class: center, middle, inverse, title-slide # Data Analysis ## in the context of wildlife ecology and management ### Joe Thorley Ph.D. R.P.Bio. ### 2019-10-31 --- ## What is Data Analysis? Data Analysis is about -- - reducing uncertainty (judgement to knowledge) -- - using information (data) -- - given assumed relationships (model) -- Data Analysis is *not* about -- - management (making optimal decisions)! --- ## Regulate Industry? <!-- --> --- <div id="htmlwidget-08fc02c913c140ac1b95" style="width:500px;height:500px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-08fc02c913c140ac1b95">{"x":{"diagram":"digraph {\n\ngraph [layout = \"neato\",\n outputorder = \"edgesfirst\",\n bgcolor = \"white\"]\n\nnode [fontname = \"Helvetica\",\n fontsize = \"10\",\n shape = \"circle\",\n fixedsize = \"true\",\n width = \"0.5\",\n style = \"filled\",\n fillcolor = \"aliceblue\",\n color = \"gray70\",\n fontcolor = \"gray50\"]\n\nedge [fontname = \"Helvetica\",\n fontsize = \"8\",\n len = \"1.5\",\n color = \"gray80\",\n arrowsize = \"0.5\"]\n\n \"1\" [label = \"Observations\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"1,1!\"] \n \"2\" [label = \"Judgement\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"3.25,0!\"] \n \"3\" [label = \"Decision\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"5,-1!\"] \n\"1\"->\"2\" [style = \"dotted\", color = \"black\"] \n\"2\"->\"3\" [style = \"dotted\", color = \"black\"] \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> > Judgement-Based Management --- background-image: url(19-analysis-wildlife_files/09_1987_1dollar_rev.jpg) ## Uncertainty is described using Probability --- ## Uncertainty is described using Probability <img src="19-analysis-wildlife_files/figure-html/unnamed-chunk-3-1.svg" style="display: block; margin: auto;" /> --- ## Uncertainty is described using Probability <img src="19-analysis-wildlife_files/figure-html/unnamed-chunk-4-1.svg" style="display: block; margin: auto;" /> --- ## Uncertainty is described using Probability <img src="19-analysis-wildlife_files/figure-html/unnamed-chunk-5-1.svg" style="display: block; margin: auto;" /> --- ## Uncertainty is described using Probability <img src="19-analysis-wildlife_files/figure-html/unnamed-chunk-6-1.svg" style="display: block; margin: auto;" /> --- layout: false ## A Tossed Coin - What is the probability of a heads before I toss the coin? -- - What is the probability after I toss it but before I look at it? -- - What is the probability after I look at it but before I tell you? -- - What is the probability after I tell you it's tails? -- - What is the probability if I then tell you I was lying and it's heads? -- - What is the probability if I'm willing to bet you $10 it's heads? -- - Are you willing to accept odds of 10:1? --- ## PROBABILITY DOES NOT EXIST -- De Finetti (1970) Theory of Probability -- - Probability is a measure of **your** uncertainty about the possible states of the world. -- <img src="19-analysis-wildlife_files/figure-html/unnamed-chunk-7-1.svg" style="display: block; margin: auto;" /> --- ## Probability Distributions <!-- --> --- ## Probability Distributions <!-- --><!-- --> -- `$$\text{Value} \sim N(0, 1)$$` --- <div id="htmlwidget-4f7c6d9b9d989bdcab91" style="width:500px;height:500px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-4f7c6d9b9d989bdcab91">{"x":{"diagram":"digraph {\n\ngraph [layout = \"neato\",\n outputorder = \"edgesfirst\",\n bgcolor = \"white\"]\n\nnode [fontname = \"Helvetica\",\n fontsize = \"10\",\n shape = \"circle\",\n fixedsize = \"true\",\n width = \"0.5\",\n style = \"filled\",\n fillcolor = \"aliceblue\",\n color = \"gray70\",\n fontcolor = \"gray50\"]\n\nedge [fontname = \"Helvetica\",\n fontsize = \"8\",\n len = \"1.5\",\n color = \"gray80\",\n arrowsize = \"0.5\"]\n\n \"1\" [label = \"Data\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"1,1!\"] \n \"2\" [label = \"Model\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"2.5,1!\"] \n \"3\" [label = \"Likelihood\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"1.75,0!\"] \n \"4\" [label = \"Judgement\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"3.25,0!\"] \n \"5\" [label = \"Knowledge\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"2.5,-1!\"] \n \"6\" [label = \"Decision\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"5,-1!\"] \n\"1\"->\"3\" [color = \"black\", color = \"black\"] \n\"2\"->\"3\" [color = \"black\", color = \"black\"] \n\"3\"->\"5\" [color = \"black\", color = \"black\"] \n\"4\"->\"5\" [color = \"black\", color = \"black\"] \n\"5\"->\"6\" [color = \"black\", style = \"dotted\"] \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> > Data Analysis -- `$$\text{Knowledge} \propto \text{Judgement} \cdot P(\text{Data}|\text{Model})$$` --- background-image: url(19-analysis-wildlife_files/bison-1801981_1920.jpg) ## Data are Coded Observations -- > At easter about an hour after midday I was walking by the river and I saw a female bison, and another female behind it and another male one behind it. I went back at sunset but didn't see anything. -- "04/01/18 1:05 two female and one male bison 44.4280 N 110.5885 W" --- background-image: url(19-analysis-wildlife_files/bison-1801981_1920.jpg) ## Data are Machine-Readable <div id="htmlwidget-6eb1102b1dd57521c889" style="width:100%;height:auto;" class="datatables html-widget"></div> <script type="application/json" data-for="htmlwidget-6eb1102b1dd57521c889">{"x":{"filter":"none","fillContainer":false,"data":[["1","2"],["male","female"],[2,1],["JLT","JT"],["2018-01-04","2018-01-04"],["01:05:00","01:05:00"],[110.5885,110.5885],[44.428,44.428]],"container":"<table class=\"display\">\n <thead>\n <tr>\n <th> <\/th>\n <th>Sex<\/th>\n <th>Count<\/th>\n <th>Obs<\/th>\n <th>Date<\/th>\n <th>Time<\/th>\n <th>Long<\/th>\n <th>Lat<\/th>\n <\/tr>\n <\/thead>\n<\/table>","options":{"pageLength":8,"columnDefs":[{"className":"dt-right","targets":[2,6,7]},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[8,10,25,50,100]}},"evals":[],"jsHooks":[]}</script> -- This dataset has at least six problems! -- -- - Numbers are mispunched -- - Two different observers -- - 4th of January -- - Just after middnight -- - In the Gobi Desert -- - Missing zero count! -- *80% of data analysis is data cleansing and tidying!!* --- ## Count and Industry Data <div id="htmlwidget-a4ed01f8510ee4e2ca88" style="width:100%;height:auto;" class="datatables html-widget"></div> <script type="application/json" data-for="htmlwidget-a4ed01f8510ee4e2ca88">{"x":{"filter":"none","fillContainer":false,"data":[["1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20","21","22","23","24","25","26","27","28","29","30"],[2,2,1,1,3,5,1,4,0,5,2,2,4,2,2,1,0,5,4,1,0,2,3,3,2,4,3,3,3,3],[0.4,0,0.7,0.7,0.2,0.3,0.6,0.3,0.6,0.5,0.9,0.7,0.7,0.9,0.5,0.6,0.8,0.2,0.4,0,0.7,1,0.2,0.7,0.9,0.8,0.1,0.4,0.4,0.7]],"container":"<table class=\"display\">\n <thead>\n <tr>\n <th> <\/th>\n <th>Count<\/th>\n <th>Industry<\/th>\n <\/tr>\n <\/thead>\n<\/table>","options":{"pageLength":10,"columnDefs":[{"className":"dt-right","targets":[1,2]},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script> --- class: inverse background-image: url(19-analysis-wildlife_files/haida-gwaii.png) --- class: inverse background-image: url(19-analysis-wildlife_files/haida-gwaii.png) # All Models are Wrong --- class: inverse background-image: url(19-analysis-wildlife_files/haida-gwaii.png) # All Models are Wrong (but some are Useful) -- > The map is not the territory Alfred Korzybski -- > Everything simple is false. Everything which is complex is unusable. Paul Valery -- > There is no such thing as an absolutely True thought. Steven Gray --- ## Data Analysis -- <!-- --> -- `$$\log(\mu) = \beta_0 + \cdots + \Delta \cdot \text{Industry}$$` -- `$$\text{Count} \sim \text{Poisson}( \mu)$$` --- ## Data Analysis <!-- --><!-- --> `$$\log(\mu) = \beta_0 + \cdots + \Delta \cdot \text{Industry}$$` `$$\text{Count} \sim \text{Poisson}(\mu)$$` `$$\Delta \sim N(0, 1)$$` --- ## Data Analysis <!-- --><!-- --> `$$\log(\mu) = \beta_0 + \cdots + \Delta \cdot \text{Industry}$$` `$$\text{Count} \sim \text{Poisson}(\mu)$$` `$$\Delta \sim N(0, 1)$$` `$$\beta_0 \sim N(0, 1)$$` --- ## Data Analysis <!-- --><!-- --> `$$\log(\mu) = \beta_0 + \cdots + \Delta \cdot \text{Industry}$$` `$$\text{Count} \sim \text{Poisson}(\mu)$$` `$$\Delta \sim N(0, 1)$$` `$$\beta_0 \sim N(0, 1)$$` --- ## Data Analysis <!-- --><!-- --> `$$\log(\mu) = \beta_0 + \cdots + \Delta \cdot \text{Industry}$$` `$$\text{Count} \sim \text{Poisson}(\mu)$$` `$$\Delta \sim N(0, 1)$$` `$$\beta_0 \sim N(0, 1)$$` --- ## Data Analysis <!-- --><!-- --> `$$\log(\mu) = \beta_0 + \cdots + \Delta \cdot \text{Industry}$$` `$$\text{Count} \sim \text{Poisson}(\mu)$$` `$$\Delta \sim N(0, 1)$$` `$$\beta_0 \sim N(0, 1)$$` --- ## Data Analysis <!-- --><!-- --> `$$\log(\mu) = \beta_0 + \cdots + \Delta \cdot \text{Industry}$$` `$$\text{Count} \sim \text{Poisson}(\mu)$$` `$$\Delta \sim N(0, 1)$$` `$$\beta_0 \sim N(0, 1)$$` --- <div id="htmlwidget-e9bd8633d07ae75337a9" style="width:500px;height:500px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-e9bd8633d07ae75337a9">{"x":{"diagram":"digraph {\n\ngraph [layout = \"neato\",\n outputorder = \"edgesfirst\",\n bgcolor = \"white\"]\n\nnode [fontname = \"Helvetica\",\n fontsize = \"10\",\n shape = \"circle\",\n fixedsize = \"true\",\n width = \"0.5\",\n style = \"filled\",\n fillcolor = \"aliceblue\",\n color = \"gray70\",\n fontcolor = \"gray50\"]\n\nedge [fontname = \"Helvetica\",\n fontsize = \"8\",\n len = \"1.5\",\n color = \"gray80\",\n arrowsize = \"0.5\"]\n\n \"1\" [label = \"Data\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"1,1!\"] \n \"2\" [label = \"Model\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"2.5,1!\"] \n \"3\" [label = \"Likelihood\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"1.75,0!\"] \n \"4\" [label = \"Judgement\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"3.25,0!\"] \n \"5\" [label = \"Knowledge\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"2.5,-1!\"] \n \"6\" [label = \"Decision\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"5,-1!\"] \n\"1\"->\"3\" [color = \"black\", color = \"black\"] \n\"2\"->\"3\" [color = \"black\", color = \"black\"] \n\"3\"->\"5\" [color = \"black\", color = \"black\"] \n\"4\"->\"5\" [color = \"black\", color = \"black\"] \n\"5\"->\"6\" [color = \"black\", style = \"dotted\"] \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> --- <div id="htmlwidget-9903c3d23fdbb93d7678" style="width:500px;height:500px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-9903c3d23fdbb93d7678">{"x":{"diagram":"digraph {\n\ngraph [layout = \"neato\",\n outputorder = \"edgesfirst\",\n bgcolor = \"white\"]\n\nnode [fontname = \"Helvetica\",\n fontsize = \"10\",\n shape = \"circle\",\n fixedsize = \"true\",\n width = \"0.5\",\n style = \"filled\",\n fillcolor = \"aliceblue\",\n color = \"gray70\",\n fontcolor = \"gray50\"]\n\nedge [fontname = \"Helvetica\",\n fontsize = \"8\",\n len = \"1.5\",\n color = \"gray80\",\n arrowsize = \"0.5\"]\n\n \"1\" [label = \"Data\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"1,1!\"] \n \"2\" [label = \"Model\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"2.5,1!\"] \n \"3\" [label = \"Likelihood\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"1.75,0!\"] \n \"4\" [label = \"Judgement\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"3.25,0!\"] \n \"5\" [label = \"Knowledge\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"2.5,-1!\"] \n \"6\" [label = \"Significance\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"3.75,-1!\"] \n \"7\" [label = \"Decision\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"5,-1!\"] \n\"1\"->\"3\" [color = \"black\"] \n\"2\"->\"3\" [color = \"black\"] \n\"3\"->\"5\" [color = \"black\"] \n\"4\"->\"5\" [color = \"black\"] \n\"5\"->\"6\" [color = \"black\"] \n\"6\"->\"7\" [color = \"black\"] \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> > 'uncertainty laundering' Gelman (2016) --- ## Significance <!-- --> --- ## Significance <!-- --> --- ## Significance <!-- --><!-- --> --- ## Significance <!-- --><!-- --> -- The effect of industry on abundance is **not significant**. -- We can't be sure it's having an effect. -- Therefore there is no need to change regulations! --- ## Significance <!-- --> -- Significance depends on effect size **and sample size**. -- Statistical significance `\(\neq\)` ecological significance -- Significance does not take account of the costs/benefits of the various options. -- ---- Significance is a reasonable criteria for model selection. --- <div id="htmlwidget-e8988b54ec7126f81d7f" style="width:500px;height:500px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-e8988b54ec7126f81d7f">{"x":{"diagram":"digraph {\n\ngraph [layout = \"neato\",\n outputorder = \"edgesfirst\",\n bgcolor = \"white\"]\n\nnode [fontname = \"Helvetica\",\n fontsize = \"10\",\n shape = \"circle\",\n fixedsize = \"true\",\n width = \"0.5\",\n style = \"filled\",\n fillcolor = \"aliceblue\",\n color = \"gray70\",\n fontcolor = \"gray50\"]\n\nedge [fontname = \"Helvetica\",\n fontsize = \"8\",\n len = \"1.5\",\n color = \"gray80\",\n arrowsize = \"0.5\"]\n\n \"1\" [label = \"Data\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"1,1!\"] \n \"2\" [label = \"Model\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"2.5,1!\"] \n \"3\" [label = \"Likelihood\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"1.75,0!\"] \n \"4\" [label = \"Judgement\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"3.25,0!\"] \n \"5\" [label = \"Knowledge\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"2.5,-1!\"] \n \"6\" [label = \"Decision\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"5,-1!\"] \n \"7\" [label = \"Options\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"5,1!\"] \n \"8\" [label = \"Loss\", shape = \"rectangle\", color = \"black\", width = \"1\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\", pos = \"5,0!\"] \n\"1\"->\"3\" [color = \"black\"] \n\"2\"->\"3\" [color = \"black\"] \n\"3\"->\"5\" [color = \"black\"] \n\"4\"->\"5\" [color = \"black\"] \n\"5\"->\"6\" [color = \"black\"] \n\"7\"->\"8\" [color = \"black\"] \n\"8\"->\"6\" [color = \"black\"] \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> > Decision Theory Choose option that maximizes expected net benefit given the uncertainty. --- ## Decision Theory -- Requires loss function (challenging to develop) -- but criteria are explicit -- and decisions 'optimal'. --- ## Loss Function <!-- --> --- ## Loss Function <!-- --> --- ## Loss Function <!-- --> --- ## Loss Function <!-- --> --- ## Loss Function <!-- --><!-- --> -- <!-- --> --- ## Loss Function <!-- --><!-- --> <!-- --><!-- --> --- ## Summary -- - Uncertainty is personal -- - Clean and tidy data is essential -- - Models are inescapable -- - Statistical significance does not indicate ecological significance -- - Decisions should maximize the expected net benefit given the uncertainty. --- ## Further Reading Amrhein, V., Greenland, S., and McShane, B. 2019. Scientists rise up against statistical significance. Nature 567(7748): 305–307. doi:10.1038/d41586-019-00857-9. McElreath, R. 2016. Statistical rethinking: a Bayesian course with examples in R and Stan. CRC Press/Taylor & Francis Group, Boca Raton. Williams, P.J., and Hooten, M.B. 2016. Combining statistical inference and decisions in ecology. Ecological Applications 26(6): 1930–1942. doi:10.1890/15-1593.1. --- class: center, middle # Thanks! For more information see www.joethorley.io www.poissonconsulting.ca