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import httpx

client = httpx.Client(base_url="https://api.rekko.ai/v1", headers={"Authorization": "Bearer YOUR_API_KEY"})
analysis = client.get("/markets/kalshi/KXFED-26MAR19/analysis", params={"expand": "causal"}).json()
for factor in analysis["causal"]["factors"]:
    print(f"  {factor['claim']}: {factor['prior']:.0%} → {factor['posterior']:.0%} (weight: {factor['weight']:.0%})")

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What this page covers

  • Why Bayesian reasoning is well-suited to prediction markets
  • Prior estimation from base rates
  • Evidence gathering and likelihood updates
  • Causal factor decomposition
  • Automated Bayesian analysis via the Rekko API
  • Interpreting causal decomposition results

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Why Bayesian reasoning for prediction markets?

Prediction markets price events as probabilities. The market price reflects the crowd’s aggregated estimate, but that estimate can be wrong — especially when:
  • New information has not been fully incorporated
  • The market is illiquid and slow to react
  • Participants have systematic biases (favorite-longshot bias, recency bias)
Bayesian reasoning provides a structured framework to form your own probability estimate by starting with a prior (base rate), updating with evidence, and arriving at a posterior probability you can compare against the market price.

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The Bayesian framework

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Step 1: Establish a prior

The prior is your starting estimate before looking at specific evidence. Good priors come from base rates:
Market questionBase rate sourcePrior
Will the Fed cut rates?Historical FOMC decisions30% of meetings result in cuts
Will Bitcoin hit $150K?Historical yearly BTC returnsTop-quartile years see 3x+ gains
Will inflation exceed 3%?Historical CPI distribution~15% of months since 2000
# Example: Fed rate decision
# Base rate: ~30% of FOMC meetings result in rate changes
prior = 0.30

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Step 2: Gather evidence and update

For each piece of evidence, estimate how likely you would see that evidence if the event happens (likelihood) vs if it does not: 
posterior = (prior × likelihood_yes) / (prior × likelihood_yes + (1-prior) × likelihood_no)
This is Bayes’ theorem applied to binary outcomes. 
def bayesian_update(prior: float, likelihood_yes: float, likelihood_no: float) -> float:
    """Update a prior probability with new evidence."""
    numerator = prior * likelihood_yes
    denominator = numerator + (1 - prior) * likelihood_no
    return numerator / denominator

# Start with base rate
prob = 0.30

# Evidence 1: PCE inflation at 2.1% (within Fed target)
# If they will cut: 80% chance we'd see this data
# If they won't cut: 40% chance we'd see this data
prob = bayesian_update(prob, 0.80, 0.40)
print(f"After PCE data: {prob:.0%}")  # ~46%

# Evidence 2: Three FOMC members signal openness to cuts
# If they will cut: 90% chance of these signals
# If they won't cut: 20% chance
prob = bayesian_update(prob, 0.90, 0.20)
print(f"After FOMC signals: {prob:.0%}")  # ~79%

# Evidence 3: Strong employment report
# If they will cut: 30% chance of strong jobs (less likely)
# If they won't cut: 70% chance of strong jobs
prob = bayesian_update(prob, 0.30, 0.70)
print(f"After jobs report: {prob:.0%}")  # ~62%

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Step 3: Compare with market price

Your posterior probability is your edge estimate: 
market_price = 0.55  # Market says 55%
my_estimate = 0.62   # Your Bayesian posterior

edge = my_estimate - market_price  # +7 points
if edge > 0.05:  # Only trade with >5% edge
    print(f"BUY YES — edge: {edge:.0%}")

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Causal factor decomposition

Instead of serial Bayesian updates, you can decompose the probability into weighted causal factors — independent claims that each push the probability in a direction. This approach:
  • Makes the analysis transparent and auditable
  • Identifies which factors matter most
  • Allows quick re-estimation when a single factor changes

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Structure

Each causal factor has:
  • Claim: What the factor asserts
  • Direction: Does it support YES or NO?
  • Weight: How important is this factor relative to others (weights sum to ~1.0)
  • Confidence: How certain are you about this factor’s assessment?
  • Prior: Base probability before this factor’s evidence
  • Posterior: Updated probability after considering the evidence
  • Evidence: Specific data points supporting the assessment

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Manual example

factors = [
    {
        "claim": "Inflation is within Fed's comfort zone",
        "direction": "supports_yes",
        "weight": 0.35,
        "confidence": 0.9,
        "prior": 0.50,
        "posterior": 0.78,
        "evidence": ["PCE Feb 2026: 2.1%", "Core CPI declining 3 months"],
    },
    {
        "claim": "Fed rhetoric is dovish",
        "direction": "supports_yes",
        "weight": 0.30,
        "confidence": 0.75,
        "prior": 0.50,
        "posterior": 0.68,
        "evidence": ["Waller speech March 12", "Bostic: 'open to adjustment'"],
    },
    {
        "claim": "Tariff uncertainty creates headwinds",
        "direction": "supports_no",
        "weight": 0.20,
        "confidence": 0.60,
        "prior": 0.50,
        "posterior": 0.42,
        "evidence": ["New tariffs announced March 5", "Trade deficit widening"],
    },
    {
        "claim": "Employment remains strong",
        "direction": "supports_no",
        "weight": 0.15,
        "confidence": 0.70,
        "prior": 0.50,
        "posterior": 0.38,
        "evidence": ["March NFP: +280K", "Unemployment: 3.8%"],
    },
]

# Weighted aggregation
overall = sum(f["weight"] * f["posterior"] for f in factors)
print(f"Overall probability: {overall:.0%}")  # ~63%

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Automated causal decomposition with Rekko

The Rekko analysis API performs this decomposition automatically. Use ?expand=causal to get the full factor breakdown: 
import httpx

client = httpx.Client(
    base_url="https://api.rekko.ai/v1",
    headers={"Authorization": "Bearer YOUR_API_KEY"},
    timeout=120.0,
)

# Get analysis with causal decomposition
analysis = client.get(
    "/markets/kalshi/KXFED-26MAR19/analysis",
    params={"expand": "causal"},
).json()

print(f"Overall probability: {analysis['probability']:.0%}")
print(f"Confidence: {analysis['confidence']:.0%}")
print(f"Edge vs market: {analysis['edge']:.1%}")
print()

causal = analysis["causal"]
print(f"Method: {causal['method']}")
print(f"Factors ({len(causal['factors'])}):")
for f in causal["factors"]:
    arrow = "↑" if f["direction"] == "supports_yes" else "↓"
    print(f"  {arrow} {f['claim']} (weight: {f['weight']:.0%}, conf: {f['confidence']:.0%})")
    print(f"    Prior: {f['prior']:.0%} → Posterior: {f['posterior']:.0%}")
    for e in f["evidence"]:
        print(f"    • {e}")

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Example response

{
  "overall_probability": 0.71,
  "overall_confidence": 0.82,
  "method": "weighted_bayesian",
  "factors": [
    {
      "claim": "Inflation is within Fed's comfort zone",
      "direction": "supports_yes",
      "weight": 0.35,
      "confidence": 0.9,
      "prior": 0.6,
      "posterior": 0.82,
      "evidence": ["PCE Feb 2026: 2.1%", "Core CPI declining 3 months"]
    },
    {
      "claim": "Fed rhetoric is dovish",
      "direction": "supports_yes",
      "weight": 0.3,
      "confidence": 0.75,
      "prior": 0.5,
      "posterior": 0.68,
      "evidence": ["Waller speech March 12", "Bostic: 'open to adjustment'"]
    },
    {
      "claim": "Tariff uncertainty creates headwinds",
      "direction": "supports_no",
      "weight": 0.2,
      "confidence": 0.6,
      "prior": 0.4,
      "posterior": 0.45,
      "evidence": ["New tariffs announced March 5", "Trade deficit widening"]
    }
  ]
}

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Aggregation methods

MethodDescription
weighted_bayesianWeighted average of factor posteriors (default)
linearSimple weighted linear combination
log_oddsAggregation in log-odds space (better for extreme probabilities)

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Using causal decomposition in a trading bot

The causal structure is useful beyond a single analysis. You can:
  1. Track factor changes over time — if the top-weighted factor shifts, re-analyze
  2. Cross-reference factors across markets — the same “tariff uncertainty” factor appears in multiple markets
  3. Build custom aggregation — weight factors differently based on your domain expertise
# Re-weight factors based on your own assessment
my_weights = {
    "Inflation is within Fed's comfort zone": 0.40,  # I weight this higher
    "Fed rhetoric is dovish": 0.25,
    "Tariff uncertainty creates headwinds": 0.25,  # I weight this higher too
}

my_prob = 0
for f in causal["factors"]:
    w = my_weights.get(f["claim"], f["weight"])
    my_prob += w * f["posterior"]

print(f"Rekko estimate: {analysis['probability']:.0%}")
print(f"My re-weighted estimate: {my_prob:.0%}")

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What’s next

Causal decomposition

Full documentation of the causal factor schema.

Signals API

Trading signals that use Bayesian analysis for sizing.

Kelly criterion

Position sizing based on your probability estimate.