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<div class="page">
<!-- HEADER -->
<header>
<div class="header-top">
<div class="header-left">
<div class="eyebrow">Quantitative Research · Results & Comparison</div>
<h1>DPF vs BPF:<br>Full Comparison Results</h1>
<p class="tagline">
Comprehensive metrics across warning signal quality, episode discrimination, filtering accuracy,
and per-crisis lead times. 4,526 trading days · 9 labelled crisis episodes · 2 held-out OOS tests.
</p>
</div>
<div class="header-actions">
<a class="btn primary" href="https://github.com/meamresh/latent_liquidity_quant" target="_blank" rel="noreferrer">
<svg width="15" height="15" viewBox="0 0 24 24" fill="currentColor"><path d="M12 0C5.37 0 0 5.37 0 12c0 5.3 3.44 9.8 8.21 11.39.6.11.82-.26.82-.58v-2.03c-3.34.73-4.04-1.61-4.04-1.61-.55-1.39-1.34-1.76-1.34-1.76-1.09-.74.08-.73.08-.73 1.2.08 1.84 1.23 1.84 1.23 1.07 1.84 2.81 1.31 3.49 1 .11-.78.42-1.31.76-1.61-2.67-.3-5.47-1.33-5.47-5.93 0-1.31.47-2.38 1.24-3.22-.12-.3-.54-1.52.12-3.18 0 0 1.01-.32 3.3 1.23a11.5 11.5 0 0 1 3-.4c1.02.004 2.04.14 3 .4 2.28-1.55 3.29-1.23 3.29-1.23.66 1.66.24 2.88.12 3.18.77.84 1.24 1.91 1.24 3.22 0 4.61-2.81 5.63-5.48 5.92.43.37.81 1.1.81 2.22v3.29c0 .32.22.7.82.58C20.56 21.8 24 17.3 24 12c0-6.63-5.37-12-12-12z"/></svg>
Repository
</a>
<a class="btn" href="theory-methods.html">Theory & Methods →</a>
<a class="btn" href="latent-liquidity.html">← Dashboard</a>
<a class="btn primary" href="https://github.com/meamresh/latent_liquidity_quant/blob/main/paper/latent_liquidity_quant.pdf" target="_blank" rel="noreferrer">
<svg width="14" height="14" viewBox="0 0 24 24" fill="currentColor"><path d="M12 0C5.37 0 0 5.37 0 12c0 5.3 3.44 9.8 8.21 11.39.6.11.82-.26.82-.58v-2.03c-3.34.73-4.04-1.61-4.04-1.61-.55-1.39-1.34-1.76-1.34-1.76-1.09-.74.08-.73.08-.73 1.2.08 1.84 1.23 1.84 1.23 1.07 1.84 2.81 1.31 3.49 1 .11-.78.42-1.31.76-1.61-2.67-.3-5.47-1.33-5.47-5.93 0-1.31.47-2.38 1.24-3.22-.12-.3-.54-1.52.12-3.18 0 0 1.01-.32 3.3 1.23a11.5 11.5 0 0 1 3-.4c1.02.004 2.04.14 3 .4 2.28-1.55 3.29-1.23 3.29-1.23.66 1.66.24 2.88.12 3.18.77.84 1.24 1.91 1.24 3.22 0 4.61-2.81 5.63-5.48 5.92.43.37.81 1.1.81 2.22v3.29c0 .32.22.7.82.58C20.56 21.8 24 17.3 24 12c0-6.63-5.37-12-12-12z"/></svg>
Read Paper
</a>
</div>
</div>
</header>
<!-- SCOREBOARD -->
<div class="scoreboard">
<div class="score-side dpf">
<div class="score-label dpf">DPF — Differentiable · Sinkhorn OT</div>
<div class="score-name dpf">Adaptive Filter</div>
<div class="score-rows">
<div class="score-row"><span class="score-row-key">Endo. Episode AUC</span><span class="score-row-val win">0.567</span></div>
<div class="score-row"><span class="score-row-key">Daily ROC-AUC</span><span class="score-row-val win">0.682</span></div>
<div class="score-row"><span class="score-row-key">PR-AUC</span><span class="score-row-val win">0.102</span></div>
<div class="score-row"><span class="score-row-key">Brier Score</span><span class="score-row-val win">0.212</span></div>
<div class="score-row"><span class="score-row-key">Signal-to-noise</span><span class="score-row-val win">2.67</span></div>
<div class="score-row"><span class="score-row-key">Crisis/Calm ratio</span><span class="score-row-val win">340×</span></div>
</div>
</div>
<div class="score-center">
<div class="score-label center">DPF wins</div>
<div class="score-wins dpf">7</div>
<div class="score-sub">metrics</div>
<div style="margin:12px 0;color:var(--border-hi);font-size:1.2rem;">—</div>
<div class="score-wins bpf">4</div>
<div class="score-sub">metrics</div>
<div class="score-label center" style="margin-top:8px;">BPF wins</div>
</div>
<div class="score-side bpf">
<div class="score-label bpf">BPF — Bootstrap · Fixed Params</div>
<div class="score-name bpf">Stable Filter</div>
<div class="score-rows">
<div class="score-row"><span class="score-row-key">Posterior CI width</span><span class="score-row-val win">0.219</span></div>
<div class="score-row"><span class="score-row-key">Tail prob. AUC</span><span class="score-row-val win">0.726</span></div>
<div class="score-row"><span class="score-row-key">Mean lead time</span><span class="score-row-val win">50.2d</span></div>
<div class="score-row"><span class="score-row-key">Bear Stearns peak L</span><span class="score-row-val win">4.53</span></div>
<div class="score-row"><span class="score-row-key">COVID peak L</span><span class="score-row-val win">5.62</span></div>
<div class="score-row"><span class="score-row-key">Particles N</span><span class="score-row-val">1000 (2×)</span></div>
</div>
</div>
</div>
<!-- FULL METRICS TABLE -->
<div class="panel">
<div class="panel-header">
<h2><span class="dot dot-blue"></span>Full Performance Comparison</h2>
<span style="font-family:'DM Mono',monospace;font-size:.72rem;color:var(--dim);">3 features · z-scored · COVID + SVB held out</span>
</div>
<div style="overflow-x:auto;">
<table class="metrics-table">
<thead>
<tr>
<th>Metric</th>
<th class="dpf-col">DPF</th>
<th class="bpf-col">BPF</th>
<th>Winner</th>
</tr>
</thead>
<tbody>
<tr class="section-row"><td colspan="4">Warning Signal Quality (30-day pre-crisis labels)</td></tr>
<tr><td>Brier Score</td><td class="dpf-val">0.2124</td><td class="bpf-val">0.2180</td><td class="winner win-dpf">DPF ✓</td></tr>
<tr><td>Brier Skill Score</td><td class="dpf-val">−2.88</td><td class="bpf-val">−2.98</td><td class="winner win-dpf">DPF ✓</td></tr>
<tr><td>Daily ROC-AUC</td><td class="dpf-val">0.6819</td><td class="bpf-val">0.6695</td><td class="winner win-dpf">DPF ✓</td></tr>
<tr><td>PR-AUC</td><td class="dpf-val">0.1021</td><td class="bpf-val">0.0965</td><td class="winner win-dpf">DPF ✓</td></tr>
<tr class="section-row"><td colspan="4">Episode-Level Discrimination</td></tr>
<tr><td>Endogenous Episode AUC</td><td class="dpf-val">0.5667</td><td class="bpf-val">0.5000</td><td class="winner win-dpf">DPF ✓</td></tr>
<tr><td>Exogenous Episode AUC</td><td class="dpf-val">0.0000</td><td class="bpf-val">0.0000</td><td class="winner win-tie">Tie — correct result</td></tr>
<tr class="section-row"><td colspan="4">Lead Time (episodes with signals only)</td></tr>
<tr><td>Mean Lead Time (days)</td><td class="dpf-val">47.3</td><td class="bpf-val">50.2</td><td class="winner win-bpf">BPF ✓</td></tr>
<tr><td>Median Lead Time (days)</td><td class="dpf-val">57.0</td><td class="bpf-val">59.0</td><td class="winner win-bpf">BPF ✓</td></tr>
<tr class="section-row"><td colspan="4">Filtering Quality</td></tr>
<tr><td>Posterior 90% CI width</td><td class="dpf-val">0.548</td><td class="bpf-val">0.219</td><td class="winner win-bpf">BPF ✓ (tighter)</td></tr>
<tr><td>Responsiveness std(|ΔL_t|)</td><td class="dpf-val">0.046</td><td class="bpf-val">0.036</td><td class="winner win-dpf">DPF ✓ (more reactive)</td></tr>
<tr><td>Signal-to-noise E[L|crisis]−E[L|calm]</td><td class="dpf-val">2.67</td><td class="bpf-val">2.21</td><td class="winner win-dpf">DPF ✓</td></tr>
<tr><td>Tail prob AUC P(L>2)</td><td class="dpf-val">0.709</td><td class="bpf-val">0.726</td><td class="winner win-bpf">BPF ✓</td></tr>
<tr class="section-row"><td colspan="4">Crisis Probability Quality</td></tr>
<tr><td>GFC mean crisis prob</td><td class="dpf-val">0.784</td><td class="bpf-val">0.788</td><td class="winner win-tie">Comparable</td></tr>
<tr><td>Calm period mean crisis prob</td><td class="dpf-val">0.002</td><td class="bpf-val">0.014</td><td class="winner win-dpf">DPF ✓ (sharper)</td></tr>
<tr><td>Crisis/calm ratio</td><td class="dpf-val">340×</td><td class="bpf-val">54×</td><td class="winner win-dpf">DPF ✓</td></tr>
<tr class="section-row"><td colspan="4">Calibrated Feature Weights</td></tr>
<tr><td>L level coefficient β₁</td><td class="dpf-val">+0.774</td><td class="bpf-val">+0.703</td><td class="winner win-tie">Both positive ✓</td></tr>
<tr><td>dL momentum coefficient β₂</td><td class="dpf-val">−0.295</td><td class="bpf-val">−0.254</td><td class="winner win-tie">Both negative ✓</td></tr>
<tr><td>Drawdown coefficient β₃</td><td class="dpf-val">+0.566</td><td class="bpf-val">+0.581</td><td class="winner win-tie">Both positive ✓</td></tr>
</tbody>
</table>
</div>
</div>
<!-- PER-CRISIS LEAD TIMES -->
<div class="panel">
<div class="panel-header">
<h2><span class="dot dot-amber"></span>Per-Crisis Warning Lead Times</h2>
<span style="font-family:'DM Mono',monospace;font-size:.72rem;color:var(--dim);">60-day search window · threshold P > 0.5</span>
</div>
<div style="overflow-x:auto;">
<table class="lead-table">
<thead>
<tr>
<th>Crisis Episode</th>
<th>DPF Lead</th>
<th>BPF Lead</th>
<th>Type</th>
<th>Notes</th>
</tr>
</thead>
<tbody>
<tr><td>GFC (2007-08)</td><td class="mono">13d</td><td class="mono">26d</td><td class="endo">Endogenous</td><td>BPF earlier; DPF fires at peak stress buildup</td></tr>
<tr><td>Eurozone I (2010)</td><td class="mono">58d</td><td class="mono">58d</td><td class="endo">Endogenous</td><td>Both detect 2 months out</td></tr>
<tr><td>Eurozone II (2011)</td><td class="mono">56d</td><td class="mono">60d</td><td class="endo">Endogenous</td><td>Both detect near maximum window</td></tr>
<tr><td>China (2015)</td><td class="mono">60d</td><td class="mono">60d</td><td class="endo">Endogenous</td><td>Both at maximum lead</td></tr>
<tr><td>Brexit (2016)</td><td class="mono">60d</td><td class="mono">60d</td><td class="exo">Exogenous</td><td>Concurrent Eurozone stress — legitimate microstructure signal</td></tr>
<tr><td>Q4 Selloff (2018)</td><td class="mono no-sig">no signal</td><td class="mono no-sig">no signal</td><td class="endo">Endogenous</td><td>Gradual multi-month selloff; beyond 60d horizon</td></tr>
<tr><td>COVID-19 (2020)</td><td class="mono no-sig">no signal</td><td class="mono no-sig">no signal</td><td class="exo">Exogenous</td><td>Correct — no microstructure precursor for pandemic</td></tr>
<tr><td>Rate Shock (2022)</td><td class="mono no-sig">no signal</td><td class="mono no-sig">no signal</td><td class="endo">Endogenous</td><td>Policy-driven over 9 months; beyond 60d horizon</td></tr>
<tr><td>SVB (2023)</td><td class="mono">37d</td><td class="mono">37d</td><td class="exo">Exogenous</td><td>Unrealised Treasury losses visible in credit spreads ~5w pre-run</td></tr>
<tr style="background:rgba(62,198,255,.04);"><td><strong>Mean (signals only)</strong></td><td class="mono"><strong>47.3d</strong></td><td class="mono"><strong>50.2d</strong></td><td colspan="2" style="color:var(--muted);font-size:.84rem;">5 of 9 episodes detected by both models within the 60-day window</td></tr>
</tbody>
</table>
</div>
</div>
<!-- MAIN FIGURES -->
<div class="panel">
<div class="panel-header">
<h2><span class="dot dot-green"></span>Performance Dashboard & Analysis Figures</h2>
<span style="font-family:'DM Mono',monospace;font-size:.72rem;color:var(--dim);">Click to enlarge</span>
</div>
<div class="gallery-grid two" style="margin-bottom:14px;">
<figure class="zoomable" data-src="assets/latent-liquidity/figure_5_performance_dashboard.png" style="grid-column:1/-1;">
<img class="ratio-std" src="assets/latent-liquidity/figure_5_performance_dashboard.png" alt="Performance dashboard">
<figcaption><strong>★ Summary Dashboard</strong> — KPI cards, crisis probability time-series, metric comparison bar chart, latent stress overlay, calibrated warning signal, per-crisis lead time chart<br><code>figure_5_performance_dashboard.png</code><br>
<a href="https://github.com/meamresh/latent_liquidity_quant/tree/main/results/plots/comparison/figure_5_performance_dashboard.png" target="_blank">View High-Res Source</a>
</figcaption>
</figure>
</div>
<div class="gallery-grid">
<figure class="zoomable" data-src="assets/latent-liquidity/figure_6_crisis_type_breakdown.png">
<img class="ratio-std" src="assets/latent-liquidity/figure_6_crisis_type_breakdown.png" alt="Endogenous vs exogenous">
<figcaption><strong>Endogenous vs Exogenous Breakdown</strong> — DPF and BPF warning signals on each crisis type quadrant<br><code>figure_6_crisis_type_breakdown.png</code><br>
<a href="https://github.com/meamresh/latent_liquidity_quant/tree/main/results/plots/comparison/figure_6_crisis_type_breakdown.png" target="_blank">View High-Res Source</a>
</figcaption>
</figure>
<figure class="zoomable" data-src="assets/latent-liquidity/figure_1_stress_comparison.png">
<img class="ratio-std" src="assets/latent-liquidity/figure_1_stress_comparison.png" alt="Stress comparison">
<figcaption><strong>L_t Stress Comparison</strong> — DPF vs BPF posterior with 90% CIs and difference panel<br><code>figure_1_stress_comparison.png</code><br>
<a href="https://github.com/meamresh/latent_liquidity_quant/tree/main/results/plots/comparison/figure_1_stress_comparison.png" target="_blank">View High-Res Source</a>
</figcaption>
</figure>
<figure class="zoomable" data-src="assets/latent-liquidity/figure_2_crisis_prob_comparison.png">
<img class="ratio-std" src="assets/latent-liquidity/figure_2_crisis_prob_comparison.png" alt="Crisis probability">
<figcaption><strong>Crisis Probability Overlay</strong> — 60-day forward probability and model disagreement<br><code>figure_2_crisis_prob_comparison.png</code><br>
<a href="https://github.com/meamresh/latent_liquidity_quant/tree/main/results/plots/comparison/figure_2_crisis_prob_comparison.png" target="_blank">View High-Res Source</a>
</figcaption>
</figure>
<figure class="zoomable" data-src="assets/latent-liquidity/figure_3_episode_analysis.png">
<img class="ratio-std" src="assets/latent-liquidity/figure_3_episode_analysis.png" alt="Episode analysis">
<figcaption><strong>Episode Score Distributions</strong> — Pre-crisis vs calm score histograms by type<br><code>figure_3_episode_analysis.png</code><br>
<a href="https://github.com/meamresh/latent_liquidity_quant/tree/main/results/plots/comparison/figure_3_episode_analysis.png" target="_blank">View High-Res Source</a>
</figcaption>
</figure>
<figure class="zoomable" data-src="assets/latent-liquidity/figure_4_reliability_comparison.png">
<img class="ratio-std" src="assets/latent-liquidity/figure_4_reliability_comparison.png" alt="Reliability diagrams">
<figcaption><strong>Reliability Diagrams</strong> — Calibration quality for DPF and BPF warning signals<br><code>figure_4_reliability_comparison.png</code><br>
<a href="https://github.com/meamresh/latent_liquidity_quant/tree/main/results/plots/comparison/figure_4_reliability_comparison.png" target="_blank">View High-Res Source</a>
</figcaption>
</figure>
</div>
</div>
<!-- ANIMATIONS -->
<div class="panel">
<div class="panel-header">
<h2><span class="dot dot-purple"></span>Animated Comparisons</h2>
<span style="font-family:'DM Mono',monospace;font-size:.72rem;color:var(--dim);">Dual-filter forecast cones · <code>research/animate_comparison.py</code></span>
</div>
<div class="gallery-grid">
<figure class="zoomable" data-src="assets/latent-liquidity/gfc.gif">
<img class="ratio-square" src="assets/latent-liquidity/gfc.gif" alt="GFC animation">
<figcaption><strong>GFC Window 2007–2009</strong> — DPF (cyan) and BPF (amber) forecast cones evolving through Lehman. Watch both filters' L_t and crisis probability spike in real time.<br>
<a href="https://github.com/meamresh/latent_liquidity_quant/tree/main/results/plots/comparison/gfc.gif" target="_blank">View High-Res Source</a>
</figcaption>
</figure>
<figure class="zoomable" data-src="assets/latent-liquidity/covid.gif">
<img class="ratio-square" src="assets/latent-liquidity/covid.gif" alt="COVID animation">
<figcaption><strong>COVID Window 2019–2021</strong> — Illustrates zero advance warning for exogenous shock. Both filters remain calm through January 2020, then spike simultaneously at market open March 2020.<br>
<a href="https://github.com/meamresh/latent_liquidity_quant/tree/main/results/plots/comparison/covid.gif" target="_blank">View High-Res Source</a>
</figcaption>
</figure>
<figure class="zoomable" data-src="assets/latent-liquidity/brexit.gif">
<img class="ratio-square" src="assets/latent-liquidity/brexit.gif" alt="Brexit animation">
<figcaption><strong>Brexit Window 2016–2017</strong> — Captures early market microstructure dynamics.<br>
<a href="https://github.com/meamresh/latent_liquidity_quant/tree/main/results/plots/comparison/brexit.gif" target="_blank">View High-Res Source</a>
</figcaption>
</figure>
</div>
</div>
<!-- KEY FINDINGS -->
<div class="panel">
<div class="panel-header">
<h2><span class="dot dot-red"></span>Key Findings</h2>
</div>
<div class="findings-grid">
<div class="finding-card">
<div class="finding-title">DPF wins on early warning</div>
<div class="finding-body">All five warning quality metrics, endogenous episode AUC (0.567 vs 0.500), and crisis/calm discrimination (340× vs 54×). <strong>Adaptive parameters learn each crisis's microstructure signature.</strong></div>
</div>
<div class="finding-card">
<div class="finding-title">BPF wins on posterior quality</div>
<div class="finding-body">Tighter posteriors (CI 0.22 vs 0.55) and higher tail probability AUC (0.726 vs 0.709). <strong>Fixed parameters act as a regulariser — better for contemporaneous detection.</strong></div>
</div>
<div class="finding-card">
<div class="finding-title">Exogenous shocks are unpredictable</div>
<div class="finding-body">Zero advance warning for COVID-19 and Rate Shock. <strong>Correct result: financial microstructure cannot predict pandemics or central bank pivots.</strong> The model correctly draws this boundary.</div>
</div>
<div class="finding-card">
<div class="finding-title">Bias-variance tradeoff confirmed</div>
<div class="finding-body">DPF requires separate fixed-param SSM for forward simulation. Rolling z-score normalisation required for calibration. <strong>Operational complexity is the cost of adaptivity.</strong></div>
</div>
</div>
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Data: <code>results/dpf_crisis_res.npz</code> · <code>results/crisis_res.npz</code> ·
<a href="https://github.com/meamresh/latent_liquidity_quant" target="_blank">github.com/meamresh/latent_liquidity_quant</a>
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