Markov model — states, transitions and validation
Specify mutually exclusive states and a transition interval before estimating probabilities. Rows of the transition matrix must sum to one; homogeneity and memorylessness are assumptions to test rather than automatic properties of the data.
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{
"nodes": [
{ "id": "states", "type": "rounded", "label": "Exhaustive mutually exclusive states", "x": 40, "y": 200, "width": 150, "height": 104, "fill": "#ede9fe", "stroke": "#6d28d9" },
{ "id": "time", "type": "octagon", "label": "Transition interval", "x": 40, "y": 520, "width": 150, "height": 104, "fill": "#e0f2fe", "stroke": "#0369a1" },
{ "id": "data", "type": "card", "label": "Observed transition counts", "x": 215, "y": 200, "width": 150, "height": 104, "fill": "#ccfbf1", "stroke": "#0f766e" },
{ "id": "matrix", "type": "rounded", "label": "Transition-probability matrix", "x": 390, "y": 200, "width": 150, "height": 104, "fill": "#fef3c7", "stroke": "#b45309" },
{ "id": "rows", "type": "octagon", "label": "Row-sum and nonnegativity checks", "x": 390, "y": 520, "width": 150, "height": 104, "fill": "#e0f2fe", "stroke": "#0369a1" },
{ "id": "prop", "type": "rounded", "label": "Propagate state distribution", "x": 565, "y": 200, "width": 150, "height": 104, "fill": "#fef3c7", "stroke": "#b45309" },
{ "id": "obs", "type": "card", "label": "Held-out state observations", "x": 740, "y": 520, "width": 150, "height": 104, "fill": "#ccfbf1", "stroke": "#0f766e" },
{ "id": "valid", "type": "rounded", "label": "Prediction / assumption checks", "x": 740, "y": 200, "width": 150, "height": 104, "fill": "#fef3c7", "stroke": "#b45309" },
{ "id": "sens", "type": "rounded", "label": "Time-step sensitivity", "x": 915, "y": 200, "width": 150, "height": 104, "fill": "#fce7f3", "stroke": "#be185d" }
],
"edges": [
{ "id": "e0", "source": "states", "target": "data", "label": "classify" },
{ "id": "e1", "source": "time", "target": "data", "label": "align intervals" },
{ "id": "e2", "source": "data", "target": "matrix", "label": "estimate" },
{ "id": "e3", "source": "rows", "target": "matrix", "label": "validate", "style": "dashed" },
{ "id": "e4", "source": "matrix", "target": "prop", "label": "iterate" },
{ "id": "e5", "source": "prop", "target": "valid", "label": "predict" },
{ "id": "e6", "source": "obs", "target": "valid", "label": "compare" },
{ "id": "e7", "source": "valid", "target": "sens", "label": "assess approximation" }
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