t rrt r tr trs - PowerPoint PPT Presentation

❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ tr♦♣✐❝❛❧ ❚r♦♣✐❝❛❧ α ✲♣r✉♥✐♥❣ ❈❤♦♦s❡✲❍♦✇✲❚♦✲❉✐✈✐❞❡ ❛♥❞ ❈♦♥q✉❡r ❆ tr♦♣✐❝❛❧ ❣❛♠❡ ❡①❛♠♣❧❡✿ ♣❛rs✐♥❣ ❍♦✇ t♦ ❝♦rr❡❝t❧② ♣r✉♥❡ tr♦♣✐❝❛❧ tr❡❡s ❏❡❛♥✲❱✐♥❝❡♥t ▲♦❞❞♦ ▲✉❝❛ ❙❛✐✉ ❤tt♣✿✴✴✇✇✇✲❧✐♣♥✳✉♥✐✈✲♣❛r✐s✶✸✳❢r✴⑦❧♦❞❞♦ ❤tt♣✿✴✴✇✇✇✲❧✐♣♥✳✉♥✐✈✲♣❛r✐s✶✸✳❢r✴⑦s❛✐✉ ▲■P◆✱ ❯♥✐✈❡rs✐té P❛r✐s ✶✸ P❛r✐s✱ ❏✉❧② ✺✱ ✷✵✶✵ ❏❡❛♥✲❱✐♥❝❡♥t ▲♦❞❞♦✱ ▲✉❝❛ ❙❛✐✉ ❍♦✇ t♦ ❝♦rr❡❝t❧② ♣r✉♥❡ tr♦♣✐❝❛❧ tr❡❡s

tr♦♣✐❝❛❧ ❣❛♠❡s ✇❤♦s❡ ❞✉❛❧ ✐s ❛❧s♦ tr♦♣✐❝❛❧ ❝❛♥ ❜❡ ❝♦♠♣✉t❡❞ ✇✐t❤ ✲ ✭♥♦t ♣r♦✈❡❞ ❢♦r♠❛❧❧②✱ ❜✉t ✐♥t✉✐t✐✈❡✮ ❚r♦♣✐❝❛❧ ❣❛♠❡s ❛r❡ ❛ ❣❡♥❡r❛❧✐③❛t✐♦♥ ♦❢ ♠✐♥✲♠❛① ❣❛♠❡s ❚r♦♣✐❝❛❧ ❣❛♠❡s s✉♣♣♦rt tr♦♣✐❝❛❧ ✲♣r✉♥✐♥❣ ❆♣♣r♦①✐♠❛t❡❞ ♣❛rs✐♥❣ ✐s ❛ tr♦♣✐❝❛❧ ❣❛♠❡ ✲♣r✉♥✐♥❣ s❡❡♠s t♦ ❜❡ ❡✛❡❝t✐✈❡ ✳✳✳✇❡ s✉s♣❡❝t ♠❛♥② ♠♦r❡ ♣r♦❜❧❡♠s t♦ ❜❡ tr♦♣✐❝❛❧ ❣❛♠❡s ❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ tr♦♣✐❝❛❧ ■♥tr♦❞✉❝t✐♦♥ ❚r♦♣✐❝❛❧ α ✲♣r✉♥✐♥❣ ❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ ⊕ ✲ ⊙ ❈❤♦♦s❡✲❍♦✇✲❚♦✲❉✐✈✐❞❡ ❛♥❞ ❈♦♥q✉❡r ❋♦r♠❛❧✐③❛t✐♦♥ ❛s ❛ r❡✇r✐t❡ s②st❡♠ ✴ s♠❛❧❧✲st❡♣ s❡♠❛♥t✐❝s ❆ tr♦♣✐❝❛❧ ❣❛♠❡ ❡①❛♠♣❧❡✿ ♣❛rs✐♥❣ ▼♦t✐✈❛t✐♦♥ ▼❛♥② ♣r♦❜❧❡♠s ❝❛♥ ❜❡ s♦❧✈❡❞ ✇✐t❤ ❛ ♥♦♥✲❞❡t❡r♠✐♥✐st✐❝ s❡❛r❝❤ ♦♥ ❛ s♣❛❝❡ ✇❤❡r❡ s♦♠❡ ♠❡tr✐❝ ✐s ♦♣t✐♠✐③❡❞✳ ✳ ✳ ❏❡❛♥✲❱✐♥❝❡♥t ▲♦❞❞♦✱ ▲✉❝❛ ❙❛✐✉ ❍♦✇ t♦ ❝♦rr❡❝t❧② ♣r✉♥❡ tr♦♣✐❝❛❧ tr❡❡s

tr♦♣✐❝❛❧ ❣❛♠❡s ✇❤♦s❡ ❞✉❛❧ ✐s ❛❧s♦ tr♦♣✐❝❛❧ ❝❛♥ ❜❡ ❝♦♠♣✉t❡❞ ✇✐t❤ ✲ ✭♥♦t ♣r♦✈❡❞ ❢♦r♠❛❧❧②✱ ❜✉t ✐♥t✉✐t✐✈❡✮ ❚r♦♣✐❝❛❧ ❣❛♠❡s s✉♣♣♦rt tr♦♣✐❝❛❧ ✲♣r✉♥✐♥❣ ❆♣♣r♦①✐♠❛t❡❞ ♣❛rs✐♥❣ ✐s ❛ tr♦♣✐❝❛❧ ❣❛♠❡ ✲♣r✉♥✐♥❣ s❡❡♠s t♦ ❜❡ ❡✛❡❝t✐✈❡ ✳✳✳✇❡ s✉s♣❡❝t ♠❛♥② ♠♦r❡ ♣r♦❜❧❡♠s t♦ ❜❡ tr♦♣✐❝❛❧ ❣❛♠❡s ❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ tr♦♣✐❝❛❧ ■♥tr♦❞✉❝t✐♦♥ ❚r♦♣✐❝❛❧ α ✲♣r✉♥✐♥❣ ❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ ⊕ ✲ ⊙ ❈❤♦♦s❡✲❍♦✇✲❚♦✲❉✐✈✐❞❡ ❛♥❞ ❈♦♥q✉❡r ❋♦r♠❛❧✐③❛t✐♦♥ ❛s ❛ r❡✇r✐t❡ s②st❡♠ ✴ s♠❛❧❧✲st❡♣ s❡♠❛♥t✐❝s ❆ tr♦♣✐❝❛❧ ❣❛♠❡ ❡①❛♠♣❧❡✿ ♣❛rs✐♥❣ ▼♦t✐✈❛t✐♦♥ ▼❛♥② ♣r♦❜❧❡♠s ❝❛♥ ❜❡ s♦❧✈❡❞ ✇✐t❤ ❛ ♥♦♥✲❞❡t❡r♠✐♥✐st✐❝ s❡❛r❝❤ ♦♥ ❛ s♣❛❝❡ ✇❤❡r❡ s♦♠❡ ♠❡tr✐❝ ✐s ♦♣t✐♠✐③❡❞✳ ✳ ✳ ❚r♦♣✐❝❛❧ ❣❛♠❡s ❛r❡ ❛ ❣❡♥❡r❛❧✐③❛t✐♦♥ ♦❢ ♠✐♥✲♠❛① ❣❛♠❡s ❏❡❛♥✲❱✐♥❝❡♥t ▲♦❞❞♦✱ ▲✉❝❛ ❙❛✐✉ ❍♦✇ t♦ ❝♦rr❡❝t❧② ♣r✉♥❡ tr♦♣✐❝❛❧ tr❡❡s

❆♣♣r♦①✐♠❛t❡❞ ♣❛rs✐♥❣ ✐s ❛ tr♦♣✐❝❛❧ ❣❛♠❡ ✲♣r✉♥✐♥❣ s❡❡♠s t♦ ❜❡ ❡✛❡❝t✐✈❡ ✳✳✳✇❡ s✉s♣❡❝t ♠❛♥② ♠♦r❡ ♣r♦❜❧❡♠s t♦ ❜❡ tr♦♣✐❝❛❧ ❣❛♠❡s ❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ tr♦♣✐❝❛❧ ■♥tr♦❞✉❝t✐♦♥ ❚r♦♣✐❝❛❧ α ✲♣r✉♥✐♥❣ ❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ ⊕ ✲ ⊙ ❈❤♦♦s❡✲❍♦✇✲❚♦✲❉✐✈✐❞❡ ❛♥❞ ❈♦♥q✉❡r ❋♦r♠❛❧✐③❛t✐♦♥ ❛s ❛ r❡✇r✐t❡ s②st❡♠ ✴ s♠❛❧❧✲st❡♣ s❡♠❛♥t✐❝s ❆ tr♦♣✐❝❛❧ ❣❛♠❡ ❡①❛♠♣❧❡✿ ♣❛rs✐♥❣ ▼♦t✐✈❛t✐♦♥ ▼❛♥② ♣r♦❜❧❡♠s ❝❛♥ ❜❡ s♦❧✈❡❞ ✇✐t❤ ❛ ♥♦♥✲❞❡t❡r♠✐♥✐st✐❝ s❡❛r❝❤ ♦♥ ❛ s♣❛❝❡ ✇❤❡r❡ s♦♠❡ ♠❡tr✐❝ ✐s ♦♣t✐♠✐③❡❞✳ ✳ ✳ ❚r♦♣✐❝❛❧ ❣❛♠❡s ❛r❡ ❛ ❣❡♥❡r❛❧✐③❛t✐♦♥ ♦❢ ♠✐♥✲♠❛① ❣❛♠❡s ❚r♦♣✐❝❛❧ ❣❛♠❡s s✉♣♣♦rt tr♦♣✐❝❛❧ α ✲♣r✉♥✐♥❣ tr♦♣✐❝❛❧ ❣❛♠❡s ✇❤♦s❡ ❞✉❛❧ ✐s ❛❧s♦ tr♦♣✐❝❛❧ ❝❛♥ ❜❡ ❝♦♠♣✉t❡❞ ✇✐t❤ α ✲ β ✭♥♦t ♣r♦✈❡❞ ❢♦r♠❛❧❧②✱ ❜✉t ✐♥t✉✐t✐✈❡✮ ❏❡❛♥✲❱✐♥❝❡♥t ▲♦❞❞♦✱ ▲✉❝❛ ❙❛✐✉ ❍♦✇ t♦ ❝♦rr❡❝t❧② ♣r✉♥❡ tr♦♣✐❝❛❧ tr❡❡s

❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ tr♦♣✐❝❛❧ ■♥tr♦❞✉❝t✐♦♥ ❚r♦♣✐❝❛❧ α ✲♣r✉♥✐♥❣ ❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ ⊕ ✲ ⊙ ❈❤♦♦s❡✲❍♦✇✲❚♦✲❉✐✈✐❞❡ ❛♥❞ ❈♦♥q✉❡r ❋♦r♠❛❧✐③❛t✐♦♥ ❛s ❛ r❡✇r✐t❡ s②st❡♠ ✴ s♠❛❧❧✲st❡♣ s❡♠❛♥t✐❝s ❆ tr♦♣✐❝❛❧ ❣❛♠❡ ❡①❛♠♣❧❡✿ ♣❛rs✐♥❣ ▼♦t✐✈❛t✐♦♥ ▼❛♥② ♣r♦❜❧❡♠s ❝❛♥ ❜❡ s♦❧✈❡❞ ✇✐t❤ ❛ ♥♦♥✲❞❡t❡r♠✐♥✐st✐❝ s❡❛r❝❤ ♦♥ ❛ s♣❛❝❡ ✇❤❡r❡ s♦♠❡ ♠❡tr✐❝ ✐s ♦♣t✐♠✐③❡❞✳ ✳ ✳ ❚r♦♣✐❝❛❧ ❣❛♠❡s ❛r❡ ❛ ❣❡♥❡r❛❧✐③❛t✐♦♥ ♦❢ ♠✐♥✲♠❛① ❣❛♠❡s ❚r♦♣✐❝❛❧ ❣❛♠❡s s✉♣♣♦rt tr♦♣✐❝❛❧ α ✲♣r✉♥✐♥❣ tr♦♣✐❝❛❧ ❣❛♠❡s ✇❤♦s❡ ❞✉❛❧ ✐s ❛❧s♦ tr♦♣✐❝❛❧ ❝❛♥ ❜❡ ❝♦♠♣✉t❡❞ ✇✐t❤ α ✲ β ✭♥♦t ♣r♦✈❡❞ ❢♦r♠❛❧❧②✱ ❜✉t ✐♥t✉✐t✐✈❡✮ ❆♣♣r♦①✐♠❛t❡❞ ♣❛rs✐♥❣ ✐s ❛ tr♦♣✐❝❛❧ ❣❛♠❡ α ✲♣r✉♥✐♥❣ s❡❡♠s t♦ ❜❡ ❡✛❡❝t✐✈❡ ✳✳✳✇❡ s✉s♣❡❝t ♠❛♥② ♠♦r❡ ♣r♦❜❧❡♠s t♦ ❜❡ tr♦♣✐❝❛❧ ❣❛♠❡s ❏❡❛♥✲❱✐♥❝❡♥t ▲♦❞❞♦✱ ▲✉❝❛ ❙❛✐✉ ❍♦✇ t♦ ❝♦rr❡❝t❧② ♣r✉♥❡ tr♦♣✐❝❛❧ tr❡❡s

❲❤❛t ✐❢ ✇❡ ❣❡♥❡r❛❧✐③❡❄ ❧❡t✬s t❛❦❡ ❛ ❣❡♥❡r✐❝ ✐♥st❡❛❞ ♦❢ ♠✐♥ ♠❛① ❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ tr♦♣✐❝❛❧ ■♥tr♦❞✉❝t✐♦♥ ❚r♦♣✐❝❛❧ α ✲♣r✉♥✐♥❣ ❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s✿ ❢r♦♠ ♠✐♥✲♠❛① t♦ ⊕ ✲ ⊙ ❈❤♦♦s❡✲❍♦✇✲❚♦✲❉✐✈✐❞❡ ❛♥❞ ❈♦♥q✉❡r ❋♦r♠❛❧✐③❛t✐♦♥ ❛s ❛ r❡✇r✐t❡ s②st❡♠ ✴ s♠❛❧❧✲st❡♣ s❡♠❛♥t✐❝s ❆ tr♦♣✐❝❛❧ ❣❛♠❡ ❡①❛♠♣❧❡✿ ♣❛rs✐♥❣ ❈♦♠❜✐♥❛t♦r✐❛❧ ❣❛♠❡s ✭✶✮✿ ♠✐♥✲♠❛① ▲❡t ❛ ❣❛♠❡ ❛r❡♥❛ ❙ = ( P , λ, s✉❝❝ ) ❛♥❞ ❛ ♣❛②♦✛ ❢✉♥❝t✐♦♥ ♣ : P ❚ → Z ∪ { + ∞ , −∞} ❜❡ ❣✐✈❡♥✳ ✳ ✳ ❚❤❡ ❣❛♠❡ ✈❛❧✉❡ ♦❢ ❛ ♣♦s✐t✐♦♥ π ∈ P ✐s tr❛❞✐t✐♦♥❛❧❧② ❞❡✜♥❡❞ ❛s✿  ♣ ( π ) , π ∈ P ❚   ♠✐♥ ♥ ✈ ♣ ( π ) = ✐ = ✶ ✈ ♣ ( π ✐ ) , s✉❝❝ ( π ) = � π ✶ ...π ♥ � , λ ( π ) = P  ♠❛① ♥ ✐ = ✶ ✈ ♣ ( π ✐ ) , s✉❝❝ ( π ) = � π ✶ ...π ♥ � , λ ( π ) = O  ✳ ❏❡❛♥✲❱✐♥❝❡♥t ▲♦❞❞♦✱ ▲✉❝❛ ❙❛✐✉ ❍♦✇ t♦ ❝♦rr❡❝t❧② ♣r✉♥❡ tr♦♣✐❝❛❧ tr❡❡s