Forward Analysis: Testing Hypotheses Through Controlled Conditioning

Forward Analysis: Testing Hypotheses Through Controlled Conditioning

Summary

Forward analysis is the experimental half of conditional reasoning.
It explores how performance changes when specific constraints or filters are applied to an event space.
By deliberately altering the sample — adding or removing conditions — we learn how context affects outcome likelihood.

This article describes how to design, interpret, and record such conditioning experiments, and how they integrate with the Distribution Pipeline Methodology.

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1. Relationship to the Distribution Pipeline

The Distribution Pipeline article defines the mechanics — the reproducible framework that transforms distributions step-by-step:

$$D_0 \xrightarrow{f_1} D_1 \xrightarrow{f_2} D_2 \xrightarrow{f_3} \ldots$$

Each transformation represents a new condition applied to the data.
In contrast, Forward Analysis operates at the reasoning layer above that pipeline.

Layer	Article	Focus
Execution layer	Distribution Pipeline Methodology	How distributions are built, conditioned, and compared deterministically.
Reasoning layer	Forward Analysis	Why each condition is chosen, what hypothesis it represents, and how to interpret the resulting performance changes.

Put simply:

The pipeline provides the instrumentation; forward analysis provides the scientific method.

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2. Experimental Framing

A forward study begins with a hypothesis about when a rule is expected to hold.
You don’t yet know whether it’s true — you’re testing it.

Example:

Hypothesis: “Slope persistence improves in high-volume environments.”

This leads to a concrete conditional experiment:

1. Baseline success rate → global (all events).
2. Add condition volume_z > 0.
3. Observe new success rate and distribution shape.

If persistence increases, the hypothesis gains support.
If not, you’ve learned something equally valuable — the condition isn’t discriminative.

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3. Defining Controlled Conditions

Forward analysis is defined by explicit, auditable conditioning.

Each added constraint narrows the sample and tests a fragment of the global distribution:

Step	Condition	Effect
1	none (global)	Baseline distribution
2	ATR_z > 1	Tests high-vol regime
3	volume_z > 0	Adds liquidity filter
4	htf_slope > 0	Adds alignment context

Each condition defines a measurable deformation in the event space.
The shift in performance between steps reveals how that factor interacts with your target variable.

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4. Measuring Outcome Deformation

Once each condition is applied, the core diagnostic is how the success rate and shape change.

At each stage:

• Calculate the new success rate (e.g., 70% → 83%).
• Record changes in median, spread, skewness, or percentile bands.
• Visualize the conditional deformation.

Example pseudo-code:

# Baseline: slope persistence
D0 = get_distribution("persistence")

# Add volatility constraint
D1 = condition(D0, where="ATR_z < 1.5")

# Add directional alignment
D2 = condition(D1, where="htf_slope > 0")

compare_success_rates([D0, D1, D2])
plot_distributions([D0, D1, D2])

Each stage isolates one cause of variation — just as the Distribution Pipeline ensures reproducibility, forward analysis ensures interpretability.

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5. Evaluating Effect Significance

Forward analysis asks whether an added condition meaningfully improves explanatory power. You can track:

Metric	Meaning
Δ Success Rate	Raw improvement in condition hold rate
Δ Median / σ	Distribution shift metrics
KS / Wasserstein	Shape difference tests
N retained	Sample size (guard against over-conditioning)

A small Δ with a large reduction in sample size signals over-conditioning — your filter became too specific. The goal is stability, not precision: conditions that consistently improve persistence across samples are robust.

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6. Contextual Reasoning: When to Add a Condition

Forward analysis is guided by world knowledge. We don’t test arbitrary filters — we test hypotheses rooted in plausible mechanisms.

Examples:

• “High ATR might disrupt trend-following setups.”
• “Persistence likely improves when higher-timeframe slope aligns.”
• “Low-volume sessions reduce breakout reliability.”

These ideas translate into filters that segment the market in interpretable ways.

This is what distinguishes forward analysis from pure statistical search: it’s the fusion of domain intuition and distributional evidence.

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7. Integrating with Backward Analysis

Forward and backward analyses operate as a feedback loop:

1. Backward identifies differentiating conditions — e.g., “Failures cluster when ATR > 1.5.”
2. Forward tests that insight as a new filter — e.g., “Restrict ATR < 1.5 → success rate +13%.”
3. Backward again diagnoses what still differs under the refined setup.

Together, they embody the virtuous cycle of analysis — observation, diagnosis, refinement, and validation.

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8. Documentation and Traceability

All forward conditioning steps should be recorded for reproducibility. When chained through the Distribution Pipeline, every state can be stored and reconstructed later.

Recommended metadata fields:

Field	Description
baseline_id	identifier for the global sample
conditions_applied	list of filters (ATR_z < 1.5, htf_slope > 0, etc.)
success_rate	persistence or outcome metric
n_events	sample size after filtering
Δ_success	change vs. previous step

This metadata makes forward analysis traceable and comparable across studies.

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Key Takeaway

Forward analysis is the active counterpart to backward diagnostics. Where backward analysis asks “What conditions were present when success or failure occurred?”, forward analysis asks “What happens if I explicitly trade only under those conditions?”

By running controlled experiments through the Distribution Pipeline, you move from descriptive observation to actionable hypothesis testing — turning intuition into verifiable, context-aware trading logic.