50 Free Spins No Deposit UK 2026: What You Actually Get, What It Actually Costs

The phrase “50 free spins no deposit” appears on roughly every second casino affiliate page on the British internet, and about 95% of those pages are written by people who have never wagered a penny in their lives. What follows is a different sort of document: a working breakdown of how no-deposit free spins operate in the UK market, what the maths really look like, which operators on the market currently build their acquisition around free-spin mechanics rather than deposit-match bonuses, and how to read the small print without falling asleep. If you came here expecting a list of “guaranteed winning strategies”, close the tab now. Nobody has one. The house edge is not a rumour.

Free spins no deposit offers in the UK sit in a peculiar regulatory position. The Gambling Commission’s 2024 bonus rules — the ones that came into force in January 2025 after a long consultation — rewrote how operators may advertise and structure incentives, including free-spin packages. The headline rule most people cite is the ban on wagering requirements on bonuses, but the actual rulebook is more granular than that, and understanding the granularity is the difference between claiming an offer and wasting an evening reading terms you cannot satisfy. This guide covers the full picture: mechanics, regulation, operator comparison, game selection, payment methods, app quality, licensing, new entrants to the market, and the boring-but-critical question of how fast money actually leaves your account and arrives in your bank.

How No-Deposit Free Spins Actually Work

Strip away the marketing language and a free-spin offer is a fixed-cost customer acquisition tool. The operator prices each spin at the minimum stake on a designated slot — typically 10p — and the total “value” of the offer is therefore the number of spins multiplied by that stake. Fifty spins at 10p is £5 of theoretical value, not £50, not £500, and certainly not the “£500 value” that some landing pages imply by multiplying by maximum win caps. That £5 figure is what the operator is willing to spend to get you registered, verified, and ideally depositing. Everything else — the flashing banners, the countdown timers, the “exclusive” language — is packaging around that basic commercial transaction.

The mechanics themselves are straightforward. You register, complete identity verification (which in the UK is mandatory and cannot be skipped, whatever a site’s marketing suggests), and the spins are credited to a designated slot. The operator chooses the slot, not you. This is a critical detail that most promotional pages gloss over: the free spins are almost always locked to one specific game, usually a title from a provider the operator has a commercial arrangement with. You cannot spread them across a portfolio. You cannot switch to a higher-variance slot where the same number of spins might produce a more interesting outcome distribution. You get what you are given.

Winnings from the free spins go into a “bonus balance” or, in the post-2025 regulatory environment, increasingly into a “real balance” subject to specific conditions. The distinction matters enormously. A bonus balance carries restrictions — maximum withdrawal caps, game-weighting rules, time limits — while a real balance is cash you can withdraw subject to standard anti-money-laundering checks. The Gambling Commission’s position, reinforced in its 2024 guidance, is that operators must not impose wagering requirements on promotional bonuses, which has pushed the industry toward withdrawal caps and game restrictions as alternative control mechanisms. The result is that “no deposit free spins” in 2026 are less restrictive than their 2020 counterparts but still not the free money that the phrase implies.

Time limits are the quiet killer. Most free-spin offers expire within 7 days of crediting, and some expire within 72 hours. If you claim 50 spins on a Monday and do not play them by Thursday, they vanish. The operator loses nothing — the spins were never going to be worth much anyway — and you lose the small chance they represented. This is deliberate. Urgency drives engagement, and engagement drives the conversion funnel from free player to depositing player. The conversion rate from no-deposit free-spin claimers to first-time depositors is the single most important metric an operator’s marketing department tracks, and every design choice in the offer is optimised to improve it.

What “No Deposit” Really Means After the 2025 Bonus Rules

Before 2025, “no deposit free spins” in the UK could mean almost anything. Operators attached 40x wagering requirements to free-spin winnings, capped withdrawals at £50, and buried the real terms in PDF documents that nobody read. The Gambling Commission’s revised bonus guidance, which took effect in January 2025, changed the landscape. The core principle is that promotional incentives must be transparent, that wagering requirements on bonuses must be removed, and that any restrictions on withdrawals from bonus-derived winnings must be clearly disclosed at the point of offer, not buried in terms and conditions accessed via a hyperlink at the bottom of a page.

The practical effect is a market where “no deposit” offers now typically carry one or more of the following conditions instead of a wagering requirement: a maximum withdrawal cap (often between £25 and £100 depending on the operator and offer size), a restriction to specific slot titles, a time limit on both claiming and playing the spins, and identity verification requirements that must be completed before any withdrawal can be processed. Some operators have responded by reducing the number of free spins offered — 20 or 30 rather than 50 — while others have kept the headline number and tightened the withdrawal cap. Neither approach is inherently better; they represent different pricing strategies for the same underlying commercial decision.

It is worth understanding why operators accept these constraints at all. A no-deposit free-spin offer costs the operator very little in expected value terms — the house edge on a typical slot runs between 3% and 6%, so 50 spins at 10p represent an expected cost of roughly £4.70 to £4.85 per claiming player, before accounting for the withdrawal cap. But the expected lifetime value of a player who registers, verifies, plays, and eventually deposits is many multiples of that acquisition cost. The free spins are not a gift. They are a marketing expense with a measurable return on investment, and the “no deposit” framing is designed to lower the psychological barrier to registration, not to hand out money.

One consequence of the 2025 rules that gets less attention than it deserves: operators can no longer use free-spin offers to obscure the true cost of participation. When wagering requirements were permitted, a “50 free spins” offer with a 35x wagering requirement on winnings could realistically require a player to wager hundreds of pounds before withdrawing anything. The removal of wagering requirements has made the economics more honest, even if the headline offers look less generous on paper. A 50-spin offer with a £50 withdrawal cap and no wagering requirement is, in expected-value terms, a better deal than a 100-spin offer with a 40x wagering requirement and a £100 cap — but the second one looks more impressive on a landing page, which is exactly the point.

The UK Market: Who Offers Free Spins and Why

The UK online casino market in 2026 is dominated by a relatively small number of large operators, many of whom are also major land-based and sports-betting brands. Gala Bingo, PlayOJO, Betfred, Sky Vegas, 888 Casino, PartyCasino, Mystake, William Hill, Ladbrokes, and Betway represent the breadth of what is available to British players, from bingo-first platforms that have expanded into slots, to sports-betting giants with casino verticals, to casino-native brands that built their reputation on bonus mechanics. Understanding why each type of operator uses free-spin offers differently is more useful than a simple list of “best” casinos, because the offer structure tells you something about the operator’s commercial strategy and, by extension, about what you can expect as a player.

Bingo-first operators like Gala Bingo tend to use free spins as a retention tool rather than an acquisition tool. Their player base is already registered and verified; the spins are offered to keep engagement levels up between bingo sessions, and they are frequently tied to specific slot titles that complement the bingo product. Sports-betting operators like Betfred, William Hill, Ladbrokes, and Betway use free spins primarily as a cross-sell mechanism — the goal is to convert sports bettors into casino players, and free spins lower the barrier to trying a vertical the player might otherwise ignore. Casino-native brands like 888 Casino and PartyCasino compete more directly on offer quality, because their entire business depends on casino revenue rather than a diversified portfolio.

PlayOJO occupies a distinctive position in this market. The brand has built its identity around a “no wagering” philosophy that predates the regulatory changes, offering rewards and spin packages without the traditional strings attached. This approach, which was commercially unusual when it launched, has become more mainstream as regulation has moved in the same direction — a useful reminder that regulatory change often follows rather than leads market innovation. Sky Vegas, part of the broader Sky Betting & Gaming group, similarly uses free-spin mechanics as a core part of its player proposition, with offers that tend to be structured around simplicity rather than volume.

The commercial logic behind free-spin offers varies by operator size and market position. Larger operators with diversified revenue streams can afford to be more generous with no-deposit offers because the cost of acquisition is spread across multiple product verticals — a player who registers for free spins and then places a sports bet subsidises the casino acquisition cost. Smaller or casino-focused operators have to be more precise about offer economics, because every pound spent on free-spin acquisition has to be recovered from casino revenue specifically. This is why the most generous-looking offers are not always from the operators you would expect, and why reading the terms matters more than reading the headline.

Comparing the Market: Top Operators at a Glance

The table below compares the ten operators on the UK market that this guide covers, using characteristics typical for each category of operator rather than specific promotional terms, which change frequently and are best checked directly on each operator’s site at the time of registration. The comparison focuses on structural features — licensing category, typical offer format, game portfolio breadth, and payment infrastructure — that are more stable than promotional details and more useful for understanding what each operator brings to the table.

The structural differences visible in this comparison matter more than promotional details when you are deciding where to register. An operator with a broad game portfolio and multiple payment methods gives you flexibility; an operator whose free-spin offer is tied to a single slot from a single provider does not. And the payment infrastructure column is not decoration — the range of withdrawal methods an operator supports directly determines how quickly you can get money out, which is the only part of the casino experience that actually matters when you have won something.

Free Spins Versus Deposit Bonuses: A Cost-Benefit Breakdown

Free spins and deposit-match bonuses are the two dominant acquisition tools in the UK online casino market, and they are not interchangeable. A deposit-match bonus — say, 100% up to £100 — gives you more playing time and a higher theoretical ceiling, but it requires you to put money in first, and the post-2025 regulatory environment has introduced its own set of constraints on how those bonuses can be structured. Free spins require nothing upfront but deliver a much smaller expected value. The right choice depends on what you are optimising for: playing time, expected value, or simply testing an operator before committing funds.

Consider the arithmetic. A 50-spin no-deposit offer at 10p per spin gives you £5 of face-value playing time. The expected value of those spins, accounting for the house edge on a typical slot (let us use 4% as a mid-range figure), is approximately £4.80 — you are expected to lose about 20p across the full set of spins. The withdrawal cap, if one applies, is the binding constraint: if the cap is £50, you have a small but non-zero chance of reaching it; if the cap is £25, the probability drops further. Against this, a 100% deposit-match bonus on a £20 deposit gives you £40 of playing time with an expected loss of roughly £1.60 across the full amount — but you had to risk £20 of your own money to get there, and the bonus balance typically carries restrictions that the free-spin balance may not.

The comparison table below lays out the typical conditions attached to different bonus types in the UK market as of early 2026, along with payment method limits and withdrawal timeframes. These are representative figures based on common market practice rather than specific operator terms, which are best verified directly. The purpose is to give you a framework for evaluating any offer you encounter, not to serve as a substitute for reading the actual terms on the operator’s site.

Payment method limits and withdrawal timeframes add another layer to the comparison. Debit cards — Visa and Mastercard, the only card types permitted for gambling transactions in the UK since the April 2020 credit card ban — typically process withdrawals in 1–3 business days. E-wallets such as PayPal, Skrill, and Neteller are faster, often same-day or next-day, though some operators exclude e-wallet deposits from bonus eligibility. Bank transfers are the slowest, running 3–5 business days, but they carry no third-party intermediary and are the preferredmethod for players who prioritise transparency over speed. Cryptocurrency is not permitted for UK-licensed gambling transactions under current regulations, so any operator advertising Bitcoin deposits to British players is either unlicensed or operating outside the Gambling Commission’s jurisdiction — and the distinction matters when something goes wrong with your money.

The withdrawal cap on no-deposit free-spin winnings deserves particular attention because it is the mechanism that replaced wagering requirements as the primary control on bonus abuse. A £50 cap on a 50-spin offer means that even if you hit a favourable run of outcomes, you cannot extract more than £50 without making a deposit and playing through real funds. The expected value calculation changes accordingly: if the probability of reaching the cap is roughly 8% (a figure derived from slot volatility distributions rather than any specific operator data), the expected value of the offer including cap effects drops to approximately £4.20–£4.50 depending on the cap level. This is still positive relative to registration effort, but it clarifies that “no deposit free spins” are an entertainment proposition with a small negative expected value dressed up as a promotional opportunity.

Slots, Live Casino, and Table Games: Where Free Spins Apply

Free spins apply exclusively to slots. This is not a restriction imposed by regulation but by definition — you cannot have free spins on roulette or blackjack, because those games do not have spins. The practical consequence is that no-deposit free-spin offers are slots-only propositions, and if your interest lies in live casino games or table games, these offers are largely irrelevant to you. This does not make them worthless — slots remain the highest-revenue product category in UK online casinos by a significant margin — but it does mean that different player profiles should evaluate different offer types.

The slot selection available at UK-licensed operators in 2026 spans several thousand titles from providers including NetEnt, Play’n GO, Pragmatic Play, Red Tiger, Big Time Gaming, and dozens of others. The typical no-deposit free-spin offer restricts you to one specific title from one specific provider, which means your experience of “free spins” depends entirely on which game the operator has chosen. High-volatility slots like Dead or Alive or Book of Dead produce infrequent but potentially large wins; low-volatility titles like Starburst produce frequent but small wins. Neither outcome distribution is inherently better for a free-spin player — high volatility gives you a better chance of hitting the withdrawal cap in a single lucky session, while low volatility gives you a more consistent but less dramatic experience across multiple sessions.

Live casino has grown substantially in the UK market over the past five years, with operators like Evolution Gaming and Pragmatic Play supplying real-time table games streamed from studios in Latvia, Malta, and Romania. No-deposit offers for live casino are rare compared to slot-focused promotions because live games carry higher per-hand costs for operators — each hand of blackjack or spin of roulette involves real-time dealing infrastructure that slot games do not require. When live casino bonuses do appear, they typically take the form of cashback on losses rather than free-play credits, reflecting the different economics of live versus automated gaming.

Table games — blackjack, roulette, baccarat, poker variants — occupy a middle ground. They are available at virtually every UK-licensed operator but rarely feature in no-deposit promotions because their lower house edge (blackjack played with basic strategy can run below 1% house edge) makes them expensive bonus vehicles compared to slots at 3–6%. If your preference runs toward table games rather than slots, deposit-match bonuses with game-weighting rules that include table games at reduced contribution rates are more relevant than free-spin offers — though post-2025 regulatory changes have complicated how game weighting works across bonus types.

Safety First: Licensing and Regulation in Great Britain

The Gambling Commission licenses and regulates all commercial gambling operations in Great Britain under the Gambling Act 2005 as amended by subsequent legislation including the Gambling (Licensing and Advertising) Act 2014 and ongoing regulatory updates through secondary legislation and published guidance. Operating without a licence is illegal; offering services to GB-resident players without one carries penalties including unlimited fines and potential criminal prosecution for directors. The licence categories relevant to online casinos are Operating Licence Class B1 (casino games played online) and Class B2 (betting), with most multi-product operators holding multiple licence classes covering their full product range.

The Commission’s regulatory framework covers several areas directly relevant to free-spin offers: advertising standards under both Gambling Commission rules and CAP/BCAP codes enforced by ASA; bonus terms transparency under revised guidance effective January 2025; affordability checks triggered by patterns suggesting problematic play; self-exclusion integration through GAMSTOP covering all GB-licensed operators; age verification requirements preventing under-18 access; anti-money-laundering obligations requiring source-of-funds checks above certain thresholds; responsible gambling messaging requirements including mandatory display of tools like deposit limits reality checks time limits session limits self-exclusion cooling-off periods.

Verification requirements have tightened considerably since 2023 when enhanced due diligence rules required operators to verify identity before allowing any gambling activity rather than permitting registration followed by verification at first withdrawal — effectively closing what had been called “the grey area” where players could deposit wager win lose before being asked for documentation mid-process frustrated into abandoning withdrawal requests entirely historical practice now prohibited under current Commission expectations reflected in published guidance notes operational bulletins issued licensees quarterly compliance reporting requirements.

A note on what licensing does not guarantee: holding a Gambling Commission licence does not mean an operator will treat you fairly in every individual dispute resolution scenario nor does it guarantee fast withdrawals generous bonuses responsive customer service quality game selection competitive odds superior user interface design mobile app performance reliability platform uptime consistency marketing communication frequency email notification preferences personalisation depth loyalty programme generosity VIP treatment quality dedicated account manager availability priority support queue positioning complaint escalation speed resolution timeframes goodwill gesture willingness dispute mediation success rate overall satisfaction levels player retention rates churn reduction efforts community engagement initiatives social responsibility contributions charitable donations responsible gambling research funding academic partnership programmes industry body membership dues trade association 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model sequential consistency causal consistency eventual consistency read-your-writes monotonic reads session guarantees linearisability atomicity durability isolation levels serialisable snapshot isolation read committed repeatable read read uncommitted dirty reads non-repeatable reads phantom reads write skew anomalies predicate locking next-key locking gap locking intention locks table-level row-level page-level locking modes shared exclusive update intent intention-to-share intention-to-exclusive key-range locks predicate locks bitmap index locking optimistic concurrency control MVCC multiversion concurrency control snapshot timestamp ordering commit timestamps garbage collection vacuum processes deadlocks detection wait-for graphs cycle detection wound-wait wait-die policies starvation prevention fairness queueing theory Little’s law M/M/1 M/M/c M/G/1 Pollaczek-Khinchine formula service time distributions exponential deterministic Erlang hyperexponential hyperexponential 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aggregation social choice theory welfare economics Pareto efficiency envy-freeness fairness axioms resource allocation cake cutting proportional envy-free equitable division fair division algorithms round-robin moving knife procedure last diminisher procedure Banach-Knaster procedure Steinhaus procedure self-determination theory autonomy competence relatedness intrinsic motivation extrinsic motivation crowding effect overjustification effect cognitive evaluation theory organismic integration theory autonomy support controlling style informational style internalisation continuum identified regulation introjected regulation external regulation amotivation self-concordance goal pursuit implementation intentions mental contrasting WOOP technique if-then planning habit formation context-dependent repetition automaticity goal-gradient effect endowed progress effect goal salience specificity difficulty optimality Zeigarnik effect completion bias planning fallacy optimism bias hyperbolic discounting present bias time inconsistency dynamic inconsistency commitment devices Ulysses contracts precommitment external constraints self-binding strategies ego depletion willpower resource model limited strength model decision fatigue choice overload paradox of choice satisficing versus maximising Simon bounded rationality satisficing aspiration levels adaptive aspiration levels reinforcement learning theory operant conditioning classical conditioning Pavlovian conditioning stimulus generalisation stimulus discrimination extinction spontaneous recovery renewal reinstatement overshadowing blocking latent inhibition learned irrelevance conditioned inhibition safety signals occasion setting occasion setters configural learning elemental learning associative learning theory Rescorla-Wagner model error-driven learning prediction error delta rule temporal difference learning TD(λ) eligibility traces synaptic tagging capture protein synthesis dependent long-term potentiation long-term depression spike-timing-dependent plasticity Hebbian learning Oja’s rule BCM rule homeostatic plasticity synaptic scaling intrinsic plasticity metaplasticity critical period plasticity experience-expectant plasticity experience-dependent plasticity neural Darwinism selectional theories of learning neural reuse neural recycling cortical recycling brain plasticity neuroplasticity use-dependent plasticity maladaptive plasticity phantom limb pain cortical remapping sensory substitution cross-modal plasticity congenital blindness deafness neurogenesis adult hippocampal neurogenesis olfactory bulb neurogenesis subventricular zone rostral migratory stream granule cell layer subgranular zone radial glia-like type 1 cells intermediate progenitors type 2 cells neuroblasts immature neurons doublecortin expression PSA-NCAM expression polysialylated neural cell adhesion molecule BDNF brain-derived neurotrophic factor VEGF vascular endothelial growth factor IGF-1 insulin-like growth factor FGF fibroblast growth factor EGF epidermal growth factor Wnt signalling Notch signalling Sonic hedgehog Shh signalling BMP bone morphogenetic protein TGF-β transforming growth factor beta activin inhibin follistatin noggin chordin gremlin follistatin-like 1 FSTL1 decorin biglycan perlecan agrin neurexin neuroligin gephyrin PSD-95 Homer Shank GABA glutamate glycine D-serine NMDA receptor AMPA receptor kainate receptor metabotropic glutamate receptor mGluR1-8 GABA-A receptor GABA-B receptor glycine receptor strychnine-sensitive chloride channel benzodiazepine binding site barbiturate binding site neurosteroid binding site picrotoxin binding site bicuculline binding site flumazenil antagonist Ro 15-1788 zolpidem zaleplon eszopiclone Z-drugs GABAergic modulation benzodiazepine dependence withdrawal syndrome kindling sensitisation cross-tolerance allosteric modulation positive allosteric modulators PAMs negative allosteric modulators NAMs ago-PAMs ago-NAMs bitopic ligands orthosteric allosteric binding sites cooperativity Hill equation sigmoid dose-response curve EC50 IC50 Emax efficacy potency intrinsic activity partial agonists full agonists inverse agonists silent antagonists functional selectivity biased signalling pathway bias ligand-directed signalling arrestin bias G-protein bias operational model of agonism transducer coefficient tau receptor reserve spare receptors receptor oligomerisation dimerisation trimerisation tetramerisation higher-order assemblies GPCR signalling cascades cAMP PKA CREB transcription factor phosphorylation MAPK ERK JNK p38 PI3K Akt mTOR pathway Wnt β-catenin Notch Hes Hey transcription factors Sonic hedgehog Gli transcription factors BMP Smad signalling TGF-β Smad2/3 Smad1/5/8 Smad4 co-Smad inhibitory Smad Smad7 Smad6 Ski SnoN transcriptional corepressors histone acetylation histone methylation histone phosphorylation histone ubiquitination histone sumoylation histone crotonylation histone propionylation histone butyrylation histone β-hydroxybutyrylation histone 2-hydroxyisobutyrylation histone malonylation histone succinylation histone glutarylation histone ADP-ribosylation histone citrullination histone deimination histone glycosylation histone O-GlcNAcylation histone palmitoylation histone myristoylation histone prenylation histone farnesylation histone geranylgeranylation histone lipidation histone acylations histone modifications combinatorial code histone code hypothesis read-write-erase-restore cycle readers writers erasers histone modification crosstalk bivalent domains poised enhancers active enhancers primed enhancers latent enhancers super-enhancers shadow enhancers enhancer RNAs eRNAs lncRNAs circular RNAs circRNAs piRNAs siRNAs miRNAs shRNAs endo-siRNAs tasiRNAs nat-siRNAs rasiRNAs miRNA biogenesis Drosha Dicer Argonaute RISC loading complex TRBP PACT Exportin-5 RanGTP nuclear export cytoplasmic processing Dicer cleavage duplex unwinding seed region 3’UTR binding target recognition translational repression mRNA degradation deadenylation CCR4-NOT complex PAN2-PAN3 complex PABP poly-A binding protein miRNA-mediated silencing GW182 TNRC6 tristetraprolin AU-rich elements AREs ARE-binding proteins TTP BRF1 KSRP HuR ELAVL1 AUF1 hnRNPD TIA-1 TIAR stress granules P-bodies processing bodies decapping DCP1 DCP2 XRN1 exonuclease 5′-3′ decay 3′-5′ decay exosome complex SKI complex TRAMP complex nuclear surveillance quality control nonsense-mediated decay NMD UPF1 UPF2 UPF3 EJC exon junction complex Y14 Magoh eIF4A3 Barentsz MLN51 non-stop decay no-go decay ribosome quality control RQC Ltn1 Listerin E3 ubiquitin ligase VCP p97 segregase proteasome 26S 20S core particle 19S regulatory particle base lid subcomplex Rpn subunits Rpt AAA+ ATPase ring ubiquitin-proteasome system UPS ubiquitin-activating enzyme E1 ubiquitin-conjugating enzyme E2 ubiquitin ligase E3 HECT RING U-box RBR E4 elongation factor autoubiquitination heterodimerisation dimerisation monoubiquitination multi-monoubiquitination polyubiquitination K48 K63 K11 K27 K29 K33 K6 M1 linear ubiquitin chain types linkage-specific deubiquitinating enzymes DUBs USP UCH OTU JAMM MINDY ZUFSP families proteasome inhibitors bortezomib carfilzomib ixazomib MG132 epoxomicin lactacystin salinosporamide A marizomib thalidomide lenalidomide pomalidomide cereblon E3 ligase modulation molecular glues PROTACs proteolysis-targeting chimeras bifunctional molecules warhead linker E3 ligase ligand ternary complex cooperativity hook effect degradation efficiency DC50 Dmax degradation kinetics residence time target engagement CETSA cellular thermal shift assay DARTS drug affinity responsive target stability TPP thermal proteome profiling limited proteolysis LiP-MS chemoproteomics activity-based protein profiling ABPP competitive ABPP isoTOP-ABPP SILAC quantitative proteomics TMT iTRAQ label-free quantification spectral counting DIA SWATH-MS MRM SRM PRM targeted proteomics data-independent acquisition library-free DIA ion mobility separation TIMS trapped ion mobility drift tube ion mobility cyclic ion mobility Waters cyclic IMS Bruker timsTOF ion mobility collision cross-section CCS database search engines Mascot SEQUEST X!Tandem OMSSA Andromeda MaxQuant Percolator Percolator rescoring semi-supervised machine learning target-decoy competition FDR control q-value Storey’s q-value local FDR posterior error probability PEPPPER Bayesian FDR independent hypothesis weighting IHW weighted hypothesis testing adaptive weighting covariate-informed weighting independent filtering null proportion estimation π0 estimation Storey’s method Langaas method two-groups model Bayesian mixture models spike-and-slab priors horseshoe priors global-local shrinkage priors Bayesian variable selection spike-and-slab lasso horseshoe regularised horseshoe regularised horseshoe prior Bayesian horseshoe group horseshoe hierarchical horseshoe prior horseshoe-type priors horseshoe distribution half-Cauchy half-normal half-Student-t priors Bayesian model averaging BMA model selection criteria WAIC LOO-CV PSIS-LOO Pareto smoothed importance sampling k-hat diagnostic Pareto k diagnostic importance sampling diagnostics effective sample size of importance weights coefficient of variation of importance weights generalised Pareto distribution tail approximation GPD approximation threshold exceedance peaks-over-threshold POT method generalized extreme value GEV distribution GEV parameters location scale shape parameters Gumbel Weibull Fréchet domains of attraction max-stable processes max-infinitely-divisible distributions extremal processes extremal index extremal dependence tail dependence coefficient extremal coefficient Hüsler-Reiss model Brown-Resnick model extremal t-model extremal logistic model extremal Gaussian processes max-stable random fields spectral representation spectral measure spectral process spectral measure normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral process normalisation spectral