{"id":183,"date":"2020-06-01T16:55:46","date_gmt":"2020-06-01T16:55:46","guid":{"rendered":"https:\/\/integrations.pressbooks.network\/testclone\/?post_type=chapter&p=183"},"modified":"2023-08-14T17:34:19","modified_gmt":"2023-08-14T17:34:19","slug":"math-testing","status":"publish","type":"chapter","link":"https:\/\/integrations.pressbooks.network\/test-clone\/chapter\/math-testing\/","title":{"raw":"Math Testing","rendered":"Math Testing"},"content":{"raw":"p<\/mi>(<\/mo>θ<\/mi><\/mrow>|<\/mo><\/mrow>y<\/mi>)<\/mo>=<\/mo>p<\/mi>(<\/mo>y<\/mi>|<\/mo><\/mrow>θ<\/mi>)<\/mo>p<\/mi>(<\/mo>θ<\/mi>)<\/mo><\/mrow>p<\/mi>(<\/mo>y<\/mi>)<\/mo><\/mrow><\/mfrac><\/math>\r\n\r\np<\/mi>(<\/mo>θ<\/mi>h<\/mi><\/msub>|<\/mo><\/mrow>y<\/mi>)<\/mo>=<\/mo><\/mtd><\/mi>∫<\/mo>⋯<\/mo>∫<\/mo>p<\/mi>(<\/mo>θ<\/mi>1<\/mn><\/msub>,<\/mo>…<\/mo>,<\/mo>θ<\/mi>h<\/mi><\/msub>,<\/mo>…<\/mo>,<\/mo>θ<\/mi>H<\/mi><\/msub>|<\/mo><\/mrow>y<\/mi>)<\/mo>d<\/mi>θ<\/mi>∖<\/mo>h<\/mi><\/mrow><\/msub><\/mrow><\/mtd><\/mtr>=<\/mo><\/mtd><\/mi>∫<\/mo>⋯<\/mo>∫<\/mo>p<\/mi>(<\/mo>θ<\/mi>h<\/mi><\/msub>|<\/mo><\/mrow>θ<\/mi>∖<\/mo>h<\/mi><\/mrow><\/msub>,<\/mo>y<\/mi>)<\/mo>p<\/mi>(<\/mo>θ<\/mi>∖<\/mo>h<\/mi><\/mrow><\/msub>|<\/mo><\/mrow>y<\/mi>)<\/mo>d<\/mi>θ<\/mi>∖<\/mo>h<\/mi><\/mrow><\/msub><\/mrow><\/mtd><\/mtr><\/mtable><\/math>\r\n\r\na<\/mi>2<\/mn><\/msup>=<\/mo>b<\/mi>2<\/mn><\/msup>+<\/mo>c<\/mi>2<\/mn><\/msup>η<\/mi>i<\/mi><\/msub>|<\/mo><\/mrow>α<\/mi>,<\/mo>β<\/mi>∼<\/mo>Gamma<\/mtext>(<\/mo>α<\/mi>+<\/mo>ξ<\/mi>,<\/mo>β<\/mi>+<\/mo>χ<\/mi>)<\/mo>,<\/mo>i<\/mi>=<\/mo>1<\/mn>,<\/mo>…<\/mo>,<\/mo>N<\/mi>α<\/mi>,<\/mo>β<\/mi>∼<\/mo>I<\/mi>G<\/mi><\/mrow>(<\/mo>0.5<\/mn>,<\/mo>0.05<\/mn>)<\/mo><\/math>","rendered":"

p<\/mi>(<\/mo>θ<\/mi><\/mrow>|<\/mo><\/mrow>y<\/mi>)<\/mo>=<\/mo>p<\/mi>(<\/mo>y<\/mi>|<\/mo><\/mrow>θ<\/mi>)<\/mo>p<\/mi>(<\/mo>θ<\/mi>)<\/mo><\/mrow>p<\/mi>(<\/mo>y<\/mi>)<\/mo><\/mrow><\/mfrac><\/math><\/p>\n

p<\/mi>(<\/mo>θ<\/mi>h<\/mi><\/msub>|<\/mo><\/mrow>y<\/mi>)<\/mo>=<\/mo><\/mtd><\/mi>∫<\/mo>⋯<\/mo>∫<\/mo>p<\/mi>(<\/mo>θ<\/mi>1<\/mn><\/msub>,<\/mo>…<\/mo>,<\/mo>θ<\/mi>h<\/mi><\/msub>,<\/mo>…<\/mo>,<\/mo>θ<\/mi>H<\/mi><\/msub>|<\/mo><\/mrow>y<\/mi>)<\/mo>d<\/mi>θ<\/mi>∖<\/mo>h<\/mi><\/mrow><\/msub><\/mrow><\/mtd><\/mtr>=<\/mo><\/mtd><\/mi>∫<\/mo>⋯<\/mo>∫<\/mo>p<\/mi>(<\/mo>θ<\/mi>h<\/mi><\/msub>|<\/mo><\/mrow>θ<\/mi>∖<\/mo>h<\/mi><\/mrow><\/msub>,<\/mo>y<\/mi>)<\/mo>p<\/mi>(<\/mo>θ<\/mi>∖<\/mo>h<\/mi><\/mrow><\/msub>|<\/mo><\/mrow>y<\/mi>)<\/mo>d<\/mi>θ<\/mi>∖<\/mo>h<\/mi><\/mrow><\/msub><\/mrow><\/mtd><\/mtr><\/mtable><\/math><\/p>\n

a<\/mi>2<\/mn><\/msup>=<\/mo>b<\/mi>2<\/mn><\/msup>+<\/mo>c<\/mi>2<\/mn><\/msup>η<\/mi>i<\/mi><\/msub>|<\/mo><\/mrow>α<\/mi>,<\/mo>β<\/mi>∼<\/mo>Gamma<\/mtext>(<\/mo>α<\/mi>+<\/mo>ξ<\/mi>,<\/mo>β<\/mi>+<\/mo>χ<\/mi>)<\/mo>,<\/mo>i<\/mi>=<\/mo>1<\/mn>,<\/mo>…<\/mo>,<\/mo>N<\/mi>α<\/mi>,<\/mo>β<\/mi>∼<\/mo>I<\/mi>G<\/mi><\/mrow>(<\/mo>0.5<\/mn>,<\/mo>0.05<\/mn>)<\/mo><\/math><\/p>\n","protected":false},"author":14,"menu_order":19,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-183","chapter","type-chapter","status-publish","hentry"],"part":18,"_links":{"self":[{"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/pressbooks\/v2\/chapters\/183","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":2,"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/pressbooks\/v2\/chapters\/183\/revisions"}],"predecessor-version":[{"id":185,"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/pressbooks\/v2\/chapters\/183\/revisions\/185"}],"part":[{"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/pressbooks\/v2\/parts\/18"}],"metadata":[{"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/pressbooks\/v2\/chapters\/183\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/wp\/v2\/media?parent=183"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/pressbooks\/v2\/chapter-type?post=183"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/wp\/v2\/contributor?post=183"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/integrations.pressbooks.network\/test-clone\/wp-json\/wp\/v2\/license?post=183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}