The Niihau Incident of December 7–13, 1941 provides a good case study for applying Bayesian reasoning to historical events, particularly in assessing decision-making under uncertainty. Bayesian reasoning involves updating probabilities based on new evidence, using Bayes’ theorem: P(A∣B) = P(B∣A) ⋅ P(A)P(B) / P(A|B), where:

• P(E∣H) is the likelihood of observing E given H
• P(H∣E) is the posterior probability of hypothesis H given evidence E
• P(H) is the prior probability of H
• P(E) is the marginal probability of E.

Terms like P(E∣H), the probability of evidence given a hypothesis, can be confusing. Alternative phrasings may help:

• The probability of observing evidence E if hypothesis H were true
• The likelihood of E given H
• The conditional probability of E under H

These variations clarify that we’re assessing how likely the evidence is under a specific scenario, not the probability of the hypothesis itself, which is P(H∣E).

In the context of the Niihau Incident, we can use Bayesian reasoning to analyze the decisions made by the island’s residents, particularly the Native Hawaiians and the Harada family, in response to the crash-landing of Japanese pilot Shigenori Nishikaichi. Below, I’ll break down the analysis, focusing on key decisions and quantifying probabilities while acknowledging the limitations of historical data.

Context of the Niihau Incident

On December 7, 1941, after participating in the Pearl Harbor attack, Japanese pilot Shigenori Nishikaichi crash-landed his damaged A6M2 Zero aircraft on Niihau, a privately owned Hawaiian island with a population of 136, mostly Native Hawaiians. The Japanese Navy had mistakenly designated Niihau as an uninhabited island for emergency landings, expecting pilots to await rescue there. The residents, unaware of the Pearl Harbor attack, initially treated Nishikaichi as a guest but confiscating his weapons. Over the next few days, tensions escalated as Nishikaichi, with the help of Yoshio Harada and his wife Irene, attempted to destroy his plane and papers, took hostages, and engaged in violence. The incident culminated in the Kanaheles, a Hawaiian couple, overpowering and killing Nishikaichi. Yoshio Harada committing suicide.

From a Bayesian perspective, we can analyze the residents updating their beliefs as new evidence emerged.

We define two primary hypotheses regarding Nishikaichi’s intentions:

• H1: Nishikaichi is a neutral (non-threatening) lost pilot needing assistance.
  
  
• H2: Nishikaichi is an enemy combatant with hostile intentions.

The residents’ decisions reflect the updating of beliefs about (credence in) these hypotheses.

Prior Probabilities

At the outset, the residents had no knowledge of the Pearl Harbor attack. Thus, their prior probability for P(H1) (Nishikaichi is non-threatening) would likely be high, as a crash-landed pilot could reasonably be seen as a distressed individual. Conversely, P(H2) (Nishikaichi is a threat) would be low due to the lack of context about the war.

We can assign initial priors based on this context:

• P(H1) = 0.9: The residents initially assume Nishikaichi is a non-threatening guest, given their cultural emphasis on hospitality and lack of information about the attack.
  
  
• P(H2) = 0.1: The possibility of hostility exists but is less likely without evidence of war.

These priors are subjective, reflecting the residents’ initial state of knowledge, consistent with the Bayesian interpretation of probability as a degree of belief.

We identify key pieces of evidence that influenced the residents’ beliefs:

E1: Nishikaichi’s Crash-Landing and Initial Behavior

Nishikaichi crash-landed in a field near Hawila Kaleohano, who disarmed him and treated him as a guest. His initial behavior (not hostile) supports H1.

Likelihoods:

• P(E1∣H1) = 0.95: A non-threatening pilot is highly likely to crash-land and appear cooperative.
  
  
• P(E1∣H2) = 0.3: A hostile pilot could be expected to act more aggressively, though deception is possible.

Posterior Calculation:

P(H1∣E1) = [P(E1∣H1)⋅P(H1)] / [P(E1∣H1)⋅P(H1) + P(E1∣H2)⋅P(H2) ]

P(H1|E1) = 0.95⋅0.9 / [(0.95⋅0.9) + (0.3⋅0.1)] = 0.97

After the crash, the residents’ belief in H1 justifies hospitality.

E2: News of the Pearl Harbor Attack

That night, the residents learned of the Pearl Harbor attack via radio, revealing Japan’s aggression. This significantly increases the likelihood that Nishikaichi was a threat.

Likelihoods:

• P(E2∣H1) = 0.1 P(E2|H1) = 0.1 P(E2∣H1) = 0.1: A non-threatening pilot is unlikely to be associated with a surprise attack.
  
  
• P(E2∣H2) = 0.9 P(E2|H2) = 0.9 P(E2∣H2) = 0.9: A hostile pilot is highly likely to be linked to the attack.

Posterior Calculation (using updated priors from E1):

P(H1∣E2) = P(E2∣H1)⋅P(H1∣E1) / [P(E2∣H1)⋅P(H1∣E1) + P(E2∣H2)⋅P(H2∣E1)]

P(H1∣E2) = 0.1⋅0.97 / [(0.1⋅0.97) + (0.9⋅0.03)] = 0.76

P(H2∣E2) = 0.24

The news shifts the probability toward H2, prompting the residents to apprehend Nishikaichi and put him under guard with the Haradas.

E3: Nishikaichi’s Collusion with the Haradas

Nishikaichi convinced Yoshio and Irene Harada to help him escape, destroy his plane, and burn Kaleohano’s house to eliminate his papers.

Likelihoods:

• P(E3∣H1) = 0.01: A non-threatening pilot is extremely unlikely to do this.
  
  
• P(E3∣H2) = 0.95: A hostile pilot is likely to attempt to destroy evidence and escape.

Posterior Calculation (using updated priors from E2):

P(H1∣E3) = P(E3∣H1)⋅P(H1∣E2) / [P(E3∣H1)⋅P(H1∣E2) + P(E3∣H2)⋅P(H2∣E2)]

P(H1∣E3) = 0.01⋅0.759 / [(0.01⋅0.759) + (0.95⋅0.241)] = 0.032

P(H2∣E3) = 0.968

This evidence dramatically increases the probability of H2, aligning with the residents’ decision to confront Nishikaichi.

E4: Nishikaichi Takes Hostages and Engages in Violence

Nishikaichi and Harada took Ben and Ella Kanahele hostage, and Nishikaichi fired a machine gun. Hostile intent is confirmed.

Likelihoods:

• P(E4∣H1) = 0.001: A non-threatening pilot is virtually certain not to take hostages or use weapons.
  
  
• P(E4∣H2) = 0.99: A hostile pilot is extremely likely to resort to violence.

Posterior Calculation (using updated priors from E3):

P(H1∣E4) = P(E4∣H1)⋅P(H1∣E3)/ [P(E4∣H1)⋅P(H1∣E3) + P(E4∣H2)⋅P(H2∣E3)P(H1|E4)]

P(H1∣E4) = 0.001⋅0.032 / [(0.001⋅0.032)+(0.99⋅0.968)] =0.00003

P(H2∣E4) = 1.0 – P(H1∣E4) = 0.99997

At this point, the residents’ belief in H2 is near certainty, justifying the Kanaheles’ decisive action to overpower Nishikaichi.

Uncertainty Quantification

Bayesian reasoning also involves quantifying uncertainty, particularly aleatoric (inherent randomness) and epistemic (model uncertainty) components.

Aleatoric Uncertainty: The randomness in Nishikaichi’s actions (e.g., whether he would escalate to violence) was initially high due to the residents’ lack of context. As evidence accumulated, this uncertainty decreased, as seen in the near-certain posterior for H2 after E4.

Epistemic Uncertainty: The residents’ model of Nishikaichi’s intentions was initially flawed due to their isolation and lack of knowledge about the war. This uncertainty reduced as they incorporated news of Pearl Harbor and observed Nishikaichi’s actions, refining their model of his behavior.

Analysis of Decision-Making

The residents’ actions align with Bayesian updating:

Initial Hospitality (E1): High prior for H1 led to treating Nishikaichi as a guest, with precautions (disarming him) reflecting slight uncertainty.

Apprehension (E2): News of Pearl Harbor shifted probabilities toward H2, prompting guards and confinement with the Haradas.

Confrontations (E3, E4): Nishikaichi’s hostile actions (collusion, hostage-taking) pushed P(H2) to near 1, leading to the Kanaheles’ lethal response.

The Haradas’ decision to assist Nishikaichi complicates the analysis. Their priors may have been influenced by cultural or personal ties to Japan, increasing their P(H1) or introducing a separate hypothesis of loyalty to Japan. Lack of detailed psychological data makes quantifying their reasoning speculative.

Limitations and Assumptions

Subjective Priors: The assigned priors (e.g., P(H1) = 0.9) are estimates based on historical context, not precise measurements. Bayesian reasoning allows subjective priors, but different assumptions could alter results.

Likelihood Estimates: Likelihoods (e.g., P(E1∣H1) = 0.95) are informed guesses, as historical records lack data on residents’ perceptions.

Simplified Hypotheses: I used two hypotheses for simplicity. In reality, residents may have considered nuanced possibilities, e.g., Nishikaichi being coerced or acting out of desperation.

Historical Bias: may exaggerate or omit details, affecting our understanding of evidence.

Conclusion

Bayesian reasoning (Subjective Bayes) provides a structured framework to understand how Niihau’s residents updated their beliefs about Nishikaichi’s intentions. Initially, a high prior for him being non-threatening (P(H1)=0.9) was reasonable given their isolation. As evidence accumulated (news of Pearl Harbor, Nishikaichi’s collusion with the Haradas, and his violent actions) the posterior probability of hostility, P(H2) approached certainty, justifying their escalating responses. Quantifying this process highlights the rationality of their decisions under uncertainty, despite limited information. This analysis demonstrates Bayesian inference used to model historical decision-making, assuming the deciders were rational agents.

Next

The Niihau Incident influenced U.S. policy decisions regarding the internment of Japanese Americans during World War II. It heightened fears of disloyalty among Japanese Americans. Applying Bayesian reasoning to the decision to intern Japanese Americans after the Niihau Incident might provide insight on how policymakers updated their beliefs about the potential threat posed by this population based on limited evidence and priors. In a future post, I’ll use Bayes’ theorem to model this decision-making process to model the quantification of risk.