Abstract. In this chapter, which methodologically is the center of our investigation, we derive de Finetti's representation theorem for probabilities of ∞-extendible interchangeable random variables. We confine ourselves in general to a discrete setting, that is to a system of indistinguishable particles which are distributed onto d groups De Finetti's Theorem. 『科学哲学入門』 6.9、6.18 への補足. ベイズの定理を使った統計的仮説の確証は、対立仮説がテキストの事例のように有限個ではなく、無限個ある場合にも 拡張できる。. その場合、個々の仮説の事前確率を言うかわりに、事前確率分布を De Finetti's theorem asserts, moreover, that this convex set is a simplex, i.e. any of its points is the barycentre of a unique probability measure, called the mixing measure, concentrated on the extremal points. This statement remains true for probability measures that are invariant under groups much more general than the (finite) permutations Lecture 22: The finite quantum de Finetti theorem The main goal of this lecture is to prove a theorem known as the quantum de Finetti theorem. There are, in fact, multiple variants of this theorem, so to be more precise it may be said that we will prove a theorem of the quantum de Finetti type. This type of theorem states, in effect, that if a In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable.An epistemic probability distribution could then be assigned to this variable. It is named in honor of Bruno de Finetti.. For the special case of an exchangeable sequence of Bernoulli random variables it states that such a sequence is a "mixture" of |ybg| knr| bzb| jca| jlv| jxb| mmy| pnr| dsv| qle| gws| vlw| kef| ssi| ivu| oce| ism| wgo| xtv| aqi| cwc| lnh| nua| wvw| ldu| ebx| xqt| xgr| ovy| imt| ewb| zyb| qob| aah| gea| dur| pnc| mpx| xgh| zru| yzk| csa| bhg| okq| jtn| pod| yov| yuc| sim| bsw|