PHYSICAL SYSTEMS
↗Weather & climate intelligence
Translate atmospheric forecasts into event probabilities. Study ensemble calibration, local observation error, and the tails of temperature and precipitation distributions.
PHYSICS · PROBABILITY · MARKETS
Physical intuition.
Quantitative rigor.
Finding structure in uncertainty.
Independent research at the intersection of physical systems, statistical inference, and financial markets.
THE GEOMETRY OF UNCERTAINTYFIG. 01
01 / RESEARCH AGENDAWhere physics
Where physics
meets the market.
Markets turn uncertain events into prices.
Our research agenda asks how physical models, statistical evidence, and market structure can inform those probabilities.
STOCHASTIC SYSTEMS
↗Probabilistic & event modeling
Explore Bayesian updating, stochastic processes, and time-to-event models. Separate parameter uncertainty from observation noise, and test forecasts against realized outcomes.
MARKET DYNAMICS
↗Microstructure & information
Investigate how information reaches prices through order books, liquidity, and execution. Examine the gap between a model probability and a realizable trading outcome.
02 / THE INTERACTIVE NOTEBOOKA forecast is a point.
A forecast is a point.
Uncertainty is
the whole curve.
A predicted daily high of 74°F does not tell us the probability of exceeding 76°F. The spread of the forecast matters.
Move the parameters to see how a simple Gaussian model translates a continuous physical quantity into a binary event probability.
MODEL NOTE
Illustrative normal distribution, not a live forecast. A research model would require calibration, tail diagnostics, and the contract’s exact observation and settlement rules.
EXPERIMENT 001INTERACTIVE DEMONSTRATION
Will the daily high exceed the threshold?
MODEL PROBABILITY
%
P(Tmax ≥ τ)
Area under the shaded tail
Area under the shaded tail
66°F84°F
0.8°F5.0°F
64°F86°F
03 / PHYSICS IN PREDICTION MARKETSReal phenomena.
Real phenomena.
Observable outcomes.
Physical science offers more than a metaphor. These listed market examples connect measurable events with questions that quantitative models can investigate.
Temperature & precipitation
Daily temperature ranges and rainfall thresholds are examples of markets tied to physical observations.
RESEARCH CONNECTION
Explore Kalshi climate markets Ensemble distributions, station-level bias, measurement error, and calibration.
Climate records & extremes
Global temperature records and hurricane events raise questions about nonstationarity and rare outcomes.
RESEARCH CONNECTION
Read Kalshi’s market overview Extreme-value theory, dependence across events, and changing baselines.
Spaceflight milestones
Starship flight-test markets provide examples of launch timing and mission-outcome questions.
RESEARCH CONNECTION
View a Polymarket case study Reliability models, survival analysis, and evidence updates; schedules also depend on operational decisions.
Market examples reviewed October 29, 2026. Some examples may be resolved. Links are research references; displayed market availability and rules may change.
04 / THE SCIENTIFIC METHODA model is only as good
A model is only as good
as the questions it survives.
Start with a mechanism.
Define the event, the physical or statistical process, and the information available at prediction time.
Make uncertainty explicit.
Build distributions, examine assumptions, and keep model uncertainty separate from observation noise.
Test beyond the sample.
Use time-aware validation, calibration diagnostics, and simple baselines to challenge an apparent signal.
Respect the measurement.
Connect the model to contract definitions, data provenance, liquidity, and the actual outcome being measured.
05 / OPEN RESEARCH QUESTIONSNotes from
Notes from
the research agenda.
Proposed lines of inquiry.
Questions that shape the work, rather than claims of completed results.
Q.01When does a better forecast become a better probability?FORECAST CALIBRATION · WEATHER
A lower temperature error does not automatically produce a better estimate of a threshold event. This question asks how ensemble spread, local bias, and tail behavior affect calibration at the exact thresholds a contract uses.
Proposed evaluation. Compare simple climatology and calibrated ensemble baselines using time-ordered holdouts, Brier scores, and reliability diagrams. Match observations to each contract’s station, date, units, and settlement source.
Background: NOAA ensemble forecasting ↗Q.02What can cosmology teach us about noisy markets?STATISTICAL INFERENCE · MODEL VALIDATION
Both problems require inference from incomplete and noisy observations. The useful connection is methodological: generative models, explicit likelihoods, selection effects, parameter degeneracy, and posterior predictive checks.
Proposed evaluation. Study which uncertainty estimates remain calibrated under missing observations, regime changes, and misspecified models. Markets also contain adaptive participants, so a physical analogy must be tested rather than assumed.
Q.03How does new information propagate through an order book?MARKET MICROSTRUCTURE · POINT PROCESSES
Information arrival, cancellations, and trades occur at different times. A price response alone does not reveal whether a modeled opportunity was executable, or which participant could have acted on it.
Proposed evaluation. Reconstruct timestamped event sequences, compare arrival-process models, and account for queue position, spreads, fees, and latency when interpreting a model-to-market discrepancy.
06 / THE FOUNDER
Peikai LiResearch across scales.
PhD in CosmologyCarnegie Mellon University
With a PhD in cosmology from Carnegie Mellon University and prior experience in the financial industry, Peikai brings a physics-trained perspective to quantitative research.
Messix is an independent research initiative built around that intersection: asking precise questions, constructing probabilistic models, and examining what the data can—and cannot—tell us.
Connect with PeikaiLet’s think
from first principles.
↗For research conversations and potential collaborations.