Take-home Exercise 1: Geospatial Analytics for Public Safety

The regency was chosen by a rule, set before the result. Highest detection density among regencies above 5,000 km², the size floor I need for second-order estimation to a 5 km lag. Pulang Pisau wins at 3,656 per 1,000 km². Ketapang leads on raw count (65,901) but is 3x the area.

My first pass used a 7-day sample, where Pulang Pisau led on count. Over the full window it does not, so I restated the rule against the whole record.

VIIRS 375 m Collection 2, both platforms, clipped to the administrative polygon in UTM 49S, 9,759 km².

The 87-day window is set by what the REST API retains. Why that is a limit of my tooling and not of the data comes later, in the correction slide.

One large peat fire fills many 375 m pixels, and two satellites re-detect it about four times a day.

I measured it: the raw count overstates distinct burning locations by 3.4x.

So the pattern I started with partly measures the satellite’s revisit schedule, which means testing against complete spatial randomness was guaranteed to reject before I computed anything.

So I changed two things. The unit becomes the 375 m cell. The null becomes an inhomogeneous Poisson process.

That is the spine of everything else I did.

Gaussian kernel, Diggle edge correction, bandwidth I fixed at 4 km.

Cross-validated selectors gave me about 0.6 km and I rejected them: they absorb the very clustering my second-order test exists to detect, which would have rigged the second-order test two slides on.

Intensity spans roughly two orders of magnitude between the southern peat belt and the northern interior.

So allocating in proportion to sub-district area is badly matched to risk. I think that is the most directly usable thing I found.

Heavily back-loaded: week 1 recorded 7 events, the week of 16 September recorded 8,087.

The day/night contrast is not a daily cycle, and I nearly read it as one. Both platforms observe at four narrow fixed local times, so if I claimed fire peaks at a given hour I would be describing the orbit.

I use the split only as a detectability covariate, since night overpasses catch cooler anomalies against a cooler background.

Against CSR, G, F and L all leave the envelope immediately. That persuades nobody, including me: the sensor guarantees it. g(r) is even suppressed below 375 m, which is the pixel, not fires avoiding each other.

So I changed the null. An inhomogeneous Poisson process with intensity from the 4 km kernel estimate, with the reference re-estimated for every simulated pattern. Everything my first-order analysis found is already inside it.

The departure survives. Both global tests reject at the Monte Carlo floor.

The two panels disagree, and that was the lesson. L_inhom never re-enters its envelope in 20 km; g_inhom, which localises scale, peaks at 438 m and is within 10% of no-excess by 7.2 km. My first draft capped r at 5 km and drew the wrong conclusion from exactly this.

An areal method agrees. Moran’s I on hexagons falls from 0.69 on raw counts to 0.28 once lambda-hat is removed, and to 0.07 at 5 km. Different weights, different test, same answer on scale.

Knox test. My null is random labelling: I hold locations and dates both fixed and permute only their pairing, across 999 permutations of 8,720,153 close pairs.

Because both marginals stay fixed, none of this can be explained away by the seasonal ramp or the spatial concentration.

Strongest at the tightest cell, decaying monotonically outward. I read that as short-range propagation: a cell that burns today raises the chance a neighbour burns tomorrow, and the effect is largely spent within days and a kilometre or two.

The decay is steeper in time than in space, which fits fire spreading over contiguous ground within days rather than recurring in the same place weeks apart.

Plantation, not access. Fitted alone, distance to plantation and farmland recovers 3,204 of the 3,550 AIC units the full model gains. Roads alone recover 1,991.

My first version had only roads and waterways and concluded access dominated. That was the thin covariate set talking.

But not the forest half of that story. Fitted alone, distance to forest explains less than roads (1,906), its curve is not monotone, and the median burned cell sits 20 km from any mapped forest. I reported it as a mechanism and it is not one.

Cluster scale 1055 m, parametric bootstrap 902 to 1025 m, with 2.2 to 2.5 km holding most of a cluster.

Resampling points with replacement gave an interval that excluded its own point estimate. That is not a valid bootstrap for a point process.

I had written that I could not tell whether 2026 was severe, blaming the API’s 90-day retention.

I was wrong. The standard archive is empty for 2026 only because reprocessing lags five months. For earlier years the same endpoint serves it normally. One query against 2019 would have shown me.

2026 ranks 2 of 14, at 54x the 2013-2025 median of 150 cells.

So everything on the previous slides describes a severe season, not a typical one. And the record is bimodal, which means an average is a useless planning number here.