_{i=1}^{n} w_{i})^{2}}{\sum_{i=1}^{n} w_{i}^{2}}$

Annotation: This formula (a common measure in statistics) reduces the nominal sample size $n$ to an effective size $n_{effective}$ depending on the weights $w_{i}$ of each testimony and the degree of correlation among them. When testimonies share a source, their effective contribution is reduced.

The time gap further complicates the analogy. Unlike tiger sightings reported immediately, resurrection testimonies were codified decades after the alleged events, introducing the possibility of legendary growth and memory distortion. To represent this decay, one can model a time-gap penalty:

$P(E_{testimony}\mid H) = P(E_{testimony}\mid H)\times e^{-\lambda t}$

Annotation: Here, $t$ is the time gap in decades, and $\lambda$ is a decay constant reflecting how reliability of testimony decreases over time.

Therefore, while the tiger analogy illustrates the mathematics of independent testimony, it fails as a parallel to the resurrection accounts. The testimonies in the Gospels are dependent, clustered, and recorded after significant delay. The independence multiplier, which drives the tiger case, cannot be legitimately applied to the resurrection case.

Part II – Evidence Walkthrough

4. Evidence 1: Crucifixion (Neutral Update)

The article begins its Bayesian walkthrough with the crucifixion of Jesus. It argues that this event is nearly universally accepted by historians, making it strong evidence for the Historical Reportage Model (HRM).

Formally, the Bayes factor for the crucifixion is defined as:

$BF_{Crucifixion} = \frac{P(E_{Crucifixion}\mid H_{Res})}{P(E_{Crucifixion}\mid H_{Alt})}$

Annotation: The Bayes factor for the crucifixion compares the probability of the evidence (that Jesus was crucified) given the resurrection hypothesis $H_{Res}$ versus the probability given an alternative hypothesis $H_{Alt}$ .

Since crucifixion is expected under both $H_{Res}$ and $H_{Alt}$ , both numerator and denominator are close to 1:

$P(E_{Crucifixion}\mid H_{Res}) \approx 1$ $P(E_{Crucifixion}\mid H_{Alt}) \approx 1$

Annotation: Both the resurrection hypothesis and naturalistic alternatives expect Jesus’ crucifixion, since it is well-attested in Roman historical practice and consistent with political and social context.

Therefore:

$BF_{Crucifixion} \approx \frac{1}{1} = 1$

Annotation: The Bayes factor is approximately 1, meaning the crucifixion does not shift the odds in favor of either the resurrection hypothesis or the alternatives.

While rhetorically included to give the appearance of accumulating evidence, this step is mathematically neutral. It neither increases nor decreases the posterior probability of the resurrection.

The significance of this neutrality is that the dramatic posterior swing later in the article cannot be attributed to E₁ (the crucifixion). It must instead come from subsequent evidence updates, especially the appearances (E₂).

5. Evidence 2: Post-Mortem Appearances (The Swing Point)

The article claims that multiple individuals and groups experienced post-mortem appearances of Jesus. These are assigned highly divergent probabilities under the resurrection hypothesis and under alternatives. The resurrection hypothesis is given a very high likelihood, while the alternatives are assigned an extremely low one.

Formally:

$BF_{Appearances} = \frac{P(E_{Appearances}\mid H_{Res})}{P(E_{Appearances}\mid H_{Alt})}$

Annotation: The Bayes factor for the appearances compares the probability of resurrection testimonies if Jesus actually rose from the dead versus the probability if he did not.

The article sets:

$P(E_{Appearances}\mid H_{Res}) \approx 0.9$ $P(E_{Appearances}\mid H_{Alt}) \approx 0.0001$

Annotation: Under the resurrection hypothesis, the probability of post-mortem appearances is set very high (90%). Under any alternative hypothesis, it is set vanishingly low (0.01%). This produces a large likelihood ratio.

Thus:

$BF_{Appearances} = \frac{0.9}{0.0001} = 9000$

Annotation: The article’s model yields a Bayes factor of 9000 for appearances, meaning it multiplies the odds in favor of the resurrection by nearly four orders of magnitude.

Critical Problems

Suppression of Alternatives
The denominator $P(E_{Appearances}\mid H_{Alt})$ is artificially minimized. In reality, alternative pathways such as grief hallucinations, visionary experiences, memory distortion, or legendary accretion make appearances not improbable. Even if rare, these mechanisms are well-documented in both religious and secular contexts. Setting their probability to 0.0001 erases them.
Dependence of Testimonies
The testimonies are treated as if independent:

$P(E_{1},E_{2},...,E_{n}\mid H) = \prod_{i=1}^{n} P(E_{i}\mid H)$

Annotation: This formula multiplies the likelihoods as if each appearance testimony were an independent datapoint. But the Gospel accounts and Pauline reports are deeply interdependent, arising from a single small community and likely sharing oral and written sources.

The correct approach is to model effective sample size:

$n_{effective} < n$

Annotation: The number of appearance reports $n$ does not equal the number of independent testimonies. The effective sample size is smaller once dependence is recognized.

Time-Gap Distortion
The appearance reports are decades removed from the alleged events. Reliability decays with time:

$P(E_{testimony}\mid H) = P(E_{testimony}\mid H)\times e^{-\lambda t}$

Annotation: Testimonial reliability decreases exponentially with time $t$ , where $\lambda$ is a decay constant capturing memory distortion and legendary growth.

Effective Bayes Factor Under Correction
If alternative mechanisms are realistically acknowledged, $P(E_{Appearances}\mid H_{Alt})$ is not 0.0001 but closer to 0.1–0.3. If dependence reduces the effective number of independent testimonies from ~21 individuals to ~1–2, the Bayes factor collapses:

$BF_{Appearances} \approx \frac{0.9}{0.1} = 9$

Annotation: With more realistic values, the Bayes factor drops from 9000 to single digits. The dramatic swing evaporates.

Conclusion

The appearances (E₂) are the engine of the article’s posterior. But the engine runs only because $P(E_{Alt})$ was suppressed to near zero and testimonies were treated as independent. Once realistic alternatives, dependence, and time-gap penalties are included, the resurrection no longer receives an evidential windfall.

6. Evidence 3: Conversion of Skeptics (James and Paul)

The article argues that the conversion of skeptics such as $James$ and $Paul$ provides further evidence for the resurrection. The claim is that such conversions are extremely unlikely under $H_{Alt}$ , but highly likely under $H_{Res}$ .

Formally, the Bayes factor is:

$BF_{Conversions} = \frac{P(E_{Conversions}\mid H_{Res})}{P(E_{Conversions}\mid H_{Alt})}$

Annotation: The Bayes factor for conversions compares the probability of hostile individuals becoming followers of Jesus if the resurrection actually happened versus if it did not.

The article assigns values approximating:

$P(E_{Conversions}\mid H_{Res}) \approx 0.8$ $P(E_{Conversions}\mid H_{Alt}) \approx 0.001$

Annotation: The probability of conversion is set at 80% if the resurrection occurred, but only 0.1% if it did not. This yields a large likelihood ratio.

Thus:

$BF_{Conversions} = \frac{0.8}{0.001} = 800$

Annotation: The model claims that conversions multiply the odds of the resurrection hypothesis by a factor of 800.

Critical Problems

Psychological and Social Motives
Religious conversions occur frequently without miraculous events. Crises, visions, charismatic influence, and the appeal of new movements all provide natural pathways. Therefore, $P(E_{Conversions}\mid H_{Alt})$ should not be set near zero.
Dependence on Existing Testimonies
The conversion accounts are preserved entirely within Christian sources. They are not independent confirmations but embedded in the same testimonial network already used in $E_{Appearances}$ . Thus, they cannot be treated as an additional independent evidence update.
Legendary Reframing
Accounts of $Paul$ ’s Damascus Road vision and $James$ ’s conversion may themselves have undergone legendary expansion. This weakens the assumption that these reports straightforwardly represent hostile witnesses suddenly persuaded by overwhelming evidence.
Effective Bayes Factor Under Correction
If natural conversion motives are acknowledged, and dependence on earlier appearance testimonies is recognized, then:

$P(E_{Conversions}\mid H_{Alt}) \approx 0.1$ $BF_{Conversions} = \frac{0.8}{0.1} = 8$

Annotation: A more realistic estimate sets the denominator far higher, reducing the Bayes factor from 800 to about 8.

Conclusion

Conversions of $James$ and $Paul$ provide at most modest support for the resurrection hypothesis. Their evidential weight is far lower once ordinary psychological pathways and textual dependence are factored in. This evidence, like the crucifixion (E₁), is only rhetorically strong. Its real force depends entirely on the inflated swing already generated by the appearance testimonies (E₂).

Part III – Likelihood Transfer & Testimony

7. Likelihood Ratio for Mundane Details

The article appeals to the presence of accurate mundane details in the Gospels—names, geography, and cultural features—as evidence for the sincerity of the testimony. The claim is that if these mundane details check out, then the entire testimony, including miracle claims, becomes more credible.

Formally, the Bayes factor for mundane accuracy is:

$BF_{Mundane} = \frac{P(E_{Mundane}\mid H_{Reportage})}{P(E_{Mundane}\mid H_{Fabrication})}$

Annotation: This ratio compares the probability of observing accurate mundane details if the authors were sincerely reporting events versus if they were fabricating them.

It is correct that accurate mundane detail can increase $P(H_{Reportage}\mid E_{Mundane})$ . For example:

$P(H_{Reportage}\mid E_{Mundane}) > P(H_{Reportage})$

Annotation: The probability of reportage sincerity is indeed higher given accurate mundane details than it was before.

But the article equivocates at the next step, transferring this credibility directly to the miracle claim:

$P(H_{Res}\mid E_{Mundane}) \not= P(H_{Res}\mid H_{Reportage}, E_{Mundane})$

Annotation: The probability of the resurrection given mundane accuracy is not the same as the probability of the resurrection given reportage sincerity plus mundane accuracy. The base rate for miracles must still be applied separately.

The correct structure distinguishes testimony from event. First, assess whether the author sincerely testified. Second, consider the probability that sincere testimony corresponds to event truth:

$P(H_{Res}\mid E_{Mundane}) = P(H_{Reportage}\mid E_{Mundane}) \times P(H_{Res}\mid H_{Reportage})$

Annotation: The probability of the resurrection given mundane detail is the product of the probability that the author was sincerely reporting and the conditional probability that a sincerely reported miracle was actually true.

Since the base rate for resurrections is vanishingly small, $P(H_{Res}\mid H_{Reportage})$ remains near zero. Therefore, no amount of mundane detail accuracy can significantly elevate the resurrection claim.

This can be expressed more starkly with odds:

$\frac{P(H_{Res}\mid E_{Mundane})}{P(H_{Alt}\mid E_{Mundane})} \approx \frac{P(H_{Res})}{P(H_{Alt})}$

Annotation: The posterior odds of the resurrection after mundane details are observed remain essentially equal to the prior odds. Mundane accuracy transfers to testimony sincerity, not to miracle occurrence.

Conclusion

Mundane detail can raise confidence in sincerity, but it does not shift the base rate of extraordinary claims. The article treats this as a likelihood transfer, but the Bayesian framework requires a firewall: sincerity of testimony and truth of miracle are not equivalent.

Part IV – Priors & Theism

8. “More Accurate Priors” (Theistic Chain)

The article argues that skeptics use unfairly low priors for the resurrection. It proposes a “more accurate” prior by beginning with agnosticism and building upward through a theistic chain:

$P(\text{Theism}) = 0.5$
$P(\text{Incarnation}\mid \text{Theism}) = 0.1$
$P(\text{Resurrection}\mid \text{Incarnation}) = 0.9$

Multiplying these yields:

$P(\text{Resurrection}) = 0.5 \times 0.1 \times 0.9 = 0.045$

Annotation: The article constructs a prior of about 4.5% for the resurrection by assigning 50% to theism, 10% to incarnation given theism, and 90% to resurrection given incarnation.

Critical Problems

Agnostic ≠ 0.5
Agnosticism does not mean splitting probability evenly between theism and atheism. Indifference must be distributed across many worldviews: atheism, deism, pantheism, polytheism, and non-interventionist theism. If spread fairly, the probability of personal interventionist theism falls far below 0.5.

Formally:

$P(\text{Personal Theism}) < \frac{1}{N}$

Annotation: If $N$ represents the number of broad worldview options, the prior probability of personal theism must be less than 1 divided by $N$ , not set arbitrarily at 0.5.

Targeting Penalty
The claim “God resurrected this person for salvific reasons” is highly specific. Bayesian reasoning requires paying a penalty for such specificity, since narrower hypotheses consume probability mass.

$P(H_{Targeted}) = P(H_{General}) \times P(\text{Specific Targeting})$

Annotation: The probability of a targeted miracle (such as Jesus’ resurrection for salvation) equals the general probability of divine action multiplied by the probability of that very specific target being chosen.

Prior Stacking
The multiplication of theological assumptions is not a neutral prior. It is a constructed chain that builds in theological commitments before the evidence is considered. The prior odds are inflated by doctrinal presuppositions.

Corrected Perspective

A more cautious allocation would spread prior weight across diverse worldviews, apply a targeting penalty, and incorporate the rarity of divine intervention. This correction shrinks the prior probability of resurrection far below the 4.5% claimed.

Formally, under correction:

$P(\text{Resurrection}) \ll 0.01$

Annotation: The corrected prior probability of the resurrection is far less than 1%. This is orders of magnitude lower than the article’s inflationary estimate.

Conclusion

The “more accurate priors” move is not Bayesian neutrality but theological front-loading. Once properly spread across worldviews and penalized for targeting, the resurrection prior returns to insignificance, leaving posterior updates to do all the work—and as we will see, those updates collapse once alternatives are properly modeled.

9. Modern Miracles as Priors

The article attempts to further justify a higher prior for the resurrection by appealing to reports of modern miracles. The claim is that if miracles occur today, then the prior probability for miracles in the past, including the resurrection, should be elevated.

Formally, the adjustment is expressed as:

$P(\text{Resurrection}) \propto P(\text{Miracle Reports Today})$

Annotation: The article suggests that the probability of the resurrection is proportional to the rate of contemporary miracle reports.

Critical Problems

Selection Bias
There are thousands of miracle claims globally, but only a fraction are ever investigated, and of those, very few withstand critical scrutiny. Most collapse under naturalistic explanations, exaggeration, or error. Using raw miracle reports inflates priors.
Calibration to Verified Cases
If priors are to be raised, the adjustment must be based only on independently verified cases. The true rate of confirmed miracles is effectively negligible. Thus:

$P(\text{Verified Miracle Reports Today}) \approx 0$

Annotation: When conditioning on independent verification, the probability of modern miracles approaches zero, offering no meaningful uplift to priors for the resurrection.

Reference Class Problem
Even if some extraordinary events were confirmed, it would remain unclear whether the proper reference class includes “miracles by the Christian God” or simply unexplained anomalies. Unless attribution is established, the evidential connection to Jesus’ resurrection is unwarranted.

Formally:

$P(\text{Resurrection}\mid \text{Unexplained Events}) \not= P(\text{Resurrection})$

Annotation: The probability of the resurrection given unexplained events is not equal to the unconditional probability of the resurrection. Unexplained anomalies do not directly increase the likelihood of Christian claims.

Corrected Perspective

If priors are uplifted only by independently verified cases, the increase is negligible:

$P(\text{Resurrection}) \approx P(\text{Resurrection})_{original}$

Annotation: The prior probability of the resurrection after considering modern miracle claims remains essentially the same as the original prior.

Conclusion

Modern miracle reports cannot be used to substantially elevate the prior for the resurrection. Once filtered for verification, their evidential value disappears. This move functions rhetorically but not probabilistically.

Part V – Synthesis

10. Swing Audit (Log-Odds Budget)

Bayesian reasoning in odds form shows that every evidence item contributes additively to the total log-odds. This makes it possible to perform a “swing audit,” identifying which pieces of evidence actually drive the posterior probability.

Formally, the log-odds update is:

$\log \frac{P(H_{Res}\mid E)}{P(H_{Alt}\mid E)} = \log \frac{P(H_{Res})}{P(H_{Alt})} + \sum_{i=1}^{n} \log BF_{i}$

Annotation: The posterior log-odds of the resurrection hypothesis $H_{Res}$ versus alternatives $H_{Alt}$ is equal to the prior log-odds plus the sum of the log Bayes factors $BF_{i}$ for each evidence item $E_{i}$ .

Where the Swing Comes From

In the article’s model, the contributions can be sketched as follows:

$E_{1}$ Crucifixion: $\log BF \approx 0$ (neutral).
$E_{2}$ Appearances: $\log BF \approx \log(9000)$ .
$E_{3}$ Conversions: $\log BF \approx \log(800)$ .
Mundane details, priors, and other steps: marginal additions.

Numerically:

$\log(9000) \approx 9.1$ $\log(800) \approx 6.7$

Annotation: The log Bayes factor for the appearances dominates at about 9.1, while conversions contribute another 6.7. Together, they swamp all other evidence.

Thus, almost the entire posterior swing arises from a single manipulated evidence item: $E_{2}$ , the appearance reports.

Corrected Swing

Once dependence and naturalistic alternatives are modeled, the Bayes factors shrink dramatically:

$BF_{Appearances} \approx 9 \quad \Rightarrow \quad \log BF \approx 2.2$ $BF_{Conversions} \approx 8 \quad \Rightarrow \quad \log BF \approx 2.1$

Annotation: With realistic values, the log Bayes factors for appearances and conversions collapse from ~9.1 and ~6.7 to ~2.2 and ~2.1, respectively.

Adding these to the prior odds leaves the resurrection posterior negligible, since the prior itself is vanishingly small.

Conclusion

The “swing” in the article’s Bayesian model is not evenly distributed. Nearly all the movement comes from artificially minimizing $P(E\mid H_{Alt})$ in the appearance testimonies and treating them as independent. A swing audit makes this transparent: the resurrection posterior depends almost entirely on a single inflated input, not on cumulative balanced evidence.

11. Corrected Posterior Bands

A full Bayesian analysis should not present a single posterior probability but a range of outcomes under different plausible modeling assumptions. This provides robustness by showing how sensitive the conclusion is to changes in priors and likelihoods.

Formally, posterior odds are:

$\frac{P(H_{Res}\mid E)}{P(H_{Alt}\mid E)} = \frac{P(H_{Res})}{P(H_{Alt})} \times \prod_{i=1}^{n} BF_{i}$

Annotation: The posterior odds of the resurrection $H_{Res}$ against alternatives $H_{Alt}$ equal the prior odds multiplied by the product of Bayes factors $BF_{i}$ from each evidence item $E_{i}$ .

(a) Article’s Assumptions

With inflated priors and suppressed alternatives, the article claims a posterior probability of roughly 88%.

$P(H_{Res}) \approx 0.045$
$BF_{Appearances} \approx 9000$
$BF_{Conversions} \approx 800$
Posterior: $P(H_{Res}\mid E) \approx 0.88$

Annotation: Under the article’s modeling choices, the resurrection hypothesis rises to nearly 90% probability.

(b) Minimal Corrections

If we apply two modest corrections—(1) reserving 10–20% of probability mass in $\neg H$ for unknowns, and (2) reducing dependence by modeling effective sample size—the posterior collapses.

$P(H_{Res}) \ll 0.01$
$BF_{Appearances} \approx 9$
$BF_{Conversions} \approx 8$
Posterior: $P(H_{Res}\mid E) \ll 0.01$

Annotation: With even minimal corrections, the posterior probability of the resurrection remains vanishingly small.

(c) Full Corrections

If we additionally (3) account for long-tail naturalistic explanations, (4) apply time-gap penalties, and (5) enforce targeting penalties for specific theological claims, the posterior probability remains negligible.

$P(H_{Res}) \approx 10^{-6}$
$BF_{Appearances} \approx 9$
$BF_{Conversions} \approx 8$
Posterior: $P(H_{Res}\mid E) \approx 10^{-5}$ or lower

Annotation: With full corrections, the resurrection hypothesis stays at or below one in one hundred thousand—negligible by any reasonable standard of belief.

Conclusion

The resurrection hypothesis reaches high posterior probability only under the article’s tendentious assumptions. Once corrected, the posterior remains indistinguishable from zero. Bayesian reasoning therefore confirms skepticism, not belief, when naturalistic mechanisms and model completeness are respected.

12. Counter-Conclusion

The article concludes that the resurrection emerges as the “best explanation” of the evidence when Bayesian reasoning is applied. It frames skepticism as irrational unless an alternative hypothesis can surpass the resurrection in likelihood.

Formally, their stance can be expressed as:

$P(H_{Res}\mid E) > P(H_{Alt}\mid E) \quad \Rightarrow \quad H_{Res} \text{ is the best explanation}$

Annotation: The article asserts that if the posterior probability of the resurrection exceeds that of any single alternative hypothesis, then the resurrection is the rational conclusion.

Critical Reversal

Bayes Aggregates Across Alternatives
Bayesian reasoning does not require skeptics to produce a single alternative that exceeds the resurrection in probability. Instead, all alternatives are collectively weighed in $\neg H_{Res}$ .

$P(\neg H_{Res}\mid E) = \sum_{j} P(H_{Alt_j}\mid E)$

Annotation: The probability of “not-resurrection” given the evidence is the sum of the posterior probabilities of all alternative hypotheses $H_{Alt_j}$ . Even if no single alternative dominates, their combined weight can still far exceed the resurrection hypothesis.

Conflation of Testimony and Event
The article consistently confuses sincerity of testimony with truth of the event. Even if the disciples sincerely believed in appearances, this does not imply the event occurred.
Posterior Fragility
Our swing audit showed that the article’s claimed posterior of 88% is achieved almost entirely by minimizing $P(E\mid H_{Alt})$ for appearances and by treating testimonies as independent. Once these assumptions are corrected, the posterior remains negligible:

$P(H_{Res}\mid E) \approx 10^{-5}$

Annotation: The posterior probability of the resurrection given the evidence is about one in one hundred thousand under realistic modeling assumptions.

Skeptical Conclusion

Bayesian reasoning does not rescue the resurrection claim. On the contrary, it exposes how fragile the argument is. With proper treatment of priors, long-tail alternatives, dependence, time-gap distortion, and targeting penalties, the resurrection hypothesis fails to rise above its vanishing base rate.

The claim that it is the “best explanation” depends on artificially narrowing the space of alternatives and transferring credibility from mundane testimony to miracle truth. Once these moves are corrected, the resurrection is not the best explanation but a dramatically disfavored one.

This analysis has followed the article’s Bayesian case point by point, showing where each lever is pulled to generate an inflated posterior for the resurrection. Far from undermining Bayesian reasoning, the critique demonstrates its strength: when all hypotheses are given their due weight, when testimony is separated from event truth, and when priors are not front-loaded with theology, the resurrection hypothesis remains negligible.

The purpose here is not to dismiss belief, but to highlight how rational tools guard against premature closure. If you found this exploration thought-provoking, I invite you to continue the discussion in the comments. Your challenges, questions, and refinements are welcome, as every exchange sharpens our collective reasoning.

◉ A Relevant Paper: Bayesian Pitfalls in Resurrection Apologetics

Bayesian_Pitfalls_in_Resurrection_Apologetics-COMPLETE Download

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