class: center, middle, title-slide .title[ # Practical 6 ] .author[ ### Olivier Gimenez ] .date[ ### last updated: 2025-11-11 ] --- ## Working with the MCMC outputs * From the values you generated in the posterior distribution of parameter say `\(\theta\)`, you may get the posterior distribution of any function of `\(\theta\)` * For example, back to the stork Bayesian analysis, get the posterior distribution of `\(b^2_{rain} + \cos(b_{temp})\)` --- ## Solutions --- * Evaluate the function for each MCMC iteration ``` r stupid <- res[,'b.rain']^2 + cos(res[,'b.temp']) ``` .tiny-font[ ``` r stupid ``` ``` ## [1] 1.0225289 1.0185692 1.0210363 1.0239548 1.0104561 1.0115538 1.0244862 ## [8] 1.0161538 1.0112129 1.0173789 1.0354614 1.0471920 1.0178679 1.0512934 ## [15] 1.0473453 1.0304472 1.0160600 1.0167138 1.0221699 1.0203629 1.0165025 ## [22] 1.0300034 1.0447633 1.0453250 1.0529685 1.0389228 1.0177527 1.0212406 ## [29] 1.0226569 1.0256140 1.0262390 1.0464533 1.0498013 1.0451940 1.0686449 ## [36] 1.0752475 1.0558799 1.0408981 1.0127249 1.0107037 1.0091556 1.0049879 ## [43] 1.0181115 1.0190714 1.0140871 1.0303091 1.0272211 1.0129718 1.0111639 ## [50] 1.0065262 1.0062267 1.0101535 1.0043905 1.0069070 1.0086909 1.0070169 ## [57] 1.0065631 1.0126677 1.0135878 1.0164130 1.0137522 1.0260071 1.0208619 ## [64] 1.0143203 1.0069416 1.0031003 1.0034508 1.0024616 1.0015045 1.0005573 ## [71] 1.0004923 0.9998690 1.0000020 1.0024973 1.0101478 1.0190348 1.0077679 ## [78] 1.0121881 1.0183040 1.0155525 1.0069767 1.0090337 1.0080334 1.0157318 ## [85] 1.0036038 1.0044557 1.0069035 1.0109377 1.0208289 1.0257627 1.0291908 ## [92] 1.0338523 1.0339013 1.0371727 1.0372262 1.0267244 1.0230507 1.0275668 ## [99] 1.0429152 1.0373897 1.0400111 1.0478651 1.0332589 1.0347110 1.0280008 ## [106] 1.0418247 1.0392492 1.0548796 1.0752201 1.0686479 1.0591133 1.0568816 ## [113] 1.0687046 1.0679688 1.0516999 1.0315257 1.0452686 1.0407256 1.0422737 ## [120] 1.0342238 1.0299298 1.0442355 1.0342539 1.0508838 1.0250928 1.0384971 ## [127] 1.0371529 1.0356478 1.0449641 1.0514859 1.0642928 1.0487513 1.0260457 ## [134] 1.0285548 1.0192066 1.0136719 1.0080258 1.0072094 1.0097003 1.0214148 ## [141] 1.0226842 1.0242964 1.0237026 1.0294917 1.0226247 1.0073286 1.0071732 ## [148] 1.0191933 1.0208669 0.9957940 0.9942705 0.9970957 1.0084277 1.0135999 ## [155] 1.0181592 1.0058772 1.0130228 1.0154857 1.0140795 1.0032629 1.0049755 ## [162] 1.0023965 1.0052387 1.0038112 1.0110412 1.0056174 1.0048383 1.0064623 ## [169] 1.0060987 1.0036873 1.0248183 1.0242718 1.0381660 1.0542144 1.0595264 ## [176] 1.0439393 1.0592234 1.0505821 1.0338239 1.0391299 1.0450257 1.0536488 ## [183] 1.0502793 1.0217969 1.0225990 1.0253881 1.0315976 1.0254902 1.0193805 ## [190] 1.0145186 1.0179150 1.0347623 1.0273355 1.0196645 1.0232877 1.0153672 ## [197] 1.0398870 1.0498132 1.0405448 1.0404615 1.0347221 1.0159239 1.0254844 ## [204] 1.0524227 1.0607745 1.0513574 1.0428739 1.0408427 1.0551045 1.0460917 ## [211] 1.0326163 1.0587508 1.0492086 1.0360522 1.0527068 1.0488738 1.0416605 ## [218] 1.0374370 1.0158384 1.0147942 1.0066227 1.0085600 1.0011172 1.0065534 ## [225] 1.0033596 1.0022815 1.0059584 1.0102896 1.0144694 1.0106040 1.0048169 ## [232] 1.0005731 0.9988049 0.9980451 1.0005035 1.0030876 0.9988321 1.0126544 ## [239] 1.0178717 1.0304273 1.0294266 1.0213979 1.0126667 1.0103914 1.0011155 ## [246] 0.9988151 0.9998586 1.0059813 1.0150760 1.0193145 1.0196897 1.0098086 ## [253] 1.0099528 1.0005271 1.0005321 1.0059668 1.0054255 1.0069864 1.0246657 ## [260] 1.0294178 1.0200120 1.0408575 1.0456853 1.0610631 1.0382464 1.0344408 ## [267] 1.0550955 1.0436024 1.0680427 1.1014579 1.1056667 1.1156165 1.0943622 ## [274] 1.0773819 1.0538644 1.0538469 1.0574577 1.0580965 1.0420971 1.0230075 ## [281] 1.0265400 1.0336347 1.0312252 1.0405094 1.0359477 1.0439230 1.0304345 ## [288] 1.0147013 1.0103873 1.0437094 1.0422029 1.0354577 1.0315099 1.0277160 ## [295] 1.0206817 1.0220430 1.0142495 1.0203753 1.0099812 1.0103253 1.0190750 ## [302] 1.0480959 1.0556456 1.0587728 1.0678670 1.0525787 1.0610661 1.0563165 ## [309] 1.0441191 1.0472689 1.0615431 1.0409312 1.0631280 1.0658932 1.0516962 ## [316] 1.0550728 1.0626172 1.0519052 1.0545962 1.0448945 1.0596866 1.0771739 ## [323] 1.0606657 1.0757199 1.0857468 1.0656935 1.0560451 1.0588750 1.0730177 ## [330] 1.0672580 1.0407591 1.0276612 1.0347759 1.0415985 1.0267993 1.0346992 ## [337] 1.0200634 1.0321739 1.0285499 1.0277195 1.0176652 1.0189899 1.0293554 ## [344] 1.0375431 1.0452870 1.0424457 1.0300612 1.0162266 1.0053416 1.0037043 ## [351] 1.0052942 1.0059748 1.0115941 1.0162182 1.0110414 1.0133696 1.0158560 ## [358] 1.0105822 1.0168539 1.0185733 1.0259695 1.0219488 1.0147579 1.0147732 ## [365] 1.0216951 1.0126829 1.0124407 0.9974349 1.0049900 1.0071782 1.0190858 ## [372] 1.0231873 1.0204310 1.0288185 1.0086307 1.0110779 1.0156687 1.0333990 ## [379] 1.0492044 1.0511952 1.0621869 1.0666114 1.0760257 1.0576979 1.0615420 ## [386] 1.0471241 1.0537191 1.0482837 1.0362054 1.0303937 1.0225204 1.0123053 ## [393] 1.0261787 1.0324026 1.0346116 1.0413195 1.0575825 1.0683174 1.0575280 ## [400] 1.0370227 1.0571215 1.0386495 1.0298446 1.0248845 1.0171977 1.0177345 ## [407] 1.0169409 1.0208549 1.0151736 1.0328464 1.0153197 1.0142009 1.0211745 ## [414] 1.0173024 1.0170614 1.0192791 1.0220087 1.0178378 1.0170146 1.0278646 ## [421] 1.0387337 1.0287244 1.0392006 1.0422477 1.0330141 1.0311418 1.0346883 ## [428] 1.0418254 1.0315434 1.0272583 1.0157672 0.9997515 0.9998477 0.9974650 ## [435] 0.9980813 1.0019125 1.0131536 1.0029672 1.0054344 1.0018095 1.0077322 ## [442] 1.0095989 1.0042784 1.0159410 1.0184007 1.0043673 1.0081972 1.0038828 ## [449] 1.0070063 1.0027131 1.0052867 1.0039165 1.0101095 1.0030186 1.0043597 ## [456] 1.0014585 1.0056108 1.0097180 1.0062601 1.0086213 1.0010046 1.0021413 ## [463] 1.0040690 1.0063303 1.0227157 1.0246114 1.0346250 1.0114399 1.0240222 ## [470] 1.0341304 1.0346275 1.0461654 1.0538865 1.0651063 1.0649030 1.0803250 ## [477] 1.0803455 1.0858495 1.0769227 1.0675245 1.0620907 1.0357635 1.0116845 ## [484] 1.0141383 1.0167720 1.0186911 1.0241905 1.0320114 1.0715153 1.0504249 ## [491] 1.0254155 1.0334815 1.0293425 1.0385405 1.0337039 1.0268697 1.0177730 ## [498] 1.0295311 1.0222296 1.0163537 1.0142824 1.0240910 1.0579358 1.0319192 ## [505] 1.0201879 1.0395800 1.0432952 1.0385818 1.0422943 1.0486958 1.0310251 ## [512] 1.0254205 1.0302968 1.0258880 1.0305529 1.0347777 1.0212856 1.0139110 ## [519] 1.0127386 1.0219811 1.0251015 1.0128855 1.0191410 1.0167373 1.0217616 ## [526] 1.0088143 1.0183699 1.0270737 1.0413635 1.0287331 1.0500294 1.0439042 ## [533] 1.0589841 1.0729600 1.0523953 1.0541503 1.0402986 1.0453829 1.0346666 ## [540] 1.0297523 1.0282886 1.0534083 1.0440397 1.0332031 1.0402661 1.0409382 ## [547] 1.0235487 1.0234344 1.0127388 1.0129907 1.0077293 1.0097339 1.0029374 ## [554] 1.0055887 1.0115629 1.0162122 1.0178050 1.0099090 1.0250680 1.0300278 ## [561] 1.0305988 1.0241151 1.0309182 1.0159379 1.0243602 1.0247902 1.0349115 ## [568] 1.0229171 1.0373511 1.0555047 1.0550088 1.0458414 1.0262722 1.0297725 ## [575] 1.0442778 1.0575764 1.0603953 1.0499021 1.0416682 1.0426045 1.0433611 ## [582] 1.0517015 1.0399806 1.0217531 1.0336790 1.0278869 1.0453528 1.0353302 ## [589] 1.0329211 1.0191714 1.0446881 1.0457643 1.0141722 1.0161957 1.0043776 ## [596] 1.0046138 1.0118962 1.0096753 1.0029645 0.9996787 1.0008591 1.0040950 ## [603] 1.0017877 1.0017081 1.0075971 1.0088114 1.0139136 1.0200413 1.0113056 ## [610] 1.0098627 1.0417141 1.0301124 1.0363101 1.0457241 1.0288577 1.0323012 ## [617] 1.0123223 1.0142239 1.0183928 1.0093801 1.0006086 1.0054191 1.0171155 ## [624] 1.0276980 1.0328224 1.0460568 1.0317112 1.0163976 1.0228784 1.0164443 ## [631] 1.0202014 1.0169436 1.0128284 1.0101925 1.0177856 1.0096049 1.0201484 ## [638] 1.0264239 1.0277080 1.0243237 1.0260185 1.0327187 1.0302928 1.0132955 ## [645] 1.0073557 1.0034997 0.9993225 0.9987293 0.9988359 0.9998984 1.0046515 ## [652] 1.0037921 1.0020342 1.0151099 1.0173237 1.0161131 1.0050550 1.0133322 ## [659] 1.0237687 1.0234193 1.0212497 1.0111479 1.0099156 1.0120838 1.0117560 ## [666] 1.0115818 1.0115788 1.0217419 1.0166773 1.0148855 1.0148581 1.0134406 ## [673] 1.0111126 1.0126136 1.0248202 1.0129699 1.0147111 1.0028681 1.0040644 ## [680] 1.0054552 1.0057280 1.0086645 1.0129610 1.0171946 1.0133200 1.0095993 ## [687] 1.0065253 1.0035271 1.0034787 1.0086470 1.0192118 1.0258102 1.0134405 ## [694] 1.0130682 1.0098093 1.0112069 1.0185899 1.0236215 1.0104624 1.0071966 ## [701] 1.0165114 1.0139829 1.0087687 1.0118950 1.0025430 1.0066083 1.0067300 ## [708] 1.0105442 1.0093694 1.0018120 1.0033438 1.0079917 1.0091183 1.0109840 ## [715] 1.0250405 1.0304789 1.0230075 1.0191460 1.0211739 1.0123949 1.0055423 ## [722] 1.0119292 1.0049315 1.0010823 0.9999067 0.9986490 1.0024417 1.0064927 ## [729] 1.0061406 1.0086235 1.0009694 1.0034748 1.0119061 1.0262455 1.0257898 ## [736] 1.0289636 1.0225982 1.0248055 1.0264841 1.0237485 1.0314577 1.0439043 ## [743] 1.0590039 1.0671403 1.0547158 1.0464857 1.0319462 1.0313489 1.0350765 ## [750] 1.0311618 1.0368528 1.0424640 1.0215673 1.0373148 1.0216537 1.0140823 ## [757] 1.0134948 1.0029353 1.0031268 0.9998472 0.9967051 0.9984704 0.9970712 ## [764] 1.0046302 1.0087242 0.9996428 1.0001676 1.0075967 1.0187421 1.0263250 ## [771] 1.0259058 1.0309847 1.0174449 1.0217733 1.0312793 1.0470698 1.0296307 ## [778] 1.0205643 1.0303488 1.0464179 1.0397981 1.0153855 1.0137617 1.0181909 ## [785] 1.0276428 1.0351639 1.0276207 1.0246029 1.0241244 1.0210638 1.0349165 ## [792] 1.0179146 1.0322622 1.0188397 1.0361652 1.0481124 1.0458490 1.0351403 ## [799] 1.0299237 1.0299602 1.0162004 1.0223382 1.0099311 1.0219172 1.0183786 ## [806] 1.0308926 1.0328173 1.0248105 1.0325357 1.0302768 1.0392592 1.0328646 ## [813] 1.0403439 1.0435745 1.0234769 1.0116407 1.0183579 1.0163988 1.0153138 ## [820] 1.0252609 1.0134740 1.0191673 1.0113749 1.0059078 1.0093178 1.0191097 ## [827] 1.0127852 1.0261688 1.0242551 1.0206553 1.0206966 1.0161659 1.0362663 ## [834] 1.0625716 1.0271764 1.0316094 1.0431958 1.0525279 1.0408812 1.0360459 ## [841] 1.0382190 1.0300430 1.0148254 1.0250343 1.0135355 1.0132908 1.0061116 ## [848] 1.0155959 1.0238466 1.0159097 1.0073931 1.0143249 1.0244685 1.0245858 ## [855] 1.0195405 1.0387910 1.0291700 1.0353794 1.0601049 1.0307072 1.0220471 ## [862] 1.0239708 1.0350171 1.0267237 1.0153346 1.0043919 1.0108214 1.0164742 ## [869] 1.0146551 1.0169858 1.0189670 1.0035271 1.0040773 1.0101755 1.0162558 ## [876] 1.0177078 1.0155638 1.0059181 1.0113192 1.0063925 1.0040310 0.9926924 ## [883] 1.0064174 1.0051113 1.0103412 1.0077584 1.0094856 1.0112223 1.0034503 ## [890] 1.0063967 1.0044092 1.0119149 1.0197146 1.0219752 1.0259785 1.0231641 ## [897] 1.0175469 1.0186628 1.0078345 1.0101742 1.0079555 1.0100453 1.0096280 ## [904] 1.0203249 1.0300927 1.0335163 1.0409407 1.0392791 1.0681874 1.0563477 ## [911] 1.0426807 1.0431929 1.0279042 1.0350300 1.0358575 1.0236466 1.0330935 ## [918] 1.0227638 1.0140150 1.0185751 1.0360824 1.0405160 1.0283625 1.0407843 ## [925] 1.0438009 1.0297658 1.0204964 1.0217693 1.0130858 1.0175741 1.0223189 ## [932] 1.0270416 1.0259337 1.0398497 1.0362845 1.0266524 1.0151127 1.0116283 ## [939] 1.0183208 1.0176064 1.0129922 1.0224573 1.0274593 1.0245359 1.0253990 ## [946] 1.0260832 1.0300900 1.0144868 1.0241597 1.0241071 1.0261144 1.0055533 ## [953] 1.0113150 1.0135069 1.0122954 1.0123805 1.0172942 1.0223215 1.0158939 ## [960] 1.0152777 1.0188518 1.0331276 1.0324102 1.0385080 1.0229893 1.0303003 ## [967] 1.0260800 1.0304621 1.0294288 1.0269114 1.0296460 1.0488394 1.0574982 ## [974] 1.0432346 1.0507373 1.0329857 1.0247285 1.0257611 1.0274579 1.0527953 ## [981] 1.0467353 1.0469272 1.0366446 1.0251868 1.0223503 1.0198416 1.0192836 ## [988] 1.0244898 1.0049525 1.0016128 1.0026449 1.0126957 1.0088384 1.0133204 ## [995] 1.0143619 1.0275098 1.0227378 1.0231637 1.0246538 1.0380711 1.0401858 ## [1002] 1.0337912 1.0150345 1.0105019 1.0074709 1.0102767 1.0119899 1.0029250 ## [1009] 1.0050045 1.0045121 1.0101521 1.0124877 1.0080173 1.0064737 1.0103346 ## [1016] 1.0155129 1.0135971 1.0156420 1.0237371 1.0100738 1.0070244 1.0059412 ## [1023] 1.0094063 1.0118213 1.0177949 1.0358516 1.0146111 1.0311382 1.0440004 ## [1030] 1.0390085 1.0279906 1.0430503 1.0291036 1.0513929 1.0446223 1.0737000 ## [1037] 1.0712316 1.0565015 1.0328123 1.0361543 1.0488991 1.0529012 1.0356554 ## [1044] 1.0303982 1.0433396 1.0254701 1.0200382 1.0122240 1.0268235 1.0189578 ## [1051] 1.0211008 1.0126181 1.0032715 1.0015685 0.9996074 0.9990954 0.9970177 ## [1058] 1.0014336 1.0010051 1.0043594 1.0014308 1.0034225 1.0052474 1.0102727 ## [1065] 1.0213841 1.0210056 1.0165428 1.0192341 1.0249143 1.0368165 1.0169111 ## [1072] 1.0122428 1.0280816 1.0318066 1.0464008 1.0402085 1.0321755 1.0183309 ## [1079] 1.0489767 1.0533643 1.0373208 1.0285990 1.0188857 1.0230141 1.0108242 ## [1086] 1.0202472 1.0215180 1.0334797 1.0277176 1.0373521 1.0482048 1.0336174 ## [1093] 1.0187058 1.0169758 1.0181291 1.0062780 1.0135885 1.0192543 1.0226674 ## [1100] 1.0203050 1.0080199 1.0236000 1.0119809 1.0054786 0.9974332 1.0013047 ## [1107] 1.0152092 1.0182368 1.0276816 1.0313988 1.0160091 1.0101137 1.0118008 ## [1114] 1.0132030 1.0106742 1.0250066 1.0432812 1.0405419 1.0188500 1.0165334 ## [1121] 1.0100342 1.0094364 1.0094959 1.0014737 1.0019081 1.0034119 1.0119604 ## [1128] 1.0047299 1.0060821 1.0020954 1.0020847 1.0012677 1.0020741 1.0036136 ## [1135] 1.0066084 1.0146563 1.0187422 1.0159690 1.0253186 1.0288789 1.0363535 ## [1142] 1.0383278 1.0385019 1.0254119 1.0356427 1.0236599 1.0245740 1.0127565 ## [1149] 1.0252559 1.0230053 1.0209867 1.0272846 1.0185569 1.0209294 1.0166827 ## [1156] 1.0137094 1.0096305 1.0131369 1.0126766 1.0173360 1.0186931 1.0125348 ## [1163] 1.0204943 1.0244194 1.0250957 1.0310037 1.0313535 1.0321324 1.0370691 ## [1170] 1.0333410 1.0361891 1.0193991 1.0173325 1.0244277 1.0371879 1.0294197 ## [1177] 1.0319569 1.0330093 1.0388181 1.0331656 1.0477732 1.0370454 1.0504595 ## [1184] 1.0396871 1.0239927 1.0359573 1.0238695 1.0223960 1.0099661 1.0185931 ## [1191] 1.0214368 1.0238843 1.0223319 1.0245006 1.0307224 1.0147386 1.0020398 ## [1198] 1.0171135 1.0328033 1.0168014 1.0237946 1.0468142 1.0299522 1.0438951 ## [1205] 1.0378191 1.0320368 1.0216374 1.0282281 1.0256008 1.0306487 1.0357334 ## [1212] 1.0487191 1.0447479 1.0340111 1.0271788 1.0071613 1.0111354 1.0093472 ## [1219] 1.0111068 1.0127913 1.0110910 1.0163095 1.0099649 1.0130681 1.0349857 ## [1226] 1.0442494 1.0583010 1.0453283 1.0506678 1.0240126 1.0294056 1.0339344 ## [1233] 1.0354180 1.0408356 1.0351212 1.0576374 1.0583102 1.0718089 1.0708731 ## [1240] 1.0530359 1.0333610 1.0403540 1.0464413 1.0355064 1.0356653 1.0326053 ## [1247] 1.0244790 1.0164010 1.0184110 1.0160098 1.0187240 1.0300127 1.0361432 ## [1254] 1.0334922 1.0383945 1.0254852 1.0250173 1.0368530 1.0425501 1.0460964 ## [1261] 1.0666251 1.0783475 1.0527463 1.0439649 1.0349935 1.0504884 1.0365033 ## [1268] 1.0310899 1.0200295 1.0205277 1.0121990 1.0024108 1.0066558 1.0120609 ## [1275] 1.0365487 1.0432072 1.0339702 1.0438958 1.0437440 1.0489180 1.0456512 ## [1282] 1.0411799 1.0465166 1.0466677 1.0257715 1.0210693 1.0160912 1.0105508 ## [1289] 1.0108389 1.0208466 1.0296873 1.0443432 1.0344495 1.0412155 1.0475445 ## [1296] 1.0470683 1.0403565 1.0326866 1.0263225 1.0277655 1.0292499 1.0323571 ## [1303] 1.0393626 1.0259195 1.0123800 1.0120291 1.0104842 1.0039041 1.0052172 ## [1310] 1.0136761 1.0095438 1.0102529 1.0244498 1.0265419 1.0429215 1.0509290 ## [1317] 1.0337248 1.0308844 1.0449191 1.0371909 1.0316698 1.0521729 1.0530595 ## [1324] 1.0402825 1.0421437 1.0250691 1.0412651 1.0566877 1.0683308 1.0696222 ## [1331] 1.0736836 1.0879672 1.1163251 1.1259284 1.1062743 1.1017751 1.0798011 ## [1338] 1.0735778 1.0530597 1.0492939 1.0752854 1.0732437 1.0540314 1.0676484 ## [1345] 1.0815355 1.0856405 1.0612351 1.0390258 1.0456765 1.0506592 1.0501070 ## [1352] 1.0551386 1.0620951 1.0646863 1.0506008 1.0297271 1.0344333 1.0271813 ## [1359] 1.0165836 1.0163883 1.0140065 1.0134168 1.0118011 1.0185206 1.0144478 ## [1366] 1.0268407 1.0265286 1.0207211 1.0218451 1.0221250 1.0215255 1.0210149 ## [1373] 1.0127815 1.0117194 1.0150961 1.0180227 1.0119871 1.0170859 1.0196932 ## [1380] 1.0125498 1.0149653 1.0105295 1.0098893 1.0075270 1.0093446 1.0058770 ## [1387] 1.0078431 1.0151529 1.0091189 1.0111704 1.0131012 1.0180827 1.0164923 ## [1394] 1.0109606 1.0148800 1.0133000 1.0187689 1.0148569 1.0131510 1.0202074 ## [1401] 1.0237383 1.0310711 1.0202927 1.0301970 1.0344507 1.0280555 1.0242929 ## [1408] 1.0355711 1.0195109 1.0316662 1.0326703 1.0355218 1.0286410 1.0222378 ## [1415] 1.0172921 1.0293136 1.0234505 1.0089656 1.0112815 1.0298387 1.0180153 ## [1422] 1.0287236 1.0268926 1.0240537 1.0387234 1.0213727 1.0247631 1.0202869 ## [1429] 1.0111496 1.0135411 1.0244140 1.0255761 1.0314067 1.0422977 1.0420345 ## [1436] 1.0677570 1.0812815 1.0792663 1.0513055 1.0407068 1.0387908 1.0589514 ## [1443] 1.0593390 1.0682723 1.0510462 1.0548454 1.0709355 1.0584172 1.0246474 ## [1450] 1.0510759 1.0496479 1.0351177 1.0243005 1.0191961 1.0124882 1.0075808 ## [1457] 1.0100145 1.0040853 1.0044235 1.0020870 1.0069408 1.0089251 1.0143610 ## [1464] 1.0118677 1.0279608 1.0239879 1.0256638 1.0161350 1.0211354 1.0113223 ## [1471] 1.0243529 1.0245707 1.0233739 1.0303417 1.0289504 1.0192498 1.0095465 ## [1478] 1.0205923 1.0170039 1.0272564 1.0090875 1.0028450 1.0008034 0.9997055 ## [1485] 1.0025704 1.0015681 1.0017929 1.0004081 0.9994331 1.0010821 1.0003808 ## [1492] 1.0015651 1.0161032 1.0277742 1.0304080 1.0296461 1.0351746 1.0362472 ## [1499] 1.0235327 1.0157129 1.0105671 1.0123818 1.0237819 1.0193713 1.0173021 ## [1506] 1.0172911 1.0142606 1.0228309 1.0234317 1.0259063 1.0259524 1.0286028 ## [1513] 1.0137979 1.0185383 1.0305547 1.0288847 1.0289020 1.0298837 1.0391268 ## [1520] 1.0383293 1.0536306 1.0664593 1.0639078 1.0824671 1.0906699 1.0974527 ## [1527] 1.0825408 1.0592925 1.0444690 1.0443106 1.0593971 1.0446706 1.0434124 ## [1534] 1.0439071 1.0393769 1.0424638 1.0489589 1.0325430 1.0407584 1.0329939 ## [1541] 1.0342973 1.0397983 1.0383233 1.0331583 1.0341155 1.0392437 1.0251916 ## [1548] 1.0355050 1.0261893 1.0307938 1.0332161 1.0230054 1.0321654 1.0351488 ## [1555] 1.0313956 1.0294277 1.0227705 1.0188859 1.0106557 1.0133387 1.0152183 ## [1562] 1.0226311 1.0210663 1.0364775 1.0393001 1.0416024 1.0587727 1.0440371 ## [1569] 1.0349767 1.0260404 1.0223151 1.0247430 1.0306911 1.0294824 1.0295860 ## [1576] 1.0372007 1.0329341 1.0288145 1.0323901 1.0433825 1.0287930 1.0216288 ## [1583] 1.0286069 1.0200013 1.0110227 1.0157940 1.0124437 1.0087118 1.0003430 ## [1590] 1.0021172 1.0042981 0.9965493 1.0075314 1.0166046 1.0134608 1.0146477 ## [1597] 1.0164732 1.0305933 1.0270184 1.0235527 1.0528178 1.0239056 1.0351717 ## [1604] 1.0382956 1.0462194 1.0288168 1.0329522 1.0542660 1.0346430 1.0201298 ## [1611] 1.0292395 1.0276287 1.0327030 1.0214745 1.0164771 1.0188413 1.0199166 ## [1618] 1.0158000 1.0201929 1.0307501 1.0344264 1.0468061 1.0710642 1.0857868 ## [1625] 1.0510903 1.0334379 1.0186987 1.0170593 1.0094507 1.0293320 1.0272680 ## [1632] 1.0204218 1.0264507 1.0133078 1.0210697 1.0255929 1.0350255 1.0292718 ## [1639] 1.0277802 1.0290511 1.0208352 1.0152029 1.0095705 1.0135579 1.0182001 ## [1646] 1.0144478 0.9998955 1.0008184 1.0049850 1.0005825 0.9992588 1.0006768 ## [1653] 0.9998158 1.0076988 1.0053470 0.9990306 0.9981788 1.0131880 1.0136796 ## [1660] 1.0167925 1.0218752 1.0080575 1.0132136 1.0107837 0.9964238 0.9988329 ## [1667] 1.0035506 1.0144066 1.0141232 1.0225698 1.0247411 1.0233672 1.0234541 ## [1674] 1.0167630 1.0101377 1.0135240 1.0119911 1.0093314 1.0196413 1.0123045 ## [1681] 1.0142755 1.0210650 1.0244789 1.0380824 1.0179203 1.0183090 1.0286703 ## [1688] 1.0119698 1.0059833 1.0241549 1.0246475 1.0218293 1.0148796 1.0095470 ## [1695] 1.0121287 1.0068551 1.0034109 1.0142997 1.0081505 1.0157227 1.0291104 ## [1702] 1.0340577 1.0249096 1.0108951 1.0156982 1.0186057 1.0118378 1.0073093 ## [1709] 1.0110783 1.0082226 1.0073746 1.0175234 1.0033668 0.9984403 1.0050601 ## [1716] 1.0010870 0.9986765 0.9985847 0.9922273 0.9929732 0.9946429 0.9972256 ## [1723] 1.0004875 1.0170989 1.0293942 1.0244403 1.0158358 1.0092494 1.0096175 ## [1730] 1.0019423 1.0045103 1.0082256 1.0134741 1.0060369 1.0070408 1.0062130 ## [1737] 1.0035536 1.0037663 1.0090849 1.0078639 1.0045018 1.0086914 1.0074781 ## [1744] 1.0146243 1.0207472 1.0257721 1.0221095 1.0118364 1.0059558 0.9987333 ## [1751] 1.0008850 1.0001320 1.0002269 0.9993088 1.0048773 1.0085762 1.0167549 ## [1758] 1.0179740 1.0141175 1.0333284 1.0347358 1.0193426 1.0181178 1.0199878 ## [1765] 1.0239444 1.0185743 1.0221920 1.0517821 1.0433516 1.0340693 1.0298082 ## [1772] 1.0242243 1.0203647 1.0107980 1.0175764 1.0250679 1.0212136 1.0146797 ## [1779] 1.0148590 1.0096398 1.0101467 1.0227728 1.0282704 1.0257802 1.0138038 ## [1786] 1.0058958 1.0052462 1.0157371 1.0281582 1.0259533 1.0148674 1.0185678 ## [1793] 1.0263098 1.0185178 1.0233311 1.0367907 1.0614906 1.0682786 1.0710441 ## [1800] 1.0511370 1.0471503 1.0345864 1.0280945 1.0293777 1.0317418 1.0487235 ## [1807] 1.0577512 1.0465098 1.0351157 1.0507699 1.0807494 1.0470160 1.0513566 ## [1814] 1.0618046 1.0753088 1.0678275 1.0776750 1.0520636 1.0422352 1.0283717 ## [1821] 1.0291143 1.0447814 1.0156296 1.0032590 0.9920933 0.9952600 0.9989512 ## [1828] 1.0012930 1.0014356 1.0016228 1.0036094 1.0099917 1.0259654 1.0248831 ## [1835] 1.0191596 1.0187350 1.0129339 1.0242665 1.0294989 1.0262265 1.0341009 ## [1842] 1.0283156 1.0158339 1.0138942 1.0081141 1.0083432 1.0153406 1.0124779 ## [1849] 1.0083709 1.0011360 1.0085101 1.0051011 1.0061023 1.0053814 1.0054188 ## [1856] 1.0127584 1.0154942 1.0223061 1.0205835 1.0287805 1.0169189 1.0111020 ## [1863] 1.0175565 1.0209609 1.0144996 1.0063185 1.0036862 1.0011107 1.0000486 ## [1870] 1.0019764 0.9999061 1.0002314 1.0124927 1.0076574 0.9989224 1.0065221 ## [1877] 1.0091071 1.0212035 1.0168220 1.0067752 1.0039811 1.0042157 1.0070467 ## [1884] 1.0087429 1.0112837 1.0037746 1.0053253 1.0008316 1.0042565 1.0149864 ## [1891] 1.0236789 1.0087606 1.0094416 1.0093262 1.0147665 1.0091000 1.0270336 ## [1898] 1.0358253 1.0280826 1.0181501 1.0268737 1.0221758 1.0089596 1.0059236 ## [1905] 1.0099828 1.0162732 1.0075878 0.9966239 1.0078611 1.0110311 1.0093752 ## [1912] 1.0181561 1.0206094 1.0139225 1.0067007 1.0143525 1.0317504 1.0402185 ## [1919] 1.0313973 1.0363512 1.0458659 1.0362728 1.0552057 1.0478317 1.0590320 ## [1926] 1.0498839 1.0362642 1.0509562 1.0289930 1.0207619 1.0202478 1.0243006 ## [1933] 1.0260198 1.0728768 1.0668000 1.0565378 1.0545410 1.0461543 1.0274347 ## [1940] 1.0217501 1.0252242 1.0263176 1.0333938 1.0166348 1.0172278 1.0242325 ## [1947] 1.0094601 1.0215403 1.0196940 1.0298249 1.0285074 1.0239944 1.0168005 ## [1954] 1.0253388 1.0142385 1.0315259 1.0423793 1.0395134 1.0467709 1.0234462 ## [1961] 1.0157276 1.0162819 1.0179809 1.0079844 1.0058903 1.0023277 0.9989222 ## [1968] 1.0009995 0.9996820 0.9995552 0.9987772 1.0011154 1.0022352 1.0049428 ## [1975] 1.0063336 1.0159125 1.0167147 1.0148892 1.0168254 1.0365826 1.0336885 ## [1982] 1.0480526 1.0576863 1.0447947 1.0456640 1.0532895 1.0333731 1.0610581 ## [1989] 1.0705516 1.0842115 1.0689933 1.0740831 1.0659020 1.0922575 1.1082804 ## [1996] 1.0803669 1.1003625 1.0960002 1.1202060 1.0953336 ``` ] --- * Plot the distribution 1/2 .center[ <!-- --> ] --- * Plot the distribution 2/2 .center[ <!-- --> ] --- * Get the probability that this quantity is strictly positive ``` r mean(stupid > 0) ``` ``` ## [1] 1 ```