Inferenza statistica, una presentazione basata sul concetto by A. Azzalini

By A. Azzalini

Il concetto di verosimiglianza gioca un ruolo fondamentale nell'impostazione corrente della Statistica, sia in step with introdurre nozioni generali della teoria che in keeping with lo sviluppo di metodi specifici. Questo libro presenta un'esposizione della teoria statistica basata sulla verosimiglianza, osservata dal punto di vista della "teoria classica", e dimostra come il corpo principale delle tecniche statistiche attualmente in uso possano essere desunte da un numero limitato di concetti-chiave. L'attuale edizione integra l. a. precedente con un capitolo sui modelli lineari generalizzati e con altri aggiornamenti quali numerose illustrazioni numeriche, basate su applicazioni reali, che facilitano l. a. percezione della rilevanza operativa dei metodi presentati.

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Extra resources for Inferenza statistica, una presentazione basata sul concetto di verosimiglianza

Example text

In the same year, the mathematician Thomas Simpson applied De Moivre’s methods to astronomical observations. ) Simpson concentrated on the errors rather than the observations, and took the important step of regarding them, for repeated measurements in identical circumstances, as having a fixed and continuous distribution of probability. Using De Moivre’s series expansions, he compared the probability that the mean of a number of errors lies within a specified range with the probability associated with a single error.

Complete lack of knowledge about some parameter implies also ignorance about any function of that parameter. Yet a uniform distribution in one case will lead to a different probability distribution in the other. Knowing nothing about the density of an object implies ignorance also of the specific volume. Yet these quantities are reciprocally related, and cannot both be uniformly distributed. Continental thinkers were no less critical. A. Cournot wrote that probabilities had little value other than the “charm of speculation” unless based on experience; Fries agreed.

Boole brought up a second objection to the principle: it was inconsistent. Complete lack of knowledge about some parameter implies also ignorance about any function of that parameter. Yet a uniform distribution in one case will lead to a different probability distribution in the other. Knowing nothing about the density of an object implies ignorance also of the specific volume. Yet these quantities are reciprocally related, and cannot both be uniformly distributed. Continental thinkers were no less critical.

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