class: center, middle, title-slide .title[ # Practical 6 ] .author[ ### Olivier Gimenez ] .date[ ### last updated: 2024-10-17 ] --- ## 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] 1.0674020 1.0325520 1.0391617 1.0439177 1.0439742 1.0480111 1.0609332 ## [8] 1.0943505 1.0784225 1.0776172 1.0597897 1.0539823 1.0552823 1.0337717 ## [15] 1.0407756 1.0766862 1.0996301 1.0949070 1.0637343 1.0652971 1.0708682 ## [22] 1.0697065 1.0472814 1.0262729 1.0503243 1.0250353 1.0120194 1.0096343 ## [29] 1.0130979 1.0076060 1.0145790 1.0234094 1.0198478 1.0223791 1.0261374 ## [36] 1.0335182 1.0255482 1.0183336 1.0145768 1.0106605 1.0114403 1.0152624 ## [43] 1.0199075 1.0346941 1.0315932 1.0329739 1.0229359 1.0260044 1.0220653 ## [50] 1.0152567 1.0045356 1.0000912 1.0055676 1.0050251 1.0028222 1.0222418 ## [57] 1.0286184 1.0345448 1.0386830 1.0522187 1.0701057 1.0911880 1.0871848 ## [64] 1.0566409 1.0605907 1.0652656 1.0735643 1.0691006 1.0635832 1.0479503 ## [71] 1.0630139 1.0812331 1.0958102 1.0725171 1.0666940 1.0905950 1.1046361 ## [78] 1.1148462 1.1007082 1.0947121 1.0617706 1.0593583 1.0528283 1.0488928 ## [85] 1.0703723 1.0734147 1.0789003 1.0689965 1.0755336 1.0867626 1.0791934 ## [92] 1.0661429 1.0361297 1.0202926 1.0382015 1.0475005 1.0612321 1.0719001 ## [99] 1.0613439 1.0774144 1.0948242 1.0758538 1.0634689 1.0466965 1.0525005 ## [106] 1.0349493 1.0560013 1.0524607 1.0277323 1.0292959 1.0297474 1.0189222 ## [113] 1.0103080 1.0103653 1.0092580 1.0224259 1.0212935 1.0191871 1.0083348 ## [120] 0.9989258 1.0023793 1.0122663 1.0107873 1.0071999 1.0135896 1.0156315 ## [127] 1.0262969 1.0139412 1.0172821 1.0125042 1.0113817 1.0117676 1.0104429 ## [134] 1.0032499 1.0052310 0.9977428 0.9965270 1.0009815 1.0028054 1.0091359 ## [141] 1.0123950 1.0232115 1.0457749 1.0298820 1.0247535 1.0419640 1.0190485 ## [148] 1.0136126 1.0201544 1.0089623 1.0022312 1.0041185 0.9990601 1.0000531 ## [155] 1.0004481 1.0003553 0.9981915 0.9953848 0.9957366 0.9989674 0.9946168 ## [162] 0.9965498 0.9972149 0.9954850 0.9981550 0.9943860 1.0017272 1.0023596 ## [169] 1.0006354 1.0002190 1.0010597 1.0006675 0.9998257 0.9982451 0.9994073 ## [176] 0.9994722 0.9982258 0.9969335 0.9984309 1.0027506 1.0038367 1.0103518 ## [183] 1.0130099 1.0273978 1.0140963 1.0107834 1.0093508 1.0181755 1.0268372 ## [190] 1.0271177 1.0474044 1.0648700 1.0461914 1.0499124 1.0272436 1.0338836 ## [197] 1.0306227 1.0226372 1.0211329 1.0195734 1.0264993 1.0352860 1.0343935 ## [204] 1.0260036 1.0326584 1.0167397 1.0201678 1.0108678 1.0096240 1.0030827 ## [211] 1.0106943 1.0232691 1.0119349 1.0036265 1.0005269 1.0043505 1.0048160 ## [218] 1.0127345 1.0154532 1.0236020 1.0145834 1.0186906 1.0116442 1.0122693 ## [225] 1.0215726 1.0298986 1.0366720 1.0278643 1.0219107 1.0115850 1.0064256 ## [232] 1.0219086 1.0317201 1.0161115 1.0204029 1.0381481 1.0435647 1.0468115 ## [239] 1.0537349 1.0500630 1.0385033 1.0275222 1.0181028 1.0202192 1.0292186 ## [246] 1.0448015 1.0433510 1.0304145 1.0448176 1.0467652 1.0769447 1.0746656 ## [253] 1.0714149 1.0827725 1.0868329 1.0792058 1.0718329 1.0519652 1.0351542 ## [260] 1.0515376 1.0156108 1.0153534 1.0129471 1.0184265 1.0119316 1.0131467 ## [267] 1.0181570 1.0185498 1.0077451 1.0127416 0.9953479 0.9975996 0.9936224 ## [274] 0.9903356 0.9907228 0.9944268 1.0113142 1.0318486 1.0152196 1.0061313 ## [281] 1.0131123 1.0278714 1.0365974 1.0259210 1.0352489 1.0352691 1.0468873 ## [288] 1.0280443 1.0169336 1.0092974 1.0159461 1.0317408 1.0440173 1.0404878 ## [295] 1.0421173 1.0534545 1.0643603 1.0928022 1.0752145 1.0511398 1.0387637 ## [302] 1.0258337 1.0387273 1.0279422 1.0204179 1.0169731 1.0192190 1.0325071 ## [309] 1.0305598 1.0157517 1.0261237 1.0221934 1.0191888 1.0273448 1.0419008 ## [316] 1.0408591 1.0463634 1.0569683 1.0832382 1.0545378 1.0572714 1.0835631 ## [323] 1.0577868 1.0629921 1.0485551 1.0313412 1.0398717 1.0330731 1.0471905 ## [330] 1.0292650 1.0565503 1.0643916 1.0557772 1.0399604 1.0532267 1.0663485 ## [337] 1.0488264 1.0572847 1.0580311 1.0249118 1.0227012 1.0098214 1.0083793 ## [344] 1.0093563 1.0081555 1.0056484 1.0130942 1.0182078 1.0138025 1.0125706 ## [351] 1.0226775 1.0059015 1.0057416 1.0140456 1.0152606 1.0177303 1.0226450 ## [358] 1.0188481 1.0138128 1.0032891 1.0047989 1.0073126 1.0020716 1.0034737 ## [365] 1.0092227 1.0025627 1.0181522 1.0294988 1.0229772 1.0299957 1.0116597 ## [372] 1.0184130 1.0160526 1.0210686 1.0216347 1.0213710 1.0301184 1.0347499 ## [379] 1.0226015 1.0329993 1.0197150 1.0170522 1.0185060 1.0109890 1.0090830 ## [386] 1.0204687 1.0164097 1.0103563 1.0048951 1.0026752 0.9972244 1.0021252 ## [393] 1.0045991 1.0042884 1.0066889 1.0070699 1.0154035 1.0215329 1.0156121 ## [400] 1.0129971 1.0219684 1.0178565 1.0213255 1.0266388 1.0261731 1.0336792 ## [407] 1.0266176 1.0228210 1.0264586 1.0324771 1.0321094 1.0195884 1.0254521 ## [414] 1.0253589 1.0256246 1.0199878 1.0396744 1.0395385 1.0366321 1.0495354 ## [421] 1.0503728 1.0448730 1.0198572 1.0141033 1.0176969 1.0193100 1.0073499 ## [428] 1.0057005 1.0059711 1.0023080 1.0005123 1.0010938 1.0052235 1.0212016 ## [435] 1.0148157 1.0154726 1.0139327 1.0211563 1.0198925 1.0430029 1.0308487 ## [442] 1.0458730 1.0556825 1.0519730 1.0593142 1.0655711 1.0469217 1.0526815 ## [449] 1.0817142 1.0722924 1.0461252 1.0460818 1.0560942 1.0490593 1.0609657 ## [456] 1.0389630 1.0488562 1.0309152 1.0237738 1.0234899 1.0147715 1.0383469 ## [463] 1.0275581 1.0580233 1.0569074 1.0447416 1.0270737 1.0282785 1.0460723 ## [470] 1.0234573 1.0133927 1.0201558 1.0052792 1.0071054 1.0008859 1.0022669 ## [477] 0.9997120 0.9993949 0.9990751 0.9974824 0.9985183 0.9952186 0.9962564 ## [484] 0.9963132 1.0025663 1.0065800 1.0010682 1.0013528 1.0062411 1.0071330 ## [491] 1.0032846 1.0075717 1.0032412 1.0053175 1.0030859 1.0053271 1.0034801 ## [498] 1.0098415 1.0257445 1.0210820 1.0161570 1.0162913 1.0040130 1.0055096 ## [505] 1.0021636 1.0116213 1.0091431 1.0091691 1.0202048 1.0395393 1.0206076 ## [512] 1.0230347 1.0195893 1.0116650 1.0063482 1.0064168 1.0012475 1.0078712 ## [519] 1.0087908 1.0181419 1.0194833 1.0058713 1.0127688 1.0223181 1.0217973 ## [526] 1.0128024 1.0209852 1.0520804 1.0525655 1.0562258 1.0216637 1.0275240 ## [533] 1.0118344 1.0189338 1.0141484 1.0143428 1.0279934 1.0483469 1.0466472 ## [540] 1.0417486 1.0283485 1.0516669 1.0548252 1.0459832 1.0460055 1.0500909 ## [547] 1.0412234 1.0435464 1.0407650 1.0408527 1.0496184 1.0422612 1.0271208 ## [554] 1.0347270 1.0358219 1.0191247 1.0304893 1.0431632 1.0493549 1.0544109 ## [561] 1.0358592 1.0499051 1.0709666 1.0689077 1.1090008 1.0700576 1.0700453 ## [568] 1.0560275 1.0513931 1.0367615 1.0394851 1.0287444 1.0224564 1.0233177 ## [575] 1.0160589 1.0078962 1.0069484 1.0020363 1.0161411 1.0288330 1.0351914 ## [582] 1.0240634 1.0184887 1.0520243 1.0534203 1.0340207 1.0279426 1.0247431 ## [589] 1.0443371 1.0313329 1.0498366 1.0532226 1.0534717 1.0861320 1.0652551 ## [596] 1.0735308 1.0552938 1.0376365 1.0269220 1.0144406 1.0254258 1.0161626 ## [603] 1.0249773 1.0268325 1.0312177 1.0256201 1.0255594 1.0271254 1.0239567 ## [610] 1.0331954 1.0403224 1.0511445 1.0562580 1.0527848 1.0412717 1.0455650 ## [617] 1.0294947 1.0347033 1.0331561 1.0214465 1.0168578 1.0242123 1.0406230 ## [624] 1.0242434 1.0175950 1.0279016 1.0229768 1.0310875 1.0216055 1.0082057 ## [631] 1.0073153 1.0050588 1.0016087 1.0019134 1.0027739 1.0147134 1.0223221 ## [638] 1.0077744 1.0096044 1.0059758 1.0008569 1.0069348 1.0010601 0.9997041 ## [645] 1.0007934 1.0004004 1.0005405 0.9986782 1.0000126 1.0011779 1.0079475 ## [652] 1.0089606 1.0098403 1.0172960 1.0086475 1.0173130 1.0173386 1.0213635 ## [659] 1.0161602 1.0225855 1.0331771 1.0203553 1.0231525 1.0212101 1.0108790 ## [666] 1.0253305 1.0227723 1.0188400 1.0198323 1.0270026 1.0411185 1.0286134 ## [673] 1.0254609 1.0339089 1.0319833 1.0400923 1.0554314 1.0674011 1.0628918 ## [680] 1.0476337 1.0614815 1.0616876 1.1052638 1.0869191 1.0938490 1.1083913 ## [687] 1.0939698 1.0785413 1.0998791 1.0894254 1.0668788 1.0511284 1.0477755 ## [694] 1.0717616 1.0546465 1.0473890 1.0515454 1.0580935 1.0540425 1.0479996 ## [701] 1.0494742 1.0555798 1.0634974 1.0588390 1.0883388 1.0857721 1.0693862 ## [708] 1.0701423 1.0908302 1.0758145 1.0572486 1.0486240 1.0347596 1.0370422 ## [715] 1.0373491 1.0361415 1.0371386 1.0419151 1.0389008 1.0304375 1.0450290 ## [722] 1.0382960 1.0203047 1.0133369 1.0168449 1.0260207 1.0208280 1.0268188 ## [729] 1.0253306 1.0225627 1.0113152 1.0238684 1.0405369 1.0333100 1.0327837 ## [736] 1.0294634 1.0161895 1.0224064 1.0286976 1.0166295 1.0169554 1.0219513 ## [743] 1.0169161 1.0260311 1.0287868 1.0410768 1.0263091 1.0274499 1.0474408 ## [750] 1.0460114 1.0403725 1.0364879 1.0355826 1.0213506 1.0168187 1.0099025 ## [757] 1.0129880 1.0081118 1.0091317 1.0053028 1.0082000 1.0073176 1.0096984 ## [764] 0.9997171 1.0001416 1.0033761 1.0038289 1.0018121 1.0027588 1.0018751 ## [771] 1.0069389 1.0027305 1.0015635 1.0078851 1.0025417 1.0019412 0.9999308 ## [778] 1.0018582 0.9993329 1.0026750 1.0021531 1.0050036 1.0129364 1.0035821 ## [785] 1.0097643 1.0034262 1.0026816 1.0091881 1.0158624 1.0191911 1.0261803 ## [792] 1.0280223 1.0250190 1.0059899 1.0153611 1.0146522 1.0236217 1.0399825 ## [799] 1.0471654 1.0302382 1.0340158 1.0290544 1.0414460 1.0282968 1.0372437 ## [806] 1.0404002 1.0234097 1.0170991 1.0302519 1.0447033 1.0521514 1.0727725 ## [813] 1.0873398 1.0637377 1.0728243 1.0694760 1.0774124 1.0636205 1.0684611 ## [820] 1.0631658 1.0403603 1.0328569 1.0601697 1.0521780 1.0576153 1.0479058 ## [827] 1.0508635 1.0671070 1.0632246 1.0465604 1.0513923 1.0470620 1.0365739 ## [834] 1.0399006 1.0627571 1.0684227 1.0487000 1.0532088 1.0563670 1.0457361 ## [841] 1.0375593 1.0477423 1.0323057 1.0232152 1.0326198 1.0345986 1.0303669 ## [848] 1.0390912 1.0335907 1.0171626 1.0095761 1.0059502 1.0093021 0.9982586 ## [855] 1.0027232 1.0043662 0.9927201 1.0017125 0.9992952 1.0069492 1.0094302 ## [862] 1.0175655 1.0256562 1.0201298 1.0215199 1.0326842 1.0229492 1.0161483 ## [869] 1.0123148 1.0084261 1.0172133 1.0201757 1.0206604 1.0204341 1.0129158 ## [876] 1.0217209 1.0267462 1.0332440 1.0318328 1.0439781 1.0315096 1.0216635 ## [883] 1.0355783 1.0271287 1.0179527 1.0198424 1.0071129 1.0088717 1.0120282 ## [890] 1.0204147 1.0166762 1.0264958 1.0182991 1.0242445 1.0253419 1.0240987 ## [897] 1.0126035 1.0135773 1.0225462 1.0214257 1.0179134 1.0212277 1.0256102 ## [904] 1.0306097 1.0295838 1.0309042 1.0163840 1.0150302 1.0179230 1.0178731 ## [911] 1.0112710 1.0046723 1.0022020 1.0038980 1.0046659 1.0141325 1.0166291 ## [918] 1.0276891 1.0199811 1.0210331 1.0282686 1.0217279 1.0161955 1.0121485 ## [925] 1.0202200 1.0151781 1.0305172 1.0455720 1.0528745 1.0483268 1.0456764 ## [932] 1.0292823 1.0402978 1.0606688 1.0601052 1.0327096 1.0184698 1.0161791 ## [939] 1.0119353 1.0271474 1.0310710 1.0276912 1.0279283 1.0285871 1.0291876 ## [946] 1.0165413 1.0262816 1.0266923 1.0279220 1.0319679 1.0383951 1.0377370 ## [953] 1.0410371 1.0415192 1.0307533 1.0364345 1.0456808 1.0706944 1.0925072 ## [960] 1.0786038 1.0650779 1.0687596 1.0563537 1.0451353 1.0196115 1.0286335 ## [967] 1.0205537 1.0196634 1.0109496 1.0105235 1.0308302 1.0257809 1.0248351 ## [974] 1.0323709 1.0248071 1.0166215 1.0248545 1.0431012 1.0277657 1.0298853 ## [981] 1.0369363 1.0362903 1.0290646 1.0435995 1.0390184 1.0347220 1.0086531 ## [988] 1.0031010 1.0084236 1.0066288 1.0025226 1.0163461 1.0118553 1.0112331 ## [995] 1.0142988 1.0168120 1.0107649 1.0116951 1.0171453 1.0145579 1.0189871 ## [1002] 1.0213817 1.0127143 1.0111960 1.0096607 1.0270396 1.0267841 1.0473919 ## [1009] 1.0280396 1.0229633 1.0343939 1.0571174 1.0428802 1.0688151 1.0856942 ## [1016] 1.0829951 1.0608490 1.0688253 1.0874791 1.0842088 1.0620576 1.0589967 ## [1023] 1.0505899 1.0417104 1.0254957 1.0205207 1.0162583 1.0235640 1.0219204 ## [1030] 1.0229453 1.0374000 1.0283003 1.0334734 1.0431857 1.0276308 1.0365142 ## [1037] 1.0353759 1.0321485 1.0202119 1.0193486 1.0245437 1.0349797 1.0423126 ## [1044] 1.0440798 1.0739042 1.0588327 1.0522295 1.0300703 1.0378020 1.0239243 ## [1051] 1.0166944 1.0124870 1.0154240 1.0077491 1.0042158 1.0048124 1.0039765 ## [1058] 1.0015314 1.0028318 1.0190695 1.0118641 1.0104874 1.0165182 1.0091245 ## [1065] 1.0146116 1.0188630 1.0242450 1.0126537 1.0105748 1.0099968 1.0107308 ## [1072] 1.0242615 1.0206716 1.0269067 1.0351586 1.0157340 1.0282932 1.0217546 ## [1079] 1.0400429 1.0450826 1.0241591 1.0199395 1.0158193 1.0160114 1.0163392 ## [1086] 1.0150611 1.0134424 1.0061625 1.0058935 1.0064882 1.0137486 1.0046852 ## [1093] 1.0162912 1.0159896 1.0160098 1.0192186 1.0221632 1.0292198 1.0296895 ## [1100] 1.0171170 1.0132723 1.0219079 1.0211678 1.0096650 1.0138149 1.0312003 ## [1107] 1.0383293 1.0440087 1.0492640 1.0574203 1.0432468 1.0291379 1.0219615 ## [1114] 1.0523156 1.0351526 1.0312123 1.0225826 1.0173545 1.0163362 1.0324904 ## [1121] 1.0426638 1.0533922 1.0394940 1.0308963 1.0363497 1.0443109 1.0377670 ## [1128] 1.0414098 1.0442722 1.0254645 1.0215666 1.0250882 1.0133354 1.0192889 ## [1135] 1.0148446 1.0187898 1.0112329 1.0107203 1.0068509 1.0070833 1.0036677 ## [1142] 1.0060652 1.0154870 1.0069148 1.0077755 1.0121890 1.0341314 1.0143344 ## [1149] 1.0172496 1.0224217 1.0279133 1.0353072 1.0187113 1.0360466 1.0248841 ## [1156] 1.0374842 1.0379398 1.0469324 1.0394498 1.0288780 1.0336637 1.0236377 ## [1163] 1.0234168 1.0380996 1.0296302 1.0329099 1.0157110 1.0120456 1.0058119 ## [1170] 1.0005334 0.9976217 0.9997074 1.0005551 0.9998862 1.0008388 0.9998348 ## [1177] 1.0084942 1.0085706 1.0118002 1.0241141 1.0218323 1.0182224 1.0232115 ## [1184] 1.0241259 1.0329376 1.0349950 1.0304447 1.0161141 1.0086590 1.0033765 ## [1191] 1.0095752 1.0089167 1.0004683 1.0054839 1.0107755 1.0161838 1.0092570 ## [1198] 1.0126113 1.0086329 1.0063753 1.0087454 1.0138816 1.0205540 1.0298809 ## [1205] 1.0367914 1.0259689 1.0125984 1.0027389 1.0001869 1.0043205 1.0050704 ## [1212] 1.0028183 1.0016240 1.0055388 1.0011037 1.0053652 1.0125238 1.0191138 ## [1219] 1.0113217 1.0261078 1.0182023 1.0135664 1.0102309 1.0245009 1.0449687 ## [1226] 1.0346468 1.0211057 1.0194088 1.0307942 1.0239154 1.0297740 1.0245246 ## [1233] 1.0282803 1.0309061 1.0192698 1.0101623 1.0026570 1.0015866 1.0043881 ## [1240] 1.0013527 0.9989665 1.0010585 1.0054321 1.0201908 1.0224356 1.0193460 ## [1247] 1.0143418 1.0147284 1.0212594 1.0178743 1.0175707 1.0121072 1.0123981 ## [1254] 1.0123318 1.0203234 1.0067642 1.0171573 1.0377465 1.0303370 1.0503327 ## [1261] 1.0556353 1.0527788 1.0312382 1.0207126 1.0126812 1.0135204 1.0176031 ## [1268] 1.0111055 1.0075554 1.0119252 1.0058035 1.0097466 1.0202208 1.0180578 ## [1275] 1.0144780 1.0093496 1.0276110 1.0168276 1.0110474 1.0098903 1.0088298 ## [1282] 1.0042723 1.0197818 1.0186808 1.0330486 1.0431865 1.0207510 1.0092155 ## [1289] 1.0170237 1.0367539 1.0550390 1.0413713 1.0303958 1.0545357 1.0462833 ## [1296] 1.0512088 1.0471784 1.0482765 1.0597593 1.0703080 1.0947929 1.0695905 ## [1303] 1.0746542 1.0800928 1.0807762 1.0764698 1.1012540 1.0701410 1.0577562 ## [1310] 1.0558188 1.0507661 1.0288482 1.0335226 1.0332090 1.0179212 1.0110868 ## [1317] 1.0223350 1.0294011 1.0249654 1.0177501 1.0167354 1.0193769 1.0296983 ## [1324] 1.0355426 1.0241777 1.0212348 1.0178825 1.0140693 1.0242103 1.0343701 ## [1331] 1.0135460 1.0035141 1.0102703 1.0168476 1.0216210 1.0122752 1.0073209 ## [1338] 1.0133842 1.0023073 0.9998712 0.9988104 0.9994246 1.0051854 1.0019340 ## [1345] 1.0114770 1.0132164 1.0037585 1.0042725 1.0015134 1.0010836 1.0029176 ## [1352] 1.0056561 1.0028312 1.0040809 1.0114083 1.0227136 1.0292698 1.0272799 ## [1359] 1.0268510 1.0296601 1.0124837 1.0190492 1.0247974 1.0054486 1.0189017 ## [1366] 1.0228343 1.0227857 1.0323508 1.0279701 1.0276331 1.0058381 1.0162476 ## [1373] 1.0169961 1.0117156 1.0088826 1.0114762 1.0045573 1.0070146 1.0111439 ## [1380] 1.0129295 1.0101465 1.0108968 1.0130278 1.0043873 1.0042065 1.0037951 ## [1387] 1.0070998 1.0115867 1.0102440 1.0014875 1.0020194 1.0005843 1.0031270 ## [1394] 1.0040875 1.0005713 0.9994845 1.0010989 1.0002784 1.0064689 1.0206802 ## [1401] 1.0124870 1.0139945 1.0047959 1.0036640 1.0064915 1.0027897 1.0063531 ## [1408] 1.0069463 1.0078573 1.0112930 1.0112008 1.0081181 1.0181835 1.0112482 ## [1415] 1.0070311 1.0105141 1.0111672 1.0150625 1.0167233 1.0205630 1.0322254 ## [1422] 1.0267943 1.0342531 1.0287649 1.0298600 1.0354670 1.0229660 1.0276729 ## [1429] 1.0238299 1.0294512 1.0449085 1.0572432 1.0434518 1.0433588 1.0344395 ## [1436] 1.0396904 1.0526563 1.0695663 1.0714166 1.0558843 1.0595566 1.0659430 ## [1443] 1.0674519 1.0585856 1.0427767 1.0393296 1.0478850 1.0493639 1.0445891 ## [1450] 1.0385722 1.0267749 1.0223297 1.0134607 1.0200847 1.0213775 1.0297589 ## [1457] 1.0252316 1.0164621 1.0194829 1.0156671 1.0058635 1.0161698 1.0085575 ## [1464] 1.0209960 1.0292659 1.0269369 1.0408534 1.0408354 1.0285660 1.0241616 ## [1471] 1.0117989 1.0082105 1.0112318 1.0223318 1.0275102 1.0140771 1.0177693 ## [1478] 1.0173141 1.0153317 1.0149444 1.0204606 1.0198456 1.0251939 1.0258903 ## [1485] 1.0121984 1.0098970 1.0150574 1.0170797 1.0346451 1.0388218 1.0306862 ## [1492] 1.0301833 1.0455009 1.0270909 1.0318023 1.0322321 1.0184486 1.0086428 ## [1499] 1.0070880 1.0040882 1.0037831 1.0028749 1.0104018 1.0282345 1.0356772 ## [1506] 1.0432326 1.0540114 1.0571292 1.0508215 1.0594885 1.0657975 1.0573000 ## [1513] 1.0373058 1.0285058 1.0281068 1.0273406 1.0248213 1.0253095 1.0299825 ## [1520] 1.0365474 1.0479692 1.0494624 1.0312505 1.0444662 1.0326884 1.0358397 ## [1527] 1.0298986 1.0267325 1.0245325 1.0276022 1.0218586 1.0286376 1.0312088 ## [1534] 1.0163839 1.0119484 1.0206474 1.0183646 1.0390931 1.0434448 1.0325070 ## [1541] 1.0216608 1.0107102 1.0134243 1.0156144 1.0247290 1.0281562 1.0298326 ## [1548] 1.0228567 1.0132629 1.0198060 1.0174687 1.0201484 1.0206681 1.0206587 ## [1555] 1.0117643 1.0164340 1.0226475 1.0133506 1.0165559 1.0240872 1.0372614 ## [1562] 1.0363208 1.0529948 1.0581583 1.0708838 1.1075006 1.1136628 1.0942629 ## [1569] 1.0614870 1.0492898 1.0666878 1.0682765 1.0710361 1.0525815 1.0385255 ## [1576] 1.0200238 1.0169317 1.0138942 1.0300853 1.0202503 1.0222049 1.0174541 ## [1583] 1.0277911 1.0263159 1.0295120 1.0055859 1.0069403 1.0037148 1.0052971 ## [1590] 1.0086927 1.0109563 1.0103049 1.0097610 1.0118789 1.0059158 1.0166892 ## [1597] 1.0146776 0.9979242 0.9907666 0.9984435 0.9927541 0.9911332 0.9972830 ## [1604] 1.0118222 1.0063866 1.0099013 1.0122456 1.0178301 1.0320068 1.0439559 ## [1611] 1.0406183 1.0306932 1.0400720 1.0298263 1.0381718 1.0272317 1.0199169 ## [1618] 1.0136751 1.0183759 1.0350596 1.0257326 1.0306363 1.0305541 1.0253512 ## [1625] 1.0172750 1.0140156 1.0080093 1.0041382 1.0073799 1.0126262 1.0133104 ## [1632] 1.0193994 1.0183001 1.0339630 1.0318470 1.0344255 1.0266352 1.0374963 ## [1639] 1.0335617 1.0273943 1.0253318 1.0204118 1.0369935 1.0362349 1.0496828 ## [1646] 1.0409751 1.0427850 1.0717111 1.1130251 1.1101423 1.0779840 1.0671045 ## [1653] 1.0650805 1.0779408 1.1043578 1.0814622 1.0825580 1.0532777 1.0534294 ## [1660] 1.0349412 1.0267715 1.0462121 1.0810670 1.0707637 1.0494895 1.0589629 ## [1667] 1.0394211 1.0265484 1.0127691 1.0180412 1.0247553 1.0173656 1.0105052 ## [1674] 1.0189506 1.0146328 1.0266080 1.0177795 1.0271544 1.0398605 1.0393828 ## [1681] 1.0687300 1.0641301 1.0661437 1.0592897 1.0391136 1.0468353 1.0618613 ## [1688] 1.0520037 1.0183398 1.0191833 1.0349345 1.0438389 1.0381873 1.0290843 ## [1695] 1.0416039 1.0532468 1.0427383 1.0445678 1.0251264 1.0312982 1.0338008 ## [1702] 1.0259602 1.0202617 1.0325849 1.0250758 1.0178226 1.0198563 1.0193527 ## [1709] 1.0176130 1.0274073 1.0170244 1.0377787 1.0215467 1.0228935 1.0267637 ## [1716] 1.0280390 1.0242965 1.0150923 1.0231391 1.0082986 1.0077617 1.0090979 ## [1723] 1.0147135 1.0090497 1.0065267 1.0101299 1.0236681 1.0215961 1.0102286 ## [1730] 1.0044078 1.0049189 1.0021545 1.0003257 1.0039903 1.0074195 1.0118300 ## [1737] 1.0152980 1.0084216 1.0102412 1.0192793 1.0278377 1.0139049 1.0206399 ## [1744] 1.0359394 1.0362459 1.0455164 1.0528741 1.0777865 1.0945989 1.0819489 ## [1751] 1.0864638 1.0712006 1.0741388 1.0830389 1.0490977 1.0548659 1.0559274 ## [1758] 1.0641151 1.0534297 1.0527547 1.0468098 1.0415969 1.0160444 1.0115780 ## [1765] 1.0081675 1.0138708 1.0057024 1.0023946 1.0085622 1.0044543 1.0046949 ## [1772] 1.0122003 1.0252528 1.0555771 1.0348765 1.0468742 1.0467877 1.0510560 ## [1779] 1.0406413 1.0288825 1.0230154 1.0223637 1.0122928 1.0201440 1.0254141 ## [1786] 1.0279449 1.0335553 1.0262041 1.0153159 1.0170291 1.0075078 1.0072129 ## [1793] 1.0058813 1.0022235 1.0065743 1.0047560 1.0058286 1.0135931 1.0227565 ## [1800] 1.0267851 1.0199591 1.0362108 1.0263140 1.0105783 1.0034450 1.0135725 ## [1807] 1.0161498 1.0073919 1.0097901 1.0027736 0.9976914 0.9976872 1.0010857 ## [1814] 0.9978452 0.9969678 0.9996277 1.0019386 0.9995750 0.9974663 1.0062788 ## [1821] 0.9952580 1.0066091 1.0106337 1.0110601 1.0233952 1.0390838 1.0395836 ## [1828] 1.0205027 1.0181830 1.0147731 1.0044091 0.9998884 0.9999607 1.0009345 ## [1835] 1.0001400 1.0057160 1.0028952 1.0136027 1.0131181 1.0237886 1.0391518 ## [1842] 1.0272598 1.0285580 1.0312245 1.0264066 1.0293983 1.0157859 1.0077922 ## [1849] 1.0098184 1.0086690 1.0146404 1.0135850 1.0221255 1.0238220 1.0385700 ## [1856] 1.0541258 1.0628654 1.0492051 1.0441473 1.0361255 1.0482969 1.0506897 ## [1863] 1.0326508 1.0481818 1.0404504 1.0313308 1.0273077 1.0321967 1.0351007 ## [1870] 1.0620393 1.0524608 1.0492080 1.0363404 1.0222522 1.0199791 1.0078401 ## [1877] 1.0026078 1.0085809 1.0324800 1.0418725 1.0507473 1.0359779 1.0438906 ## [1884] 1.0349211 1.0328796 1.0310744 1.0160188 1.0141534 1.0164657 1.0170922 ## [1891] 1.0100183 1.0291985 1.0466430 1.0378900 1.0186172 1.0174059 1.0319825 ## [1898] 1.0433223 1.0464222 1.0342479 1.0359641 1.0410638 1.0471996 1.0140182 ## [1905] 1.0162749 1.0232412 1.0227709 1.0098479 1.0048709 0.9989925 0.9946983 ## [1912] 0.9902643 0.9903574 1.0039140 1.0128266 1.0111317 1.0121115 1.0096713 ## [1919] 1.0195738 1.0149146 1.0178615 1.0187077 1.0182935 1.0172040 1.0091290 ## [1926] 1.0034698 1.0012739 1.0003868 1.0010393 1.0038473 1.0049475 1.0074420 ## [1933] 1.0070134 1.0020170 1.0036433 1.0061894 1.0019500 1.0006196 1.0033117 ## [1940] 1.0018040 1.0084981 1.0148280 1.0193928 1.0168202 1.0199983 1.0172661 ## [1947] 1.0088281 1.0098257 1.0077416 1.0055568 1.0094902 1.0130908 1.0264014 ## [1954] 1.0274095 1.0288870 1.0212853 1.0261004 1.0241335 1.0353504 1.0338361 ## [1961] 1.0258690 1.0324591 1.0508586 1.0583649 1.0579962 1.0748908 1.0979178 ## [1968] 1.1076265 1.0876035 1.0904914 1.0751337 1.0815377 1.0607632 1.0510297 ## [1975] 1.0449146 1.0550651 1.0437730 1.0388012 1.0229244 1.0053647 1.0016106 ## [1982] 1.0054494 1.0204866 1.0347440 1.0420197 1.0398582 1.0501531 1.0718289 ## [1989] 1.0548906 1.0596717 1.0673213 1.0469185 1.0592200 1.0460011 1.0363261 ## [1996] 1.0336067 1.0216727 1.0222575 1.0351213 1.0287205 ``` ] --- * 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 ```