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Modelli probabilistici

Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will

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Page 1: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will

Modelli probabilistici

Page 2: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will

010 1 0 1 1 010 0

PopulationSample

1 01 1 00 1 11 10 10

• On the basis of what we have observed we want to predict properties on what we will observe in the future [Laplace 1868, Fisher 1948, De Finetti 1975, Geisser 1993]

Inference framework: a string of characters separated by a time pointer

Inference: a way of well organizing the observed data

A predictive approach

0 1 1 0 1 0 01 1 11 00

01

1

0 1 0 0 1 1 01 1 11 001

10

Page 3: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will

Una collezione A di eventi è un’algebra se:

Le regole del buon vivere

Page 4: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will
Page 5: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will

Uhmm… we have already Kolmogorov approach

010 1 010 0

Sample

1 1 0

Population

1 01 1 00 1 11 10 10

The Truth

Page 6: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will
Page 7: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will
Page 8: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will

Modello equiprobabile

Page 9: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will
Page 10: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will
Page 11: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will
Page 12: Modelli probabilistici. 0101011010 0 PopulationSample 1011001111010 On the basis of what we have observed we want to predict properties on what we will