Annual Report to Stakeholders 2015-16

As a grad student, I had to submit an annual report on my academic activities and the progress I was making in the PhD.

This year, I neglected to submit one, but since it's a good exercise in perspective, I’m doing a more general one here for myself and the major stakeholders in my life.

Executive Summary (informally, the ‘TL;DR’): 

The two most important things of this year were meeting Gabriela and defending my PhD thesis. Both of those successes owe a great deal to the development and effort of the previous years than anything particular I did this year.

Personal:

This year I enjoyed a lot more success in making personal connections than professional progress; a year and a day ago I met Gabriela and we are very much in love. This may seem sappy and out of place in an annual report, but this is a life report and it’s easy to understate these sort of things because they’re difficult to quantify. Gabi is  extremely important to me, and she deserves to be mentioned here. Establishing a relationship of this quality takes a lot of effort, but it has been tremendously rewarding.

Education (Learning):

They say completing a doctorate is a marathon, not a sprint. If that’s true, mine felt like the Boston Marathon; some parts crossed the finish line a lot sooner than others. The spirit of the thesis was done a year ago - written, submitted, and with a defense scheduled. This year, I added a new short chapter, and added a new layer of proofreading to the old chapters, but that’s it. While writing this extra chapter, which was an application of my new method to a database, I learned enough about the Canadian legal system to spark an appetite for more (so, very little).

For projects and curiosity, I’ve learned about meta-analysis, validation, item response theory, web-crawling, copy editing, and an introductory amount about the statistical method INLA.  

Duolingo says I’m now about 20% fluent in Portuguese. In the near-term future, I hope to push that higher at a rate of 10% per month.

In the short/mid-term, I hope to gain more depth in using SAS (and take more SAS certification exams to solidify this), and to learn more about the law (and to take the LSAT, likewise).

Education (Teaching):

In the spring I lectured Stat 302 to about 300 students. I’ve already talked about this in detail in my postmortem. Student evaluations rated my teaching higher than both the school and faculty average in almost every category. Also, I got applause, so 2/2 there.

Only 10-20% of the material was able to be recycled from Stat 203 and from other notes. However, that means a LOT of new notes and assignments and assignments were added to my personal corpus of notes.

One of the two courses I’m teaching in the fall, Stat 305, will recycle 50% of its material from 302 and 203. Of the other half, I already have the notes of five lectures completed.

I also have been doing some assignment design for a 400-level course on big data methods that Luke Bornn is teaching in the fall, and I did a guest lecture for the 400-level Statistics of Sport course.

Research:

Lots of little scattered things. 

Harsha, Tim, and I wrote another cricket paper. Rajitha, Tim, and I wrote a hockey paper. Kurt Routley (in Computer Science) and I co-presented a talk on data mining in hockey. A health sciences paper linking depression and sexually risky behaviour in South Africa was published after years of delay.

Not really shown in the thesis was the additional development of the Approximate Bayesian Computation work that Steve Thompson and I made in the last year. Very recently we got some coveted data from the CDC that we can use to revive some analyses from 2014-5.

I’ll be presenting some hockey research on the overtime loss rule at the Cascadia Sports Conference in Vancouver in September, and Paramjit and I will be reviving a old paper on this with some new depth.

I’ve met with at least five other groups about other research projects all across the board, but without any deliverables that I can mention here.

Publishing:

4 papers were refereed: 3 for the Open Journal of Statistics, 1 for the Canadian Journal of Statistics. 

6 papers were copy-edited: 3 for networking purposes, 1 that did the analysis for as well, 1 at the request of a faculty member, and 1 as a skill test for the Canadian Journal of Statistics.

26 blog posts were made and kept, not including this one.

Game Design:

I haven’t posted the details here, but a very basic (pre-alpha) working prototype of Scrabble Dungeon on PC. A player place tiles in a crossword grid from a designated starting tile to an ending point in order to win the game. Wall tiles, pre-placed tiles, and gem pickups are functioning. Boards of any layout and size can be loaded into the game that contain these elements. Parts of the card system are working, and two of the cards (life relic and meta relic) are included.

The goal is to eventually get the game onto the Android Play Store, but I may also settle for a PC version if it’s less of a headache. 

Thesis Defence Notes - Approximate Bayesian Computation

These are notes from the slides that were given during my defense. I've clarified some points since then.

The other half of the notes, on the cricket simulator, are found here.

------------------

Approximate Bayesian Computation (ABC) is a method of estimating the distribution of parameters when the likelihood is very difficult to find. This feature makes ABC applicable to a great variety of problems.

The classical ABC method can be summarized as:

Step 1: Select a prior joint distribution F(theta) for the parameters of interest.

Step 2: Observe a sample s from the population you wish to characterize.

Step 3: Compute T(s), a statistic, or set of statistics, from the sample.

Step 4: Repeat the following many times

4A: Generate random parameter values p from F(theta)

4B: Use the values p to simulate a sample s'

4C: Compute the distance between T(s') and T(s), the statistics taken from the simulated and observed samples, respectively.

4D: If the difference is less than some tuning value, epsilon, then accept the values p.

Step 5: The collection of values p from all accepted values is taken as the posterior distribution of the parameters of interest.

Step 6: If the parameters of interest are continuous, a smoothing method is applied to this collection to produce a continuous posterior distribution.

The distance between two statistics can be determined by Manhattan or Euclidean distance, or a weighted distance if deviations between some statistic values are more important than others.

The tuning parameter epsilon determines the balance between accuracy and computational efficiency. A small epsilon will ensure that only generated samples that are very similar to the observed sample will be used. That is, only samples that produce statistics very close to the real sample's statistics. However, many samples will be rejected.

A large epsilon will ensure that many samples will be produced, but some of those samples will have statistics that deviate from the observed sample. Since the process of producing new samples could be time-consuming, depending on the application, this may be a worthwhile trade-off.

Compared to classical Approximate Bayesian Computation method, I made some modifications.

- Instead of having an accept-reject rule, I opted to use every sample but assign weights to the parameters behind each sample based on the distance between T(s') and T(s).

- The weights and smoothing mechanism are determined through a Kernel Density Estimator (KDE)

Specifically, every generated sample is gets treated as a point mass in a space across the statistic values and parameter values.

Consider the example in the following MS-Paint diagrams. 

In Figures 1-3, we have a sample with a single statistic value, T(s), vertical, and a single parameter of interest, theta, horizontal. We don't know the parameter value of the observed sample, so we represent the observed sample as a blue horizontal line.

Points A and B represent the statistic and parameter values from each of two generated samples (also A and B, respectively). These are points instead of lines because these samples are simulated using known parameter values. 

The gray area at the bottom of each figure is the conditional density of the parameter of the observed sample. The thin lines around points A and B are the contour lines of the probability density, with peaks at the points and decreasing outwards.

Figure 1: A generated sample that's far from the observed sample.

In Figure 1, we see the effect of generated sample A on the parameter estimate. The statistic from sample A is far from the statistic of the observed sample, so point A is far from the line. As a result, the probability density does increase or decease much along the line, and therefore the conditional density of the parameter estimate is diffuse, as shown by the shallow gray hill.

Figure 2: A generated sample that's close to the observed sample.

 In Figure 2, we see sample B's effect. This sample's statistic is close to that of the observed sample. Therefore, point B is close to the line. The conditional density is much steeper around sample B's parameter value. This is because the probability density increases and decreases a lot along the blue line.

Figure 3: The combined estimate from both samples.

In Figure 3, we see the cumulative effect of both samples. The conditional density from both resembles that from generated sample B. This is because sample B's effect was given more weight. Generated samples that more closely resemble the observed sample contribute more to the parameter estimate.

I used this method on two applications

1. A theoretical network based on a network of sexual partners in Africa.

2. A real network of precedence citations between decisions of the Supreme Court of Canada.

The theoretical dataset was based on a respondent driven sample. An initial seed of people was selected, presumably by a simple random process. Members of this seed were polled about the number of sexual partners they had in the previous year, their HIV status, and their sexual orientation. For each reported partner, contact information was taken in order to recruit these partners into the sample as well. If the recruitment pool was exhausted before the desired number of respondents, new seed members were found.

Like the basis dataset, we assumed that the sample we were given contained the mentioned covariates of those polled, including the number of partnerships, and we assumed that only the partnerships that led to successful recruitment were available. This implies that large parts of the network could be hidden to us, such as partnerships that 'lead back' into the sample already taken.

Consider these two figures.

Figure 4 is from a sample of a network with identifying information about every reported partnership is given.  Figure 5 is from the same sample, where only the partnerships that led to recruitment are known. Notice that Figure 4 includes lines going out to points that we did not sample directly. Notice also that Figure 4 includes cycles, in which you could go from one point to itself by following the lines and without backtracking.

We don't see these cycles in Figure 5, the recruitment-only network, because a person cannot be recruited if they are already in the sample. A cycle might be a triangle between persons J, K, and L, where all three are connected. Person J can recruit both K and L through those connections, but K cannot recruit L, so we never see the K-L connection. What we see is one person, J, with two distinct partners instead of the whole picture.  

Socially, the K-L connection is key information, and mathematically this lack of cycles makes estimation of anything about this network a lot harder.

Figure 4: A network with identifying information from the sample.

Figure 5: A network with only recruitment information from the sample.

 Nevertheless, I used ABC to estimate some features (parameters) of the population that this sample came from.

 

The parameters of interest were:

- The number of members in the population, (prior: geometric, mean 2000, truncated minimum 400)

- The probability of an HIV infection passing along a partnership, (prior: uniform 0 to 0.3)

- The proportion of this network that was already infected before any of these partnerships (prior: uniform 0 to 0.5)

- The 'closeness preference', a parameter governing the propensity to select partners that are similar to oneself. Zero is no preference, 10 is a strong preference, and a negative number represents a general dislike for those similar to you. (prior: uniform -2 to 10)

I conducted two rounds of Approximate Bayesian Computation by producing 500 and 2500 samples, respectively. The results are here. The yellow and red represent regions of high conditional probability. ABC allows us to narrow down the likely value of the real parameters to these yellow and red regions.

Parameter sets at points all across these graphs were tried, but only those in the non-blue regions produced samples that were anything like the observed sample.

Figure 6: Coloured contour maps of conditional densities, social network data.

From these, we can calculate marginal means to get our parameter estimates.

Parameter	True Value	Mean (Initial Round)	Mean (Final Round)
Population Size	1412	2049	2094
Initial Infection Rate	0.467	0.399	0.374
Transmission Chance	0.093	0.175	0.201
Closeness Preference	7.298	6.753	9.352

The second application was on the precedence citations of decisions in the Supreme Court of Canada (SCC). Because this is real data, I am not able to find the ground truth with which to compare my results, but I can showcase how the method behaves with real data.

When this data was collected, there were 10623 documents produced by the SCC, 9847 of which are cases (e.g. disputes between two parties). These decisions are among the more than 3,000,000 cases and other documents recorded in the Canadian Legal Information Institute (CanLII). Figure 7 shows part of the network of SCC cases.

Figure 7: Induced subgraph of cases and citations in Supreme Court of Canada

Cases span from 1876 to 2016, with more recent cases represented as points near the top. The larger points are those that have been cited often in Canadian law. Lines between points represent citations between SCC cases. Only 1000 cases are shown here, so the true network between SCC cases has roughly 10 times as many nodes and 100 times as many links.

My general interest in this dataset is to identify the features that make a law prone to being obscure over a long time.

I modelled each SCC case as 'vendor' that was trying to 'sell' citations to future Canadian legal cases. Each SCC case had an attractiveness a, where

  

and where

β_irrel : Parameter determining the decay in attractiveness over time (per 5 years without a citation).

β_pa : Parameter determining a preferential attachment factor, assuming that a case becomes more well-known whenever it is cited.

β_corp , β_crown , β_dis : Parameters determining increased/decreased attractiveness based on whether a case involved a corporation, the crown, or dissent between Supreme Court Judges, respectively.

what I found was less clear that in was in the synthetic data case, as shown in Figure 8.

Figure 8: Coloured contour maps of conditional densities, Supreme Court of Canada data.

 It's impossible to read the variable names in this figure, I'm afraid. The jist, however, is that...

- a case that is not cited in five or more is less and less likely to receive citations over time.

- a case that is cited often is more likely to receive citations in the next five years.

- a case that involves a corporation is less likely to be cited.

- a case that involves the crown is more likely to be cited.

- a case that had dissenting opinions by some of the judges is more likely to be cited.

I read this: Spatial and Spatio-Temporal Bayesian Models with R-INLA

Spatial and Spatio-temporal Bayesian Models with R-INLA, by Marta Blandiardo and Michela Cameletti is a short textbook that introduces INLA (Integrated nested Laplace approximations) and some preliminaries, and works through the math and R-code of a variety of problems that the R-INLA package can tackle. Several non-spatial regression models are also covered in enough detail to get you started on R-INLA in general.

Thesis Defence Notes - Cricket Simulator

These are notes from the 'lost slides' on cricket that I didn't have time to cover in my PhD defense, which I completed two weeks ago.

The other half of the notes, on approximate Bayesian computation (ABC) for networks, is found here.


------------------

Cricket is a sport popular in the emerging economies of the Indian subcontinent. Most of my cricket work has focused on the Twenty20 format of Cricket, in which matches are designed to last only three hours, roughly the same time as matches in other popular team sports. This format has only been played professionally for about 10 years, and it growing quickly in terms of spectator and commercial interest. The intricacies of this format are also poorly understood, which provides many good research opportunities.

In the Twenty20 format, each team is allowed one innings to score runs. (Yes, 'innings', not 'inning') That inning is over if either...

1) 10 of the 11 players are dismissed (a dismissal is also called an 'out' or a 'wicket'), or
2) 120 'fair' balls are thrown. A group of 6 throws is called an 'over', making 20 overs per innings. Hence the name Twenty20.

A small number (typically fewer than 10) of throws per innings do not count against the limit of 120 because they were not thrown in a prescribed manner. A small number of throws also incur a one-run penalty that is added to the These cases are similar to 'balls' and 'hits-by-pitch' in baseball, respectively.

Each of these 120+ throws has a discrete result that we simplified into six categories: Wicket, 0 Runs, 1 Run, 2-3 Runs, 4-5 Runs (Ground Rule Double), and 6 Runs (Home Run).  Cases where 3 runs and 5 runs occurred were rare, so we treated them as a fixed proportion of 2-3 runs (~6.4%) and 4-5 (~1.5%) runs respectively. Likewise, throws not counting against the 120 limit, and those resulting in a penalty run, were treated as a fixed proportion of each of the six categories.

Here is table of a team's batting and bowling summaries of a recent T20I match from ESPN CricInfo.

All of these metrics, such as 'Strike Rate', are based solely on the number of events (e.g. balls faced,  times dismissed, runs scored), without respect to when they happened. The inherit weakness of all these metrics is that they treat each throw as an identical event, independent of the number of wickets and throws remaining. For the baseball crowd, consider the difference between overall batting average, and the batting average with runners in scoring position.

Reality is more complex. Consider this:

 This is a heat map of the empirical chance of any throw/ball/pitch ending as a six (a home run in baseball terms) as a function of overs and wickets taken. All games start in the upper-left corner, with 20 overs and 10 wickets remaining. From there, plausible game situations 'fan out', where games with situations following the top of the fan are those where relatively few batters are dismissed by the time most of the overs are used.

In these games, many sixes occur in the late game. Scoring a six involves hitting the ball with great power, which involves taking a greater risk of a dismissal. Since in these low-dismissal games, remaining throws are a more precious resource than remaining wickets, this high-risk, high-reward strategy is rational.

Here's the raw probability of scoring a four, which is similar to a ground rule double in baseball. This is a ball that touches the ground in bounds, but bounces or rolls out of bounds. As such, the fielders have an effect on the outcome that they cannot usually have on sixes. Notice that the general pattern of fours are similar to those of the sixes, except for the major drop at between the 6th and 7th overs. From the 7th over onwards, the players in the field are more restricted, and so more balls are able to roll out of bounds to score 4 runs

 

Likewise, the batting team gets really desperate in the last few overs, so they try reckless moves that frequently end in a wicket (a dismissal of a batting player). We also see wickets getting more likely when there are very few batters left. This seems counter to the intuitive strategy - that running out of batters would cause the remaining batters to be more cautious. Instead, you're seeing the effect of putting the worst batters on a team last in the batting order - they just get dismissed more often.

Here's the major confound: A batting player continues to bat until dismissed or until the innings ends. So a starting batter will rarely, if ever, see a situation where there are few wickets remaining. Likewise, a player batting late in the lineup will never enjoy the game situations with many wickets remaining. Therefore, a late-batting player has less opportunity to aim for those sweet, sweet, sixes.

We developed a system for estimating 'situational effects', which are the relative propensities towards a given outcome (i.e. wicket, 0, 1, 2-3, 4-5, 6) holding batter and bowler constant. These effects were estimated by first estimating odds ratios of events between 'adjacent' situations (those differing by one over or one wicket), within individual player records.

The data in these heatmaps are used to find these situational effects, which control for individual player effects.

Having these situational effects in place, we were able to estimate a great deal of additional parameters. First, we estimated the probability of any given player to produce a given outcome at some 'baseline' situation. To do this, we gave each ball faced, or ball thrown for bowlers, a weight. If a six happened in a situation when sixes were more likely (again, controlling for player difference), a small weight was given. If a six happened at a time when sixes were rare, a large weight was given. This way, we could compare batters and bowlers to each other, even we they played under very different situations.

To knit this all together into estimates of a players batting or bowling outcomes at a 'baseline' situation, we used a Metropolis-Hastings within Gibbs sampling method. More specifically, we draw a set of values from a Dirichlet distribution (an extension of the Beta distribution to multinomial cases), and propose those as a player's outcome probabilities at baseline. Then we compute the likelihood of these probabilities given the player's history and the estimated situational effects. Proposals that fit the data better have a higher likelihood, and these are given more weight in the final estimate. The final estimate for a player is an aggregate of thousands of these proposals.

I treated situational effects as normalized multiplicative effects on these baseline probabilities. in the following formula,

the situational effects are the tau owj's and pi70j is a player's ability at the baseline situation (7 overs, 1st wicket). The left-hand part, piowj, represents the probability of any player getting any outcome in any situation (o overs, w wickets). From here, making a simulation was just a matter of making a Markov Chain that followed the rules of the game.

This simulator has been the basis of five published or submitted papers, including the two in the first half of my thesis (bolded)

Davis, J., Perera, H., & Swartz, T. B. (2015). A simulator for Twenty20 cricket. Australian & New Zealand Journal of Statistics, 57(1), 55-71.

 

Davis, J., Perera, H., & Swartz, B. (2015). Player evaluation in Twenty20 cricket. Journal of Sports Analytics, (Preprint).

 Perera, H., Davis, J., & Swartz, T. B. (2016). Optimal lineups in Twenty20 cricket. Journal of Statistical Computation and Simulation, 1-13.

Perera, H., Davis, J., & Swartz, T. B. (2016). Assessing the impact of fielding in
twenty20 cricket. In submission.

Silva, R., Davis, J., & Swartz, T. B. (2016). Mismatches in Twenty20 cricket. In submission.

The NHL is half as good as it should be.

The soul of the National Hockey League feels like it's gone.

1. Every 8 years or so, at least half, sometimes a whole season is simply lost because of labor dispute. The backbone of sport is ritual and tradition, and a ritual adhered to only sometimes is just a habit.

2. Teams are playing to tie instead of to win, as demonstrated by fivethirtyeight, and later in greater detail in a paper I'm writing with Paramjit Gill. Half a win is awarded to any team that loses in overtime, and this incentivizes some very risk-averse behaviour late in games. Despite other changes to overtime including
- the introduction of a shootout,
- 4-on-4 overtime play, and later
- 3-on-3 overtime play, the overtime bonus point has persisted.

3. Some teams are hopeless year-after-year failures. In the past, expansion teams have had one or two terrible seasons while they get established, but no team has that excuse now.  There are several 'rubber band' mechanics in play to pull the level of competitiveness of teams closer together over time.
- There is an upper limit on the total salaries that can be paid to players, and many teams are at this limit.
- Top-earning teams subsidize other teams.
- Teams that rank at the bottom in one season are given first pick of players in next year's draft.

The overtime bonus is itself a form of rubber-banding because a team can still earn season points by losing, and if the game goes to a shoot-out, then the game is effectively a coin toss regardless of team strength.

In spite of all these mechanics to prop up teams after a bad season, there are some have been hopeless for a decade. Looking at you, Oilers.

My guess is that isn't enough talent coming from second-tier 'feeder' leagues (WHL, OHL, QMJHL, AHL, and the European leagues) to properly fill 30 NHL teams anymore. In turn, these feeder leagues are working from a diminished talent pool because of demographic changes; compared to 15 years ago, there are fewer children being born in hockey-playing countries, and their parents are poorer and less able to enroll these children in organized hockey.


Here are my suggestions to improve the state of professional hockey.


1. Remove (at least) two teams from the league.

As a Canadian, my inclination would be to remove the Arizona Coyotes and the Columbus Blue Jackets because of their tiny home fanbases and financial troubles. Realistically, the Edmonton Oilers should go, simply for being the worst.

With 28 teams, all four divisions could have 7 teams, and the talent would be spread 7% less thinly. Cutting out a couple teams might be enough deterrent to 'diving', an alleged practice where bottom-tier teams intentionally lose games to improve their draft prospects for the next season.


2. Optimize the talent pool.

The first chapter of the book Outliers points out the phenomenon where boys born in the first 3 months of the year are overwhelmingly more likely to make a career out of hockey. The explanation given for this was that, as a fluke of the age cutoff system for children's leagues, these children of January are the oldest of their 4-6 year old peers on the ice. Since they are the best players in their leagues, they get filtered into more competitive leagues with better support. To my knowledge, Hockey Canada still uses this cutoff system.

Players that were both late in the year that may have been NHL material instead never reach their potential because they were outclassed and looked over when they were very young. Fairness aside, if early age cutoffs were done at 6-month intervals instead of 1-year intervals, we could see more players at their potential.

We wouldn't notice the difference for a generation, but it would offset future demographic changes.


3. Increase support for women's hockey.

At the moment there are only a handful of competitive teams in women's hockey in Canada, so the developed talent pool can't be exceedingly large. Even then, the Canadian and US teams were so much better than teams from other countries that the IOC was considering removing women's hokcey from the olympics because it wasn't competitive enough. Things are improving, as Finland has been showing strength in recent competitions. If we want more high quality hockey, maybe it's time to look elsewhere.

Biochar farming idea

Here's an idea I hope gets stolen if it's good, and shot down early if it's bad. Also, I claim no expertise in biology, apiary science, or soil ecology, so this could be drastically off the mark.



1. Pyrolyze massive amounts of organic waste to make biochar.
2. Use the biochar to make a soil that mimics land after a forest fire.
3. Grow high-value crops that grow best after a forest fire.
4. Incorporate secondary processes like beehives.

------------

First, pyrolysis is a technique for burning lingen-rich plant matter (i.e. wood, bamboo, corn stalks) in a low oxygen environment. Pyrolysis can produce a stable, porous form of charcoal called biochar. Biochar is commonly applied to soil to improve its capacity to store water and nutrients. Soil with large amounts of biochar can approximate a very high quality topsoil call terra preta.

Also, the process of creating biochar is carbon-negative. The carbon in the biochar is effectively locked out of the atmosphere more permanently than it would be if the biological matter is left to rot. It certainly keeps carbon out of the atmosphere more effectively than simple burning.

What happens, however, when the soil is mostly biochar, with just enough other parts (or a layer on top) to keep it from blowing away? I suspect that you would have a soil similar to what would be found on the ground after a forest fire.

Pioneer species are the first organisms to thrive after a forest fire. These include valuable plants like morel mushrooms, and, particularly, fireweed. Specifically, I've heard that honey derived from fireweed is valuable. However, the cultivation of fireweed honey is difficult because it has to be done in areas of recent forest fires, and therefore can't be done in the same place for very long.

My idea is to make soil that mimics the ground after a recent fire, and maintain that state with frequent renewal of  biochar. Then, I want to use that soil to cultivate pioneer species.

With enough biochar, my hope is to have some farmland that can grow fireweed every year, and have permanently installed beehives amongst the fireweed. Rather than move the hives to where the land is suitable, I will work to maintain the land in a suitable state. With luck, the practice will pay for itself in harvests of fireweed honey, morels, and excess biochar.

If this works, then it can become a business that is both long-term profitable and carbon negative. There is an established demand for morels, and with more consumer awareness there could be a large demand for fireweed honey, so there is room for lots of people to try this.

--------

One potential issue is that bees prefer some flowers to others, and growing fireweed near the beehives doesn't guarantee that those are the flowers that will be used. Having a honey with a precursor that was part fireweed and part wildflowers may be acceptable, but it even guaranteeing that would mean influence an area much larger than the farmland.

Another issue is a sustainable supply of lingen-rich organic matter. Piles of slash and scrap wood are unreliable, one-time sources. Corn husks work nicely, but aren't available everywhere. Low-grade wood chips, called hog, would also work, but those are already used by pulp mills for energy. The city of Vancouver is already collecting organic waste for industrial composting, so it may be possible to tap into that pipeline. It will take some research to find how to use whatever is regularly available from local food processing and agriculture.


--------

ADDENDUM: user Osageandrot on Reddit, who does research on biochar for soil restoration, was kind enough to critique this idea and give some input. It was enough to show that this idea needs a major rework before anything more goes forward with this

First, any fresh biochar would need to be pre-aged by mixing with existing soil. This is because Polycyclic Aromatic Hydrocarbons (PAHs) are in too high of a concentration originally, and these will suppress microbal life.

Second, fresh application of biochar may not be necessary anyways. Most pioneer species are simply fast growers that need anything else that grows slower, but to a higher maximum, to be gone. Forest fires are not a necessary ingredient for a lot of these, but they just happen to provide the necessary conditions; clearcutting would do the same thing.

Course Notes on the PitchRx package

These are the notes I recently delivered as a guest lecturer for Simon Fraser University's course on Sports Analytics. It's a course for people with some experience with R, but not necessarily experts. As such, I made these notes with a beginners in mind.

If you want to see what PitchRx can really do, I recommend the below links. However, if you want to get started and you don't have much familiarity with R, and possibly none with SQL, the following notes are for you.