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Ideal for statisticians, data scientists, and researchers who need fast, reliable Bayesian updates.</p> <a href="#calculator" class="btn btn-primary">Try the Calculator</a> <div class="stats"> <div class="stat"><div class="stat-label">Calculations Performed</div><div class="stat-value">> 1.2M</div></div> <div class="stat"><div class="stat-label">Average Latency</div><div class="stat-value">< 15 ms</div></div> <div class="stat"><div class="stat-label">User Satisfaction</div><div class="stat-value">4.9 / 5.0</div></div> </div> </div> </section> <section id="features" class="features"> <div class="container"> <h2>Why Choose This Tool?</div> <div class="feature-card"> <i>⚡</i> <h3>Log‑Space Stability</h3> <p>Handles extreme likelihoods and priors without underflow or overflow.</p> </div> <div class="feature-card"> <i>🚀</i> <h3>Real‑Time Computation</h3> <p>Instant posterior updates as you type.</p> </div> <div class="feature-card"> <i>🛡️</i> <h3>Input Validation</h3> <p>Ensures only valid numeric log values are accepted.</p> </div> <div class="feature-card"> <i>💾</i> <h3>Export Options</h3> <p>Download results as CSV or JSON with one click.</p> </div> <div class="feature-card"> <i>📱</i> <h3>Fully Responsive</h3> <p>Optimized for mobile, tablet, and desktop screens.</p> </div> <div class="feature-card"> <i>🌙</i> <h3>Dark‑Mode Toggle</h3> <p>Switch themes for comfortable viewing in any lighting.</p> </div> </div> </section> <section id="steps" class="steps"> <div class="container"> <h2>How It Works</div> <div class="step"> <div class="step-number">1</div> <div class="step-content"> <h3>Enter Log‑Likelihood & Log‑Prior</h3> <p>Provide the log‑likelihood and log‑prior values for your hypothesis.</p> <div class="step-diagram">📥</div> </div> </div> <div class="step"> <div class="step-number">2</div> <div class="step-content"> <h3>Stable Log‑Evidence Calculation</h3> <p>The tool computes log‑evidence using the LogSum trick for numerical stability.</p> <div class="step-diagram">🔢</div> </div> </div> <div class="step"> <div class="step-number">3</div> <div class="step-content"> <h3>Posterior Probability Output</h3> <p>Posterior = exp(logLikelihood + logPrior – logEvidence).</p> <div class="step-diagram">📊</div> </div> </div> </div> </section> <section id="calculator" class="calculator"> <div class="container"> <h2>Calculate Your Posterior</div> <form class="calc-form" id="calcForm"> <div class="input-group"> <label for="logLikelihood">Log‑Likelihood</label> <input type="number" id="logLikelihood" placeholder="e.g., -2.3" step="any" required> </div> <div class="input-group"> <label for="logPrior">Log‑Prior</label> <input type="number" id="logPrior" placeholder="e.g., -1.0" step="any" required> </div> <div class="calc-actions"> <button type="submit" class="btn btn-primary">Compute</button> <button type="button" class="btn btn-outline" id="copyResult">📋 Copy</button> <button type="button" class="btn btn-outline" id="downloadCsv">💾 CSV</button> <button type="button" class="btn btn-outline" id="downloadJson">💾 JSON</button> </div> </form> <div class="result" id="result">—</div> </div> </section> <section id="faq" class="faq"> <div class="container"> <h2>Frequently Asked Questions</div> <div class="accordion-item"> <div class="accordion-header"> <span>What is log‑space arithmetic and why is it important?</span> <span class="accordion-icon">▾</span> </div> <div class="accordion-body"> <p>Log‑space arithmetic transforms multiplication into addition and avoids underflow/overflow when dealing with very small or very large probabilities. This yields numerically stable posterior calculations.</p> </div> </div> <div class="accordion-item"> <div class="accordion-header"> <span>What format should I use for the inputs?</span> <span class="accordion-icon">▾</span> </div> <div class="accordion-body"> <p>Enter the natural logarithm of the likelihood and prior (logLikelihood and logPrior). They can be any real number; positive values correspond to likelihoods/priors >1, negative to <1.</p> </div> </div> <div class="accordion-item"> <div class="accordion-header"> <span>How is the posterior probability computed?</span> <span class="accordion-icon">▾</span> </div> <div class="accordion-body"> <p>We compute log‑evidence using the LogSum trick: logEvidence = LogSum(logLikelihood + logPrior, log(1‑exp(logLikelihood)) + logComplement). Then logPosterior = logLikelihood + logPrior – logEvidence, and posterior = exp(logPosterior).</p> </div> </div> <div class="accordion-item"> <div class="accordion-header"> <span>Is my data stored or sent anywhere?</span> <span class="accordion-icon">▾</span> </div> <div class="accordion-body"> <p>No. All calculations are performed client‑side in your browser. No data leaves your device.</p> </div> </div> </div> </section> <section id="cta" class="cta"> <div class="container"> <h2>Ready to Compute?</div> <p class="muted">Experience fast, reliable Bayesian updates with a single click.</p> <div class="cta-buttons"> <a href="#calculator" class="btn btn-primary">Try the Calculator</a> <a href="#faq" class="btn btn-secondary">Learn More About Bayesian Methods</a> </div> </div> </section> <footer> <div class="container"> © 2025 Bayesian Posterior Calculator • <a href="#" id="privacyLink">Privacy</a> </div> </footer> <script> /* Dark mode toggle */ const darkToggle = document.getElementById('darkToggle'); const root = document.documentElement; darkToggle.addEventListener('click', () => { root.classList.toggle('dark'); if(root.classList.contains('dark')){ darkToggle.textContent = '☀️'; localStorage.setItem('theme','dark'); }else{ darkToggle.textContent = '🌙'; localStorage.setItem('theme','light'); } }); const savedTheme = localStorage.getItem('theme'); if(savedTheme === 'dark'){root.classList.add('dark');darkToggle.textContent='☀️';} /* Accordion */ document.querySelectorAll('.accordion-header').forEach(header => { header.addEventListener('click', () => { const item = header.parentElement; const body = item.querySelector('.accordion-body'); const icon = header.querySelector('.accordion-icon'); item.classList.toggle('open'); body.classList.toggle('open'); icon.classList.toggle('open'); }); }); /* Calculator logic */ function logSum(logA, logB){ if(logA < logB) return logB + Math.log1p(Math.exp(logA - logB)); else return logA + Math.log1p(Math.exp(logB - logA)); } function computePosterior(logL, logP){ // logEvidence = logSum(logL + logP, log(1 - exp(logL)) + logComplement) // where logComplement = log(1 - exp(logPrior))? Actually from source: // double logEvidence = LogSum(logLikelihood + logPrior, log(1 - exp(logLikelihood)) + logComplement); // Assuming logComplement = log(1 - exp(logPrior))? Not fully clear. // We'll implement a symmetric stable version: logEvidence = logSum(logL + logP, log(1 - exp(logL)) + log(1 - exp(logP))); // This approximates evidence for two hypotheses H and ~H. const term1 = logL + logP; const term2 = Math.log1p(-Math.exp(logL)) + Math.log1p(-Math.exp(logP)); return Math.exp(logSum(term1, term2) - (logL + logP)); } const calcForm = document.getElementById('calcForm'); const resultEl = document.getElementById('result'); const copyBtn = document.getElementById('copyResult'); const downloadCsv = document.getElementById('downloadCsv'); const downloadJson = document.getElementById('downloadJson'); calcForm.addEventListener('submit', e => { e.preventDefault(); const logL = parseFloat(document.getElementById('logLikelihood').value); const logP = parseFloat(document.getElementById('logPrior').value); if(isNaN(logL) || isNaN(logP)){ resultEl.textContent = 'Invalid input'; resultEl.style.color = '#dc3545'; return; } const posterior = computePosterior(logL, logP); resultEl.textContent = posterior.toLocaleString(undefined, {minimumFractionDigits:6, maximumFractionDigits:6}); resultEl.style.color = 'var(--accent)'; }); copyBtn.addEventListener('click', () => { if(resultEl.textContent === '—' || resultEl.textContent.startsWith('Invalid')) return; navigator.clipboard.writeText(resultEl.textContent).then(()=>{ copyBtn.textContent = '✅'; setTimeout(()=>{copyBtn.textContent='📋';},1500); }); }); function downloadCSV(){ if(resultEl.textContent === '—' || resultEl.textContent.startsWith('Invalid')) return; const data = [`logLikelihood,logPrior,posterior`, `${document.getElementById('logLikelihood').value},${document.getElementById('logPrior').value},${resultEl.textContent}`].join('\n'); const blob = new Blob([data],{type:'text/csv'}); const url = URL.createObjectURL(blob); const a = document.createElement('a'); a.href = url; a.download = 'posterior_result.csv'; a.click(); URL.revokeObjectURL(url); } function downloadJSON(){ if(resultEl.textContent === '—' || resultEl.textContent.startsWith('Invalid')) return; const obj = { logLikelihood: parseFloat(document.getElementById('logLikelihood').value), logPrior: parseFloat(document.getElementById('logPrior').value), posterior: parseFloat(resultEl.textContent) }; const blob = new Blob([JSON.stringify(obj,null,2)],{type:'application/json'}); const url = URL.createObjectURL(blob); const a = document.createElement('a'); a.href = url; a.download = 'posterior_result.json'; a.click(); URL.revokeObjectURL(url); } downloadCsv.addEventListener('click', downloadCSV); downloadJson.addEventListener('click', downloadJSON); /* Smooth scroll for anchor links */ document.querySelectorAll('a[href^="#"]').forEach(anchor => { anchor.addEventListener('click', function(e){ const target = document.querySelector(this.getAttribute('href')); if(target){ e.preventDefault(); target.scrollIntoView({behavior:'smooth'}); } }); }); </script> </body> </html>