MCMC Sampler Dashboard

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A simple Metropolis-Hastings sampler with a Gaussian random-walk proposal.\n// Designed to be stepped incrementally so the UI can animate it.\n\nimport type { Target } from \"./distributions.ts\";\n\nexport type Sample = { x: number; y: number };\n\nexport type SamplerState = {\n current: Sample;\n currentLogProb: number;\n accepted: number;\n proposed: number;\n samples: Sample[];\n};\n\n// Box-Muller standard normal\nfunction randn(): number {\n let u = 0, v = 0;\n while (u === 0) u = Math.random();\n while (v === 0) v = Math.random();\n return Math.sqrt(-2 * Math.log(u)) * Math.cos(2 * Math.PI * v);\n}\n\nexport function initSampler(target: Target, start: Sample): SamplerState {\n return {\n current: start,\n currentLogProb: target.logProb(start.x, start.y),\n accepted: 0,\n proposed: 0,\n samples: [start],\n };\n}\n\n// Advance the chain by `steps` iterations, mutating + returning the state.\nexport function step(\n state: SamplerState,\n target: Target,\n stepSize: number,\n steps = 1,\n): SamplerState {\n for (let i = 0; i < steps; i++) {\n const proposal: Sample = {\n x: state.current.x + randn() * stepSize,\n y: state.current.y + randn() * stepSize,\n };\n const proposalLogProb = target.logProb(proposal.x, proposal.y);\n const logAccept = proposalLogProb - state.currentLogProb;\n\n state.proposed++;\n if (Math.log(Math.random()) < logAccept) {\n state.current = proposal;\n state.currentLogProb = proposalLogProb;\n state.accepted++;\n }\n state.samples.push(state.current);\n }\n return state;\n}\n\nexport function acceptanceRate(state: SamplerState): number {\n return state.proposed === 0 ? 0 : state.accepted / state.proposed;\n}\n\n// Mean and standard deviation of the collected samples (post burn-in).\nexport function summarize(samples: Sample[], burnIn: number) {\n const used = samples.slice(burnIn);\n const n = used.length || 1;\n let mx = 0, my = 0;\n for (const s of used) {\n mx += s.x;\n my += s.y;\n }\n mx /= n;\n my /= n;\n let vx = 0, vy = 0;\n for 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@jsxImportSource https://esm.sh/react@18.2.0 */\nimport { createRoot } from \"https://esm.sh/react-dom@18.2.0/client\";\nimport { App } from \"./components/App.tsx\";\n\nconst root = document.getElementById(\"root\");\nif (!root) {\n throw new Error(\"No root element found\");\n}\n\ncreateRoot(root).render();\n",[],[145,175],"560dc038-5ee8-11f1-9c2a-1607ee4eb77e","index.html","560dc0d8-5ee8-11f1-9c2a-1607ee4eb77e",10,["D",1780448739426],"\n\n \n \n \n MCMC Sampler Dashboard\n \n \n \n \n

\n \n \n \n\n",[],[145,183],"4e122a0e-5ee8-11f1-a5a1-1607ee4eb77e","favicon.svg","4e122acc-5ee8-11f1-a5a1-1607ee4eb77e",8,["D",1780448726035],"\n",[],[145,191],"6123abae-5ee8-11f1-a7c1-1607ee4eb77e","distributions.ts","6123ac62-5ee8-11f1-a7c1-1607ee4eb77e","a88a4204-bf6e-4106-b9d1-39a0b0b7ec31",12,["D",1780448758023],"// Target distributions for the sampler. Each returns an (unnormalized) log-density\n// over a 2D point [x, y]. Working in log-space keeps things numerically stable.\n\nexport type Target = {\n id: string;\n name: string;\n description: string;\n // Unnormalized log probability density at point [x, y]\n logProb: (x: number, y: number) => number;\n // Suggested view bounds [xmin, xmax, ymin, ymax]\n bounds: [number, number, number, number];\n};\n\nfunction logGaussian2D(\n x: number,\n y: number,\n mx: number,\n my: number,\n sx: number,\n sy: number,\n rho = 0,\n): number {\n const dx = (x - mx) / sx;\n const dy = (y - my) / sy;\n const z = dx * dx - 2 * rho * dx * dy + dy * dy;\n return -z / (2 * (1 - rho * rho));\n}\n\n// log(sum(exp(...))) helper for mixtures\nfunction logSumExp(values: number[]): number {\n const max = Math.max(...values);\n let sum = 0;\n for (const v of values) sum += Math.exp(v - max);\n return max + Math.log(sum);\n}\n\nexport const TARGETS: Target[] = [\n {\n id: \"banana\",\n name: \"Banana (Rosenbrock)\",\n description: \"A curved, correlated density that trips up naive samplers.\",\n logProb: (x, y) => {\n // Rosenbrock-style banana\n const a = 1;\n const b = 1.5;\n return -((a - x) ** 2 + b * (y - x * x) ** 2) / 2;\n },\n bounds: [-3, 3, -1, 6],\n },\n {\n id: \"bimodal\",\n name: \"Bimodal\",\n description: \"Two separated Gaussian modes — tests mode hopping.\",\n logProb: (x, y) =>\n logSumExp([\n logGaussian2D(x, y, -2, -2, 0.7, 0.7),\n logGaussian2D(x, y, 2, 2, 0.7, 0.7),\n ]),\n bounds: [-5, 5, -5, 5],\n },\n {\n id: \"donut\",\n name: \"Donut\",\n description: \"A ring-shaped density — mass on an annulus, not the center.\",\n logProb: (x, y) => {\n const r = Math.sqrt(x * x + y * y);\n const sigma = 0.4;\n return -((r - 2.6) ** 2) / (2 * sigma * sigma);\n },\n bounds: [-4, 4, -4, 4],\n },\n {\n id: \"gaussian\",\n name: \"Correlated Gaussian\",\n description: \"A single tilted Gaussian with strong correlation.\",\n logProb: (x, y) => logGaussian2D(x, y, 0, 0, 1.6, 1.6, 0.8),\n bounds: [-5, 5, -5, 5],\n },\n];\n\nexport function getTarget(id: string): Target {\n return TARGETS.find((t) => t.id === id) ?? TARGETS[0];\n}\n",[],[145,207,199],"lib","6123d8c2-5ee8-11f1-a7c1-1607ee4eb77e",["D",1780448758023],[165],[145,207],"4d8d1968-5ee8-11f1-a5a1-1607ee4eb77e","components","4d8d1a3a-5ee8-11f1-a5a1-1607ee4eb77e",7,["D",1780448725164],[],[145,213],["D",1780448721351],[163,164,166,167,168],[145],["D",1780448525311],{"_103":102,"_110":105},{"_103":102,"_104":105,"_106":105,"_19":62,"_107":108,"_109":55},{"_13":92,"_38":93,"_49":48,"_94":50,"_95":-5,"_96":-5,"_97":-5,"_98":-5,"_99":-5,"_100":51,"_101":102},"ctx",{"_85":-5,"_129":259,"_260":261,"_262":263,"_264":55,"_265":55,"_266":55,"_267":31,"_268":-5,"_269":-7,"_270":-7,"_271":69,"_272":55,"_273":55,"_274":-5,"_275":55,"_276":55,"_277":55,"_278":-5},"ENV",{"_230":231,"_232":233,"_234":93,"_235":236,"_237":238,"_239":240,"_241":242,"_243":244,"_245":246,"_247":248,"_249":250,"_251":252,"_253":254,"_255":256,"_257":258},"REACT_APP_SENTRY_DSN","https://586020d86f05489db63a554690acf1e9@o1398359.ingest.sentry.io/6724499","RENDER_GIT_COMMIT","5015b8df46402d8bba4f485ecc37aec202b0e06b","RENDER_GIT_BRANCH","POSTHOG_API_TOKEN","phc_nmoyuAkStEZuUp69rYlg1DZgrIt19Gx0Y4Hwf8tGgJP","POSTHOG_API_HOST","https://wart.val.town","WEB_API_TEMPLATE","https://{val}.web.val.run","APP_URL","https://www.val.town","MODULE_URL","https://esm.town","VANITY_WEB_API_TEMPLATE","https://{label}.val.run/","DENOLS_URL","https://lsp.val.town","NODE_ENV","production","CLOUDFLARE_TURNSTILE_SITE_KEY","0x4AAAAAACtaIZJH7s9rBMZ6","GOOGLE_CLIENT_ID","875989696899-jtsqkhlbdv5jrlsk8631p7ipjg3c6o62.apps.googleusercontent.com","STRIPE_PUBLISHABLE_KEY","pk_live_51N2zvWEpZTTLipIkVEwXrUG9AT0yeOOEYxszarZT1jpsZV58Ly6wlg3SltZpHN26CUalOBmUSY7adQRQiSkCZz2500qSXNkf8Y","API_URL","https://api.val.town",[],"preferencesKeybindings","default","preferencesTheme","light","preferencesFixers","preferencesCopilot","preferencesSelectionAi","preferencesCloseBrackets","preferencesChatPanelState","preferencesDprint","preferencesDenofmt","notificationCount","flagDenols","isBusinessOrgMember","businessOrgHandle","isBusinessOrgAdmin","isHigherTownieTier","navCollapsed","currentOrgId"]

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